Is it the solution of a Sudoku? P16893


Statement
 

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Remember that a Sudoku is a game that consists of completing a 9×99 \times 9 grid with numbers between 1 and 9, so that the final result has not repeated numbers in the same row, column or 3×33 \times 3 submatrix. For example, this is a Sudoku and its solution:

(9,9) (0,0)(0,9) (1,0)(1,9) (2,0)(2,9) (3,0)(3,9) (4,0)(4,9) (5,0)(5,9) (6,0)(6,9) (7,0)(7,9) (8,0)(8,9) (9,0)(9,9)

(0,0)(9,0) (0,1)(9,1) (0,2)(9,2) (0,3)(9,3) (0,4)(9,4) (0,5)(9,5) (0,6)(9,6) (0,7)(9,7) (0,8)(9,8) (0,9)(9,9)

(0.5,0.5)4 (2.5,0.5)5 (3.5,0.5)6

(1.5,1.5)2 (2.5,1.5)9 (3.5,1.5)1

(4.5,2.5)7 (5.5,2.5)5 (8.5,2.5)8

(2.5,3.5)6 (3.5,3.5)4 (4.5,3.5)2

(1.5,4.5)4 (2.5,4.5)8 (6.5,4.5)5 (7.5,4.5)6

(4.5,5.5)6 (5.5,5.5)1 (6.5,5.5)8

(0.5,6.5)1 (3.5,6.5)9 (4.5,6.5)3

(5.5,7.5)6 (6.5,7.5)4 (7.5,7.5)5

(5.5,8.5)2 (6.5,8.5)3 (8.5,8.5)7

(9,9) (0,0)(0,9) (1,0)(1,9) (2,0)(2,9) (3,0)(3,9) (4,0)(4,9) (5,0)(5,9) (6,0)(6,9) (7,0)(7,9) (8,0)(8,9) (9,0)(9,9)

(0,0)(9,0) (0,1)(9,1) (0,2)(9,2) (0,3)(9,3) (0,4)(9,4) (0,5)(9,5) (0,6)(9,6