Sudoku Analyst

Sudoku Analyst -- Check the level of a Sudoku prior to solving it. how to use this site

back to the Sudoku Assistant

Samples: 1* 4* 5* 5+* 6a 6b 6+ Y-cycles Proof +Depth Hard ??

[steps] [chains]

This page checks for several fundamental techniques to solve any Sudoku that has a UNIQUE solution. Click on a technique listed below to find out more about that technique, or click on a step shown to illustrate it.

state

Sudoku Difficulty Analysis:

 number of clues: 34
 number of tidbits: 566
 number of steps required: 5
 number of eliminations from...
 ...hidden singles: 29
 ...naked singles: 18
 ...hidden pairs: 0
 ...hidden tuples: 0
 ...hidden quads: 0
 ...naked pairs: 0
 ...naked tuples: 0
 ...naked quads: 0
 ...locked candidates: 0
 ...X-wings: 0
 ...swordfish: 0
 ...4x4 grids: 0
 ...strong Medusa cycles: 0
 ...weak Medusa cycles: 0
 ...hypothesis and proof: 0

||||/,,,,5,,,,,,,3,,,,,,,1,2,,4,,,,,,,2,,,,6,,,,,,,,,,7,,,,2,,4,,6,,8,,1,,,4,,,,8,9,1,2,,4,,,,,9,,2,,,,,,8,,,,,,,6,,,,,2,,4,,,7,,,,2,,4,,,7,,,1,,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,4,,,7,8,,,2,,4,,,,,,,2,,,,,7,8,,1,2,,,,,,,,,,,,,,,,9,,,,,,,,8,,,2,3,,,,,,,,,3,4,,,,,,,2,,4,,,,,,1,,3,4,5,,7,,,,,,,,6,,,,,2,,,,,7,,,,,,,,,,8,,1,2,,,5,,,,,1,2,,,5,,,,9,,,,,,,7,,9,,,,,,6,,,,1,,,4,,,,,,,,,4,5,,7,,9,,2,,4,5,,,,9,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,2,,,,6,,,9,,,,,,,,8,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,9,,2,,,,,,,9,1,,,,,,,,,,,,,,,7,,,1,,,,5,,,,,1,,3,,5,,,,9,,,,,,,,,9,,2,,,,,,,,1,,,4,,,,,,,,,4,5,,,8,9,,,,4,5,,,,9,,,,,,6,,,,1,,3,,,,,,9,,,,,,6,,,,1,,3,,5,,,,9,,,3,,5,,,,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,,2,,,,,,,,,2,,,,,7,8,,,2,,,,,7,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,,1,2,3,,,,,,,1,2,,4,5,,,,,1,2,3,4,5,,,,,,2,3,,5,6,,,,,,,,,,,8,,,2,,,,6,,,,1,,,,,6,,,,,,,,,,7,,,,,,,,,,,9/,,,,5,,,,,,,3,,,,,,,,2,,4,,,,,,,2,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,4,,,,,9,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,4,,,7,,,,2,,4,,,7,,,1,,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,2,,4,,,,,,,2,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,,,,,8,,,2,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,7,,,,,,,,,,8,,1,,,,5,,,,,1,,,,5,,,,9,,,,,,,7,,,,,,,,6,,,,1,,,4,,,,,,,,,4,,,,,9,,2,,4,5,,,,9,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,7,,,1,,,,5,,,,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,4,,,,,,,,,,,,,8,,,,,4,5,,,,,,,,,,6,,,,,,,,,,,,9,,,,,,6,,,,1,,,,5,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,,2,,,,,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,4,5,,,,,,,,4,5,,,,,,2,,,5,6,,,,,,,,,,,8,,,2,,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,,,,,,,9/,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,1,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,6,,,,1,,,4,,,,,,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,7,,,1,,,,5,,,,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,4,,,,,,,,,,,,,8,,,,,4,5,,,,,,,,,,6,,,,,,,,,,,,9,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,,2,,,,,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,4,5,,,,,,,,4,5,,,,,,2,,,,,,,,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,,,,,,,9/,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,6,,,,1,,,,,,,,,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,,,,,,,9,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,,2,,,,,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,2,,,,,,,,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,,,,,,,9/,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,,,,,,9,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,7,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,6,,,,1,,,,,,,,,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,,,,,,,9,,,,,,6,,,,1,,,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,,2,,,,,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,,,,,5,,,,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,2,,,,,,,,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,,,,,,,9

Sudoku Difficulty Analysis:

 number of clues: 27
 number of tidbits: 509
 number of steps required: 16
 number of eliminations from...
 ...hidden singles: 34
 ...naked singles: 20
 ...hidden pairs: 0
 ...hidden tuples: 0
 ...hidden quads: 0
 ...naked pairs: 0
 ...naked tuples: 1(step 6)
 ...naked quads: 0
 ...locked candidates: 2(step 4)
 ...X-wings: 0
 ...swordfish: 0
 ...4x4 grids: 0
 ...strong Medusa cycles: 0
 ...weak Medusa cycles: 0
 ...hypothesis and proof: 0

||||/,,,,,,,,9,1,,3,4,,,,,,1,,3,,,,,8,,,2,,,,,,,,1,,3,,,6,7,,,1,,3,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,5,,,,9,1,,3,,5,,,,,,,,,,,,8,,1,2,,,,,,,9,,,,4,,,,,,1,,,,,,,,9,1,,,,5,,,8,,1,,,,5,,,,,1,2,,,5,,,8,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,2,,,,6,7,8,9,1,2,,,,6,,8,9,,,3,,,,,,,,,,,5,,7,8,,,,,,,6,,,,,,3,,5,,7,8,9,1,,,,,,,,,,2,3,,5,,7,8,,,2,3,,,,7,,,,2,3,,,,,8,9,,2,,,,,,8,9,,,,4,,,,,,1,,,,,,7,8,,1,,3,,,,,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,2,3,,,,7,,,,,,,5,,,,,1,2,,,,6,,8,,1,,,,,6,,8,,,2,,,,,,,,1,,3,,5,,,,9,1,,3,,5,,,8,9,,,3,,5,,,,,,,3,4,5,,,8,,,,,,,6,,,,1,,3,,,,,8,9,,,,,,,7,,,1,,,,,,,8,9,,,3,,,,,,,1,,,,5,,,,9,1,,,,5,,7,,9,,,,,,6,7,,9,1,2,,,,6,7,,,,,,4,,,,,,1,,,,,6,7,8,9,1,,,,,6,,8,9,1,,,,5,6,7,8,9,1,,,,5,6,7,,,,2,,,,,,,,1,,,,5,,7,,9,,,,,,,,8,,1,,,,,6,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,1,,,,5,6,7,,9,1,,,4,,6,7,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,7,,9,1,,3,,,6,7,,,,,,,5,,,,,1,,,,,6,7,,9,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,1,,3,,,,,8,,,2,,,,,,,,1,,3,,,6,7,,,1,,3,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,5,,,,9,1,,3,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,9,1,,,,5,,,8,,1,,,,5,,,,,,2,,,,,,,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,,,,,6,7,8,9,1,,,,,6,,8,9,,,3,,,,,,,,,,,5,,7,8,,,,,,,6,,,,,,3,,5,,7,8,9,1,,,,,,,,,,,3,,5,,7,8,,,2,3,,,,7,,,,,3,,,,,8,9,,2,,,,,,8,9,,,,4,,,,,,1,,,,,,7,8,,1,,3,,,,,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,2,3,,,,7,,,,,,,5,,,,,1,2,,,,6,,8,,1,,,,,6,,8,,,2,,,,,,,,1,,3,,5,,,,9,1,,3,,5,,,8,9,,,3,,5,,,,,,,,4,,,,,,,,,,,6,,,,1,,3,,,,,8,9,,,,,,,7,,,1,,,,,,,8,9,,,3,,,,,,,1,,,,5,,,,9,1,,,,5,,7,,9,,,,,,6,7,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,6,7,8,9,1,,,,,6,,8,9,1,,,,5,6,7,8,9,1,,,,5,6,7,,,,2,,,,,,,,1,,,,5,,7,,9,,,,,,,,8,,1,,,,,6,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,1,,,,5,6,7,,9,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,7,,9,1,,3,,,6,7,,,,,,,5,,,,,1,,,,,6,7,,9,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,6,7,,,1,,,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,5,,,,9,1,,3,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,9,1,,,,5,,,8,,1,,,,5,,,,,,2,,,,,,,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,,,,,6,7,8,9,1,,,,,6,,8,9,,,3,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,5,,7,,9,1,,,,,,,,,,,,,,,,8,,,2,3,,,,7,,,,,3,,,,,,9,,2,,,,,,,9,,,,4,,,,,,1,,,,,,7,8,,1,,3,,,,,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,2,3,,,,7,,,,,,,5,,,,,1,2,,,,6,,8,,1,,,,,6,,8,,,2,,,,,,,,1,,3,,5,,,,9,1,,,,5,,,8,9,,,3,,5,,,,,,,,4,,,,,,,,,,,6,,,,1,,3,,,,,8,9,,,,,,,7,,,1,,,,,,,8,9,,,3,,,,,,,1,,,,5,,,,9,1,,,,5,,7,,9,,,,,,6,7,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,6,7,8,9,1,,,,,6,,8,9,1,,,,5,6,7,8,9,,,,,,6,,,,,2,,,,,,,,1,,,,5,,7,,9,,,,,,,,8,,1,,,,,,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,1,,,,5,,7,,9,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,7,,9,1,,3,,,6,7,,,,,,,5,,,,,1,,,,,6,7,,9,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,6,7,,,1,,,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,9,1,,3,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,9,,,,,,,,8,,1,,,,5,,,,,,2,,,,,,,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,,,,,6,7,,9,1,,,,,6,,,9,,,3,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,5,,7,,9,1,,,,,,,,,,,,,,,,8,,,2,3,,,,7,,,,,3,,,,,,9,,2,,,,,,,9,,,,4,,,,,,1,,,,,,7,,,1,,3,,,,,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,2,3,,,,7,,,,,,,5,,,,,1,2,,,,6,,8,,1,,,,,6,,8,,,2,,,,,,,,1,,3,,,,,,9,,,,,,,,8,,,,,,5,,,,,,,,4,,,,,,,,,,,6,,,,1,,3,,,,,,9,,,,,,,7,,,1,,,,,,,,9,,,3,,,,,,,1,,,,5,,,,9,1,,,,5,,7,,9,,,,,,6,7,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,6,7,8,9,1,,,,,6,,8,9,1,,,,5,6,7,8,9,,,,,,6,,,,,2,,,,,,,,1,,,,5,,7,,9,,,,,,,,8,,1,,,,,,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,1,,,,5,,7,,9,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,7,,9,1,,3,,,6,7,,,,,,,5,,,,,1,,,,,6,7,,9,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,6,7,,,1,,,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,9,1,,3,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,9,,,,,,,,8,,1,,,,5,,,,,,2,,,,,,,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,,,,,6,7,,9,1,,,,,6,,,9,,,3,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,5,,,,9,1,,,,,,,,,,,,,,,,8,,,2,3,,,,7,,,,,3,,,,,,9,,2,,,,,,,9,,,,4,,,,,,1,,,,,,7,,,1,,3,,,,,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,2,3,,,,7,,,,,,,5,,,,,1,2,,,,6,,8,,1,,,,,6,,8,,,2,,,,,,,,1,,3,,,,,,9,,,,,,,,8,,,,,,5,,,,,,,,4,,,,,,,,,,,6,,,,1,,3,,,,,,9,,,,,,,7,,,1,,,,,,,,9,,,3,,,,,,,1,,,,5,,,,9,1,,,,5,,7,,9,,,,,,6,7,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,6,7,8,9,1,,,,,6,,8,9,1,,,,5,6,7,8,9,,,,,,6,,,,,2,,,,,,,,1,,,,5,,7,,9,,,,,,,,8,,1,,,,,,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,1,,,,5,,7,,9,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,7,,9,1,,3,,,6,7,,,,,,,5,,,,,1,,,,,6,7,,9,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,6,7,,,1,,,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,9,1,,3,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,9,,,,,,,,8,,1,,,,5,,,,,,2,,,,,,,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,,,,,6,7,,9,1,,,,,6,,,9,,,3,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,5,,,,9,1,,,,,,,,,,,,,,,,8,,,2,3,,,,7,,,,,3,,,,,,9,,2,,,,,,,9,,,,4,,,,,,1,,,,,,7,,,1,,3,,,,,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,2,3,,,,7,,,,,,,5,,,,,1,2,,,,6,,8,,1,,,,,6,,8,,,2,,,,,,,,1,,3,,,,,,9,,,,,,,,8,,,,,,5,,,,,,,,4,,,,,,,,,,,6,,,,1,,3,,,,,,9,,,,,,,7,,,1,,,,,,,,9,,,3,,,,,,,1,,,,5,,,,9,1,,,,5,,7,,9,,,,,,6,7,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,6,7,8,9,1,,,,,6,,8,9,1,,,,5,6,7,8,9,,,,,,6,,,,,2,,,,,,,,1,,,,5,,7,,9,,,,,,,,8,,1,,,,,,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,1,,,,5,,7,,9,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,7,,9,1,,3,,,,7,,,,,,,5,,,,,1,,,,,6,7,,9,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,6,7,,,1,,,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,9,1,,3,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,9,,,,,,,,8,,1,,,,5,,,,,,2,,,,,,,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,,,,,6,7,,9,1,,,,,6,,,9,,,3,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,5,,,,9,1,,,,,,,,,,,,,,,,8,,,2,3,,,,7,,,,,3,,,,,,9,,2,,,,,,,9,,,,4,,,,,,1,,,,,,7,,,1,,3,,,,,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,2,,,,,,,,,,,,5,,,,,,2,,,,6,,8,,,,,,,6,,8,,,2,,,,,,,,1,,3,,,,,,9,,,,,,,,8,,,,,,5,,,,,,,,4,,,,,,,,,,,6,,,,1,,3,,,,,,9,,,,,,,7,,,1,,,,,,,,9,,,3,,,,,,,1,,,,5,,,,9,1,,,,5,,7,,9,,,,,,6,7,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,6,7,8,9,1,,,,,6,,8,9,1,,,,5,6,7,8,9,,,,,,6,,,,,2,,,,,,,,1,,,,5,,7,,9,,,,,,,,8,,1,,,,,,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,1,,,,5,,7,,9,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,7,,9,1,,3,,,,7,,,,,,,5,,,,,1,,,,,6,7,,9,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,6,7,,,1,,,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,9,1,,3,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,9,,,,,,,,8,,1,,,,5,,,,,,2,,,,,,,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,,,,,6,7,,9,1,,,,,6,,,9,,,3,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,5,,,,9,1,,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,9,,,,4,,,,,,1,,,,,,7,,,1,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,2,,,,,,,,,,,,5,,,,,,,,,,6,,8,,,,,,,6,,8,,,2,,,,,,,,1,,3,,,,,,9,,,,,,,,8,,,,,,5,,,,,,,,4,,,,,,,,,,,6,,,,1,,3,,,,,,9,,,,,,,7,,,1,,,,,,,,9,,,3,,,,,,,1,,,,5,,,,9,1,,,,5,,7,,9,,,,,,6,7,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,6,7,8,9,1,,,,,6,,8,9,1,,,,5,6,7,8,9,,,,,,6,,,,,2,,,,,,,,1,,,,5,,7,,9,,,,,,,,8,,1,,,,,,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,1,,,,5,,7,,9,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,7,,9,1,,3,,,,7,,,,,,,5,,,,,1,,,,,6,7,,9,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,6,7,,,1,,,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,1,,,,,6,7,8,,1,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,9,1,,3,,5,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,9,,,,,,,,8,,1,,,,5,,,,,,2,,,,,,,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,,,,,6,7,,,1,,,,,6,,,9,,,3,,,,,,,,,,,,,7,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,2,,,,,,,,,,,,5,,,,,,,,,,6,,8,,,,,,,6,,8,,,2,,,,,,,,1,,,,,,,,9,,,,,,,,8,,,,,,5,,,,,,,,4,,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,1,,,,5,,,,9,1,,,,5,,7,,9,,,,,,6,,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,6,7,8,,1,,,,,6,,8,9,1,,,,5,6,7,8,9,,,,,,6,,,,,2,,,,,,,,1,,,,5,,7,,9,,,,,,,,8,,1,,,,,,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,1,,,,5,,7,,9,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,,,9,1,,3,,,,7,,,,,,,5,,,,,1,,,,,6,7,,,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,6,7,,,1,,,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,9,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,1,,,,5,6,7,,,1,,,,,,7,,9,1,,,,,6,7,,,1,,,,,6,,,9,,,3,,,,,,,,,,,,,7,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,2,,,,,,,,,,,,5,,,,,,,,,,6,,8,,,,,,,6,,8,,,2,,,,,,,,,,,,,,,,9,,,,,,,,8,,,,,,5,,,,,,,,4,,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,1,,,,5,,,,,1,,,,,,7,,9,,,,,,6,,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,6,7,8,,1,,,,,6,,8,9,,,,,5,6,7,8,9,,,,,,6,,,,,2,,,,,,,,1,,,,,,7,,9,,,,,,,,8,,1,,,,,,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,,,,,5,,7,,9,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,,,9,1,,3,,,,7,,,,,,,5,,,,,1,,,,,6,7,,,1,,,,,6,,,9,,2,,,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,1,,,,,6,7,8,,,,,,5,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,,1,,,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,,9,,,,,,6,7,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,2,,,,,,,,,,,,5,,,,,,,,,,6,,8,,,,,,,6,,8,,,2,,,,,,,,,,,,,,,,9,,,,,,,,8,,,,,,5,,,,,,,,4,,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,,,,,5,,,,,1,,,,,,7,,9,,,,,,6,,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,6,7,8,,1,,,,,6,,8,9,,,,,,6,7,8,,,,,,,6,,,,,2,,,,,,,,1,,,,,,7,,9,,,,,,,,8,,,,,,,,7,,,1,,,,,,7,,9,,,,4,,,,,,,,3,,,,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,3,,,6,,,9,,,3,,,,7,,,,,,,5,,,,,1,,,,,6,7,,,1,,,,,6,,,9,,2,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,,1,,,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,2,,,,,,,,,,,,5,,,,,,,,,,,,8,,,,,,,6,,8,,,2,,,,,,,,,,,,,,,,9,,,,,,,,8,,,,,,5,,,,,,,,4,,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,,,,,5,,,,,1,,,,,,7,,9,,,,,,6,,,9,,2,,,,,,,,,,,4,,,,,,,,,,,6,7,8,,1,,,,,,,8,9,,,,,,6,7,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,,,,,,,,8,,,,,,,,7,,,1,,,,,,,,,,,,4,,,,,,,,3,,,,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,9,,,,,,6,,,9,,,3,,,,,,,,,,,5,,,,,,,,,,6,7,,,1,,,,,,,,9,,2,,,,,/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,,1,,,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,2,,,,,,,,,,,,5,,,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,,,,,,,,8,,,,,,5,,,,,,,,4,,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,9,,2,,,,,,,,,,,4,,,,,,,,,,,,,8,,1,,,,,,,,9,,,,,,,7,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,,,,,,,,8,,,,,,,,7,,,1,,,,,,,,,,,,4,,,,,,,,3,,,,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,1,,,,,,7,,,,,,,,6,,,9,,,3,,,,,,,,,,,5,,,,,,,,,,6,,,,1,,,,,,,,9,,2/,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,,1,,,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,4,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,2,,,,,,,,,,,,5,,,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,,,,,,,,8,,,,,,5,,,,,,,,4,,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,,7,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,,,,,,,,8,,,,,,,,7,,,1,,,,,,,,,,,,4,,,,,,,,3,,,,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,,,,,,,,,9,,,3,,,,,,,,,,,5,,,,,,,,,,6,,,,1,,,,,,,,9,,2

Sudoku Difficulty Analysis:

 number of clues: 28
 number of tidbits: 522
 number of steps required: 27
 number of eliminations from...
 ...hidden singles: 33
 ...naked singles: 20
 ...hidden pairs: 2(step 11)
 ...hidden tuples: 0
 ...hidden quads: 0
 ...naked pairs: 0
 ...naked tuples: 0
 ...naked quads: 0
 ...locked candidates: 10(step 4)
 ...X-wings: 1(step 18)
 ...swordfish: 1(step 18)
 ...4x4 grids: 0
 ...strong Medusa cycles: 0
 ...weak Medusa cycles: 0
 ...hypothesis and proof: 0

||||/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,7,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,6,7,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,7,,,1,,3,4,,,,,,,,,4,,6,7,8,,,,,4,5,6,,8,,,,,,,,,,9,1,2,3,,,,7,,,1,,3,,,6,7,8,,,2,,,5,6,7,8,,,2,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,9,,2,3,4,5,,,8,9,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,2,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,4,,6,,8,9,,2,3,4,5,6,,8,9,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,7,8,9,1,,,,5,,7,8,,1,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,1,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,7,8,9,1,2,,,,,7,8,,1,,,,,,,,9,1,,,,,,,8,9,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,7,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,7,,,1,,3,4,,,,,,,,,4,,6,7,8,,,,,,5,,,,,,,,,,,,,9,1,2,3,,,,7,,,1,,3,,,6,7,8,,,2,,,,6,7,8,,,2,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,9,,2,3,4,,,,8,9,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,2,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,4,,6,,8,9,,2,3,4,,6,,8,9,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,7,8,9,1,,,,5,,7,8,,1,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,1,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,7,8,9,1,2,,,,,7,8,,1,,,,,,,,9,1,,,,,,,8,9,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,7,,,1,,3,4,,,,,,,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,1,2,3,,,,7,,,1,,3,,,6,7,8,,,2,,,,6,7,8,,,2,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,9,,2,3,4,,,,8,9,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,2,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,4,,,,8,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,7,8,9,1,,,,5,,7,8,,1,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,1,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,7,8,9,1,2,,,,,7,8,,1,,,,,,,,9,1,,,,,,,8,9,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,7,,,1,,3,4,,,,,,,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,1,2,3,,,,7,,,1,,3,,,6,7,8,,,2,,,,6,7,8,,,2,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,2,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,7,8,9,1,,,,5,,7,8,,1,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,1,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,7,8,9,1,2,,,,,7,8,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,7,,,1,,3,4,,,,,,,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,1,2,3,,,,7,,,1,,3,,,6,7,8,,,2,,,,6,7,8,,,2,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,2,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,7,8,9,1,,,,5,,7,8,,1,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,1,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,7,8,9,1,2,,,,,7,8,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,7,,,1,,3,4,,,,,,,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,1,,3,,,6,7,8,,,2,,,,6,7,8,,,2,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,2,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,7,8,9,1,,,,5,,7,8,,1,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,1,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,7,8,9,1,2,,,,,7,8,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,7,,,1,,3,4,,,,,,,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,7,8,,,2,,,,6,7,8,,,2,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,2,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,7,8,9,1,,,,5,,7,8,,1,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,1,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,7,8,9,1,2,,,,,7,8,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,7,,,1,,3,4,,,,,,,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,7,8,,,2,,,,6,7,8,,,2,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,2,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,,8,9,1,,,,5,,7,8,,1,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,1,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,7,8,9,1,2,,,,,7,8,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,7,,,1,,3,4,,,,,,,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,7,8,,,2,,,,6,7,8,,,2,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,2,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,,8,9,,,,,5,,,8,,1,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,1,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,7,8,9,1,2,,,,,7,8,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,7,,,1,,3,4,,,,,,,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,7,8,,,2,,,,6,7,8,,,2,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,2,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,,8,9,,,,,5,,,8,,,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,1,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,7,8,9,1,2,,,,,7,8,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,7,,,1,,3,4,,,,,,,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,7,8,,,2,,,,6,7,8,,,2,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,2,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,,8,9,,,,,5,,,8,,,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,7,8,9,1,2,,,,,7,8,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,7,,,1,,3,4,,,,,,,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,7,8,,,2,,,,6,7,8,,,2,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,2,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,,8,9,,,,,5,,,8,,,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,7,8,9,1,,,,,,7,,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,7,,,1,,3,4,,,,,,,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,7,8,,,2,,,,6,7,8,,,,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,,8,9,,,,,5,,,8,,,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,,,,1,,,,,,7,,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,,,,1,,3,4,,,,,,,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,7,8,,,2,,,,6,7,8,,,,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,,8,9,,,,,5,,,8,,,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,,,,,,3,4,,,,,,,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,7,8,,,2,,,,6,7,8,,,,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,,8,9,,,,,5,,,8,,,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,8,9,,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,,,,,,3,4,,,,,,,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,7,8,,,2,,,,6,7,8,,,,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,,8,9,,,,,5,,,8,,,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,,9,,,3,4,,,,8,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,7,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,,,,,,3,4,,,,,,,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,7,8,,,2,,,,6,7,8,,,,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,,8,9,,,,,5,,,8,,,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,,9,,,3,4,,,,,,1,,,,,,7,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,,,,,,3,4,,,,,,,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,7,8,,,2,,,,6,7,8,,,,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,4,,,,8,,,,3,4,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,4,,,,8,,1,,,4,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,4,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,,8,9,,,,,5,,,8,,,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,,9,,,3,4,,,,,,1,,,,,,,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,8,,,,,4,,,7,8,,1,,,,,,,,9,1,,,,,,7,8,,,,,,,,7,8,9,,,3,4,,,7,,,1,,,,,,,,,,,3,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,,8,,,2,,,,6,,8,,,,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,8,,,2,3,,,,,8,,,,3,,5,,7,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,8,,,2,,,,,,8,,1,,,,,,7,8,,,,,,5,,,,,,,,,,,,,9,,2,,,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,4,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,2,,4,,,,8,,,,3,,,6,,8,9,,,,,5,,,8,,,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,,9,,,3,4,,,,,,1,,,,,,,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,3,4,,,7,,,1,,,,,,,,,,,3,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,,,,,2,,,,6,,,,,,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,,,,2,3,,,,,8,,,,3,,5,,,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,1,,,4,,,7,,,,2,,,,,,8,,1,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,2,,,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,,,4,,,,,,,,3,,,6,,8,9,,,,,5,,,8,,,,3,,5,,,,9,,2,,,,,,,,,,3,4,,,,,9,,,3,4,,,,,,1,,,,,,,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,,,,,,,,,,7,,,1,,,,,,,,9,1,,,,,,,,,,,,,,,,8,9,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,1,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,3,4,,,7,,,1,,,,,,,,,,,3,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,,,,,2,,,,6,,,,,,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,9,,,,4,,,7,,,,2,3,,,,,,,,,3,,5,,,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,,,,4,,,7,,,,2,,,,,,,,1,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,2,,,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,3,,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,,,4,,,,,,,,3,,,6,,8,9,,,,,5,,,8,,,,3,,5,,,,9,,2,,,,,,,,,,3,,,,,,9,,,,4,,,,,,1,,,,,,,,9,1,,,,,6,7,,,,,,,,6,7,,9,,2,,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,3,,,6,,,9,,,,4,,,,,,1,,3,,,,,,9,,,,,5,,,,,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,1,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,9,,,3,4,,,7,,,1,,,,,,,,,,,3,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,2,3,,,,7,,,,,3,,,6,,,,,2,,,,6,,,,,,,4,,,,8,9,,2,,,5,,,8,,,,,4,5,,,,,,,,4,,,7,,,,,3,,,,,,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,7,8,,1,,,,,,,,,,,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,,,,4,,,7,,,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,8,,1,,,,,,,,,,2,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,,,5,,,8,,,2,3,,,,,,,,,3,,,,,8,,,,,4,,,,,,,,3,,,6,,8,,,,,,5,,,8,,,,3,,5,,,,,,2,,,,,,,,,,,,,,,,9,,,,4,,,,,,1,,,,,,,,,1,,,,,6,7,,,,,,,,6,7,,,,2,,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,6,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,8,,,,,,,,,8,,,,3,4,,,7,,,1,,,,,,,,,,,3,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,6,,,,,2,,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,5,,,,,,,,4,,,7,,,,,3,,,,,,,,,,,5,,,8,,,,,,,6,,,,,,,,,,7,8,,1,,,,,,,,,,,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,,,,4,,,7,,,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,8,,1,,,,,,,,,,,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,,,5,,,8,,,2,,,,,,,,,,3,,,,,8,,,,,4,,,,,,,,3,,,,,8,,,,,,5,,,8,,,,3,,5,,,,,,2,,,,,,,,,,,,,,,,9,,,,4,,,,,,1,,,,,,,,,,,,,,6,7,,,,,,,,6,7,,,,2,,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,3,4,,,7,,,1,,,,,,,,,,,3,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,,3,,,,7,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,5,,,,,,,,4,,,7,,,,,3,,,,,,,,,,,5,,,8,,,,,,,6,,,,,,,,,,7,8,,1,,,,,,,,,,,,4,,,,8,,,,3,,,,,,,,,,,,6,,,,,,,4,,,7,,,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,1,,,,,,,,,,,,,5,,,8,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,,,5,,,8,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,3,,,,,8,,,,,,5,,,8,,,,3,,5,,,,,,2,,,,,,,,,,,,,,,,9,,,,4,,,,,,1,,,,,,,,,,,,,,,7,,,,,,,,6,,,,,2,,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,,9/,,3,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,3,4,,,7,,,1,,,,,,,,,,,3,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,,3,,,,7,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,5,,,,,,,,4,,,7,,,,,3,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,6,,,,,,,4,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,,,5,,,8,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,3,,,,,,,,,,,5,,,8,,,,3,,5,,,,,,2,,,,,,,,,,,,,,,,9,,,,4,,,,,,1,,,,,,,,,,,,,,,7,,,,,,,,6,,,,,2,,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,,9/,,,,,,7,,,,,,,,,,,9,,,,,,,,8,,,,,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,,,3,,,,7,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,,9,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,3,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,6,,,,,,,4,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,,,9,,,,,,,7,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,,,,,,,8,,,2,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,3,,,,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,,,,,,,9,,,,4,,,,,,1,,,,,,,,,,,,,,,7,,,,,,,,6,,,,,2,,,,,,,,,,,,,,7,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,,6,,,,,,,4,,,,,,,,,,5,,,,,,,3,,,,,,,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,,7,,,,,3,,,,,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,,9

Sudoku Difficulty Analysis:

 number of clues: 40
 number of tidbits: 568
 number of steps required: 14
 number of eliminations from...
 ...hidden singles: 21
 ...naked singles: 20
 ...hidden pairs: 0
 ...hidden tuples: 0
 ...hidden quads: 0
 ...naked pairs: 0
 ...naked tuples: 0
 ...naked quads: 0
 ...locked candidates: 4(step 1)
 ...X-wings: 0
 ...swordfish: 1(step 5)
 ...4x4 grids: 0
 ...strong Medusa cycles: 0
 ...weak Medusa cycles: 0
 ...hypothesis and proof: 0

||||/,2,3,,,6,,,9,,2,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,2,3,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,6,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,6,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,2,,4,,6,7,,9,,2,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,5,6,,,,,2,,,5,,7,,9,,2,,,,6,,,,,,,4,,,,,,,2,,,,6,7,,,,,3,,5,6,,,9,,,3,,,6,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,2,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,3,,,6,,,9,,2,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,2,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,6,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,6,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,2,,4,,6,7,,9,,2,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,5,6,,,,,2,,,5,,7,,9,,2,,,,6,,,,,,,4,,,,,,,2,,,,6,7,,,,,3,,5,6,,,9,,,3,,,6,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,2,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,3,,,6,,,9,,2,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,2,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,6,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,6,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,2,,4,,6,7,,9,,2,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,5,,,,,,2,,,5,,7,,9,,2,,,,6,,,,,,,4,,,,,,,2,,,,6,7,,,,,3,,5,6,,,9,,,3,,,6,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,2,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,3,,,6,,,9,,2,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,2,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,6,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,6,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,2,,4,,6,7,,9,,2,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,5,,,,,,2,,,5,,7,,9,,2,,,,6,,,,,,,4,,,,,,,2,,,,6,7,,,,,3,,5,,,,9,,,3,,,6,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,2,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,3,,,6,,,9,,2,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,2,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,6,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,6,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,2,,4,,6,7,,9,,2,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,5,,,,,,2,,,5,,7,,9,,2,,,,6,,,,,,,4,,,,,,,2,,,,6,7,,,,,3,,5,,,,9,,,3,,,,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,2,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,3,,,6,,,9,,2,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,2,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,6,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,6,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,2,,4,,6,7,,9,,2,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,,,,,,,2,,,5,,7,,9,,2,,,,6,,,,,,,4,,,,,,,2,,,,6,7,,,,,3,,5,,,,9,,,3,,,,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,2,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,3,,,6,,,9,,,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,2,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,6,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,6,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,4,,6,7,,9,,,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,,,,,,,,,,5,,7,,9,,,,,,6,,,,,,,4,,,,,,,,,,,6,7,,,,,3,,5,,,,9,,,3,,,,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,2,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,3,,,6,,,9,,,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,5,6,,,9,,2,3,,,6,,,9,,,,,,,,8,,,2,,,,,,,9,,2,3,,,,,,,1,,,,,,,,,,2,,,5,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,4,,6,7,,9,,,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,,,,,,,,,,5,,7,,9,,,,,,6,,,,,,,4,,,,,,,,,,,,7,,,,,3,,5,,,,9,,,3,,,,7,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,2,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,7,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,2,3,,,,7,8,,1,,,,,,,,,,2,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,2,,,,,7,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,5,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,,,,,,,,,,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,,6,,,9,,,3,,,6,,,9,,,,,,,,8,,,,,,,,,,9,,2,3,,,,,,,1,,,,,,,,,,2,,,,6,,,,,,3,,5,6,,,9,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,4,,6,7,,9,,,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,9,,,,,,6,,,,,,,4,,,,,,,,,,,,7,,,,,3,,5,,,,9,,,3,,,,,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,5,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,5,6,,,,,,,,,,7,8,,,,,,,,,,9,,2,,,5,,7,,,,2,,,,,,8,,,,,,,6,,,,,2,,,5,,,8,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,3,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,2,,,,,,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,3,4,,,,,,,,3,4,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,,,,,,,,,,3,,,6,,,,1,,,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,3,,,6,,,9,,,,,,6,,,9,,,,,,6,,,,,,,,,,,8,,,,,,,,,,9,,2,3,,,,,,,1,,,,,,,,,,2,,,,6,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,,8,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,4,,6,7,,9,,,,4,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,9,,,,4,,6,,,9,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,,,,,,,7,,,,,3,,,,,,9,,,3,,,,,,9,,,,,,,,8,,,,,4,,6,7,,,,,,4,,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,,5,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,8,,,,,,,6,,,,,,,,5,,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,,,,6,,,9,,,,,,6,,,9,,,,,,6,,,,,,,,,,,8,,,,,,,,,,9,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,,,3,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,7,,,,,,4,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,,,,,,,7,,,,,3,,,,,,9,,,3,,,,,,9,,,,,,,,8,,,,,,,,7,,,,,,4,,6,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,7,,,,,,,5,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,,,,6,,,9,,,,,,6,,,9,,,,,,6,,,,,,,,,,,8,,,,,,,,,,9,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,,3,,,,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,9,,,,,5,,,,,,,,,,6,,,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2/,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,4,,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,,,,,,6,,,,,,,,,,,8,,,,,,,,,,9,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,,,,,4,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,,3,,,,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,,8,,1,,,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,8,,,,,,,,,,9,,,,,,,7,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,,,,5,,,,,,,,,,,,,9,,,,4,,,,,,,,,,5,,,,,,,,,,6,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,,9,,,,,,,7,,,,,,,,,,8,,,2

Sudoku Difficulty Analysis:

 number of clues: 32
 number of tidbits: 528
 number of steps required: 33
 number of eliminations from...
 ...hidden singles: 24
 ...naked singles: 25
 ...hidden pairs: 3(step 5)
 ...hidden tuples: 0
 ...hidden quads: 0
 ...naked pairs: 4(step 4)
 ...naked tuples: 1(step 20)
 ...naked quads: 0
 ...locked candidates: 9(step 1)
 ...X-wings: 0
 ...swordfish: 0
 ...4x4 grids: 0
 ...strong Medusa cycles: 2(step 10)
 ...weak Medusa cycles: 0
 ...hypothesis and proof: 0

||||/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,5,6,,,9,1,,,,5,6,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,5,6,,,9,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,5,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,5,,,,,,2,3,4,,6,7,,,1,2,3,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,5,6,,,9,,2,,,,,,,,,,,,5,,,8,9,,,3,,5,,7,8,9,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,5,,7,,9,,,,4,,,,,,,,3,4,,,7,,9,,,,4,,,,,9,,,3,4,,,7,,9,1,,,4,,,,,,,,,,5,,,,,1,2,3,,,,,,9,,,,,,6,,,,,2,,,,,7,,9,,,,,,,,8,,,,,4,5,,,,9,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,9,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,5,6,,,9,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,5,6,,,9,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,5,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,5,,,,,,2,3,4,,6,7,,,1,2,3,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,5,6,,,9,,2,,,,,,,,,,,,5,,,8,9,,,3,,5,,7,8,9,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,5,,7,,9,,,,4,,,,,,,,3,4,,,7,,9,,,,4,,,,,9,,,3,4,,,7,,9,1,,,4,,,,,,,,,,5,,,,,1,2,3,,,,,,9,,,,,,6,,,,,2,,,,,7,,9,,,,,,,,8,,,,,4,5,,,,9,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,9,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,5,6,,,9,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,5,6,,,9,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,5,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,5,,,,,,2,,4,,6,7,,,1,2,3,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,5,6,,,9,,2,,,,,,,,,,,,5,,,8,9,,,3,,5,,7,8,9,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,5,,7,,9,,,,4,,,,,,,,3,4,,,7,,9,,,,4,,,,,9,,,3,4,,,7,,9,1,,,4,,,,,,,,,,5,,,,,1,2,3,,,,,,9,,,,,,6,,,,,2,,,,,7,,9,,,,,,,,8,,,,,4,5,,,,9,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,9,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,5,6,,,9,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,5,6,,,9,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,5,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,5,,,,,,2,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,5,6,,,9,,2,,,,,,,,,,,,5,,,8,9,,,3,,5,,7,8,9,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,5,,7,,9,,,,4,,,,,,,,3,4,,,7,,9,,,,4,,,,,9,,,3,4,,,7,,9,1,,,4,,,,,,,,,,5,,,,,1,2,3,,,,,,9,,,,,,6,,,,,2,,,,,7,,9,,,,,,,,8,,,,,4,5,,,,9,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,9,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,5,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,5,,,,,,2,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,5,6,,,9,,2,,,,,,,,,,,,5,,,8,9,,,3,,5,,7,8,9,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,5,,7,,9,,,,4,,,,,,,,3,4,,,7,,9,,,,4,,,,,9,,,3,4,,,7,,9,1,,,4,,,,,,,,,,5,,,,,1,2,3,,,,,,9,,,,,,6,,,,,2,,,,,7,,9,,,,,,,,8,,,,,4,5,,,,9,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,9,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,5,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,,,,,,,2,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,5,6,,,9,,2,,,,,,,,,,,,5,,,8,9,,,3,,5,,7,8,9,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,5,,7,,9,,,,4,,,,,,,,3,4,,,7,,9,,,,4,,,,,9,,,3,4,,,7,,9,1,,,4,,,,,,,,,,5,,,,,1,2,3,,,,,,9,,,,,,6,,,,,2,,,,,7,,9,,,,,,,,8,,,,,4,5,,,,9,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,9,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,,,,,,,2,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,9,,,3,,5,,7,8,9,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,5,,7,,9,,,,4,,,,,,,,3,4,,,7,,9,,,,4,,,,,9,,,3,4,,,7,,9,1,,,4,,,,,,,,,,5,,,,,1,2,3,,,,,,9,,,,,,6,,,,,2,,,,,7,,9,,,,,,,,8,,,,,4,5,,,,9,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,9,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,,,,,,,2,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,7,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,3,4,,,7,,9,,,,4,,,,,9,,,3,4,,,7,,9,1,,,4,,,,,,,,,,5,,,,,1,2,3,,,,,,9,,,,,,6,,,,,2,,,,,7,,9,,,,,,,,8,,,,,4,5,,,,9,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,9,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,,,,,,,2,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,7,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,3,4,,,7,,9,,,,4,,,,,9,,,3,4,,,7,,9,1,,,4,,,,,,,,,,5,,,,,1,2,,,,,,,9,,,,,,6,,,,,2,,,,,7,,9,,,,,,,,8,,,,,4,5,,,,9,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,9,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,,,,,,,2,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,7,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,3,4,,,7,,9,,,,4,,,,,9,,,3,4,,,7,,9,1,,,4,,,,,,,,,,5,,,,,1,2,,,,,,,,,,,,,6,,,,,2,,,,,7,,9,,,,,,,,8,,,,,4,5,,,,9,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,,,,,,,2,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,7,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,3,4,,,7,,9,,,,4,,,,,9,,,3,4,,,7,,9,1,,,4,,,,,,,,,,5,,,,,1,2,,,,,,,,,,,,,6,,,,,2,,,,,7,,9,,,,,,,,8,,,,,4,,,,,9,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,,,,,,,2,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,7,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,4,,,7,,9,,,,4,,,,,9,,,3,4,,,7,,9,1,,,4,,,,,,,,,,5,,,,,1,2,,,,,,,,,,,,,6,,,,,2,,,,,7,,9,,,,,,,,8,,,,,4,,,,,9,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,,,,,,,2,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,4,,,7,,9,,,,4,,,,,9,,,3,4,,,7,,9,1,,,4,,,,,,,,,,5,,,,,1,2,,,,,,,,,,,,,6,,,,,2,,,,,,,9,,,,,,,,8,,,,,4,,,,,9,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,,,,,,,2,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,4,,,,,9,,,3,,,,7,,,1,,,4,,,,,,,,,,5,,,,,1,2,,,,,,,,,,,,,6,,,,,2,,,,,,,9,,,,,,,,8,,,,,4,,,,,9,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,4,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,4,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,6,,,,,,,,,6,,,,,,,,5,,,8,9,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,4,5,,7,,9,,2,,4,5,,,,9,,,3,4,5,,7,,9,1,,,4,,,,,,,2,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,4,,,,,9,,,3,,,,7,,,1,,,4,,,,,,,,,,5,,,,,1,2,,,,,,,,,,,,,6,,,,,2,,,,,,,9,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,5,,,8,9,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,5,,,8,,,,,4,5,,7,8,,,,,,,,,,9,,2,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,6,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,5,,7,,9,,,,4,,,,,,,2,,,,,,,,,,3,,5,,7,,9,,2,,4,5,,,,,,,3,4,5,,7,,9,1,,,4,,,,,,,2,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,9,,,,,,,,8,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,1,,,4,,,,,,,,,,5,,,,,1,2,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,2,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,5,,,8,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,7,8,,1,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,6,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,5,,7,,9,,2,,4,5,,,,,,,3,,5,,7,,9,1,,,,,,,,,,,,4,,6,7,,,1,2,,,5,6,7,,,,,,,5,,7,,,,,,,,,,8,,1,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,5,,,8,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,7,8,,,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,6,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,5,,7,,9,,2,,4,5,,,,,,,3,,5,,7,,9,1,,,,,,,,,,,,4,,6,7,,,,2,,,5,6,7,,,,,,,5,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,5,,,8,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,7,8,,,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,5,,7,,9,,2,,4,5,,,,,,,3,,5,,7,,9,1,,,,,,,,,,,,4,,,7,,,,2,,,5,,7,,,,,,,5,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,,,,,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,7,8,,,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,5,,7,,9,,2,,4,,,,,,,,3,,5,,7,,9,1,,,,,,,,,,,,4,,,7,,,,2,,,5,,7,,,,,,,5,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,,,,,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,7,8,,,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,4,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,7,,,,2,,,5,,7,,,,,,,5,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,,,,,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,,8,,,2,,,5,6,7,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,4,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,7,,,,2,,,5,,7,,,,,,,5,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,,,,,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,,8,,,2,,,5,6,,,,,,,,5,,7,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,4,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,7,,,,2,,,5,,7,,,,,,,5,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,5,,7,8,,,2,,4,,,,,,,,,,5,,7,8,,,,,,,,,,9,,,,4,,6,,8,,,2,,,5,6,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,4,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,7,,,,2,,,5,,7,,,,,,,5,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,5,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,5,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,,,7,8,,,2,,4,,,,,,,,,,,,7,8,,,,,,,,,,9,,,,4,,6,,8,,,2,,,,6,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,8,,1,,,,,,,,,,,,,5,,,8,,,,3,,,,7,8,,,,3,,5,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,4,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,,,,,2,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,5,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,5,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,8,,,,,,,6,7,8,9,,,,,,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,5,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,5,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,,,7,8,,,2,,4,,,,,,,,,,,,7,8,,,,,,,,,,9,,,,,,6,,8,,,2,,,,6,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,7,8,,,,3,,,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,,5,,,8,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,5,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,9,,,,,,,7,,,1,,,,,,,8,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,6,7,8,9,,,,,,6,7,,9,,2,,,,,,,,1,,,,,6,,,,,,,,,,,,9,1,,,,5,,,8,9,,,,,,,7,,,,,,,,,,8,9,,2,,,,,,,,,,,,,6,,8,9,,,,,,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,,,7,8,,,,,4,,,,,,,,,,,,7,8,,,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,7,,,,,3,,,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,,,9,,,,,5,,,,9/,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,7,,,1,,,,,,,8,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,8,,,,,,,6,7,,,,2,,,,,,,,1,,,,,6,,,,,,,,,,,,9,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,9,,2,,,,,,,,,,,,,,,8,9,,,,,,6,,,9,,,,4,,,,,,1,,,,,6,,,,,,3,,,,,,,,,,,,,7,8,,,,,4,,,,,,,,,,,,7,8,,,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,7,,,,,3,,,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,9,,2,,,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,,,,5/,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,8,,,,,,,6,7,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,8,9,,,,,,6,,,9,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,7,8,,,,,4,,,,,,,,,,,,7,8,,,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,7,,,,,3,,,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,,,2,,,,,,,,,,3,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,,,,5/,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,,,,,,7,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,3,,,,7,,,,,3,,,,7,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,,,2,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,9,,,3,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,,3,,,,7,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,,,,5/,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,3,,,,,,,1,,,,,,,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,7,,,1,,,,,,,,,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,,8,,,,,,,,7,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,,9,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,2,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,,4,,,,,,1,,,,,,,,,,,3,,,,,,,,,,,,,,8,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,,,,,6,,,,,2,,,,,,,,,,,,5,,,,,,,3,,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,5,,,,,1,,,,,,,,,,,,,,,,8,,,,,,,,7,,,,,3,,,,,,,,,,,,,,,9,,,,4,,,,,,,2,,,,,,,,,,3,,,,,,,,2,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,4,,,,,,,,,,5,,,,,,,,,,,7,,,,,,,,,,8,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,7,,,,,,,,,,,9,,,3,,,,,,,,,,4,,,,,,,,,,5,,,,,1,,,,,,,,,,,,,,6,,,,,2,,,,,,,,,,,,,,,8,,,,,4,,,,,,1,,,,,,,,,,,,,,6,,,,,,,,,,7,,,,2,,,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,,,9,,,,,5

Sudoku Difficulty Analysis:

 number of clues: 47
 number of tidbits: 583
 number of steps required: 24
 number of eliminations from...
 ...hidden singles: 5
 ...naked singles: 29
 ...hidden pairs: 0
 ...hidden tuples: 0
 ...hidden quads: 0
 ...naked pairs: 1(step 15)
 ...naked tuples: 0
 ...naked quads: 0
 ...locked candidates: 11(step 1)
 ...X-wings: 1(step 9)
 ...swordfish: 0
 ...4x4 grids: 0
 ...strong Medusa cycles: 4(step 10)
 ...weak Medusa cycles: 0
 ...hypothesis and proof: 0

||||/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,6,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,7,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,8,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,8,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,7,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,6,7,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,7,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,8,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,8,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,7,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,6,7,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,8,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,8,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,7,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,6,7,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,8,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,7,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,6,7,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,7,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,6,7,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,6,7,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,,7,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,,,8,,,,3,,,6,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,8,,,,,,,6,7,8,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,,,8,,,,3,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,,,8,,,,3,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,7,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,3,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,3,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,3,,5,,,8,,,,3,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,7,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,7,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,5,6,,,,,,3,,,6,7,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,7,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,8,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,7,8,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,,,,,,,5,,,,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,7,,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,,,,,,,5,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,7,,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,6,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,6,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,8,,,,,,,,7,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,7,,,,,,,5,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,5,,7,,,,,,,5,6,,,,,,,,,6,7,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,8,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,7,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,8,,,,,4,,,,,,,,,,5,,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,,8,,,2,,,,,,,,,,,,,6,7,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,3,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,7,,,,,3,,,6,,,,,,3,,,6,,,,,,,,5,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,6,,,,,2,,,,,,,,,,,,,6,7,,,,,,4,,,,,,,,,,5,,,8,,,,,,,,7,8,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,5,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,7,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,6,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,,8,9,,,,,5,,,,,,,3,,,6,,8,9,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,5,6,,,,,,,,,,,,9,1,,,,,,,,,,,3,,,,7,8,,,,,4,,,,,,,,3,,,6,,8,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,8,9,,,,,,,,8,,,,3,,,,,8,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,,2,,,,,,,,,,,,,6,,,,,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,3,,,,,,9,,,,,5,,,,,,,3,,,,,8,9,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,,9,,,,,,,,8,,,,3,,,,,,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,,2,,,,,,,,,,,,,6,,,,,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,,8/1,,,,,,,,,,,,,,,,,9,,,,,,,7,,,,,3,,,,,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,,8,,,,,,5,,,,,,2,,,,,,,,,,,,,6,,,,,,,,5,,,,,,,,,,,,8,,1,,,,,,,,,,,,,,,,,9,,,,4,,,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,3,,,,,,,,,,,,,7,,,,,,,5,,,,,,,,,,6,,,,,2,,,,,,,,1,,,,,,,,,,,,,,,,,9,,,,,,6,,,,,,3,,,,,,,1,,,,,,,,,,2,,,,,,,,,,,,,,,,9,,,,,5,,,,,,,,,,,,8,,,,,,,,7,,,,,,4,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,7,,,,,,4,,,,,,,,3,,,,,,,,2,,,,,,,,,,,,,6,,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,,6,,,,,,3,,,,,,9,,,,,,,,8,,,,,,,,,,9,,,,,5,,,,,1,,,,,,,,,,,,,,,,,9,1,,,,,,,,,,,,,,,,8,,,,,,5,,,,,,,,,,6,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,2,,,,,,,,,,,,5,,,,,,2,,,,,,,,,,,,,6,,,,,,,4,,,,,,,,,,,,,8,,,,,,,,7,,,1,,,,,,,,,,,,,,,,,9,,,3,,,,,,,,,3,,,,,,,,,,,,,7,,,,,,4,,,,,,,,,,,,,,9,,2,,,,,,,,1,,,,,,,,,,,,,5,,,,,,,,,,6,,,,,,,,,,,8||6b

Sudoku Difficulty Analysis:

 number of clues: 17
 number of tidbits: 409
 number of steps required: 63
 number of eliminations from...
 ...hidden singles: 35
 ...naked singles: 29
 ...hidden pairs: 6(step 22)
 ...hidden tuples: 0
 ...hidden quads: 0
 ...naked pairs: 1(step 52)
 ...naked tuples: 0
 ...naked quads: 0
 ...locked candidates: 32(step 2)
 ...X-wings: 0
 ...swordfish: 0
 ...4x4 grids: 0
 ...strong Medusa cycles: 1(step 53)
 ...weak Medusa cycles: 0
 ...hypothesis and proof: 0

Sudoku Analyst -- Check the level of a Sudoku prior to solving it. how to use this site

Entering Puzzles

Difficulty Ratings

Credits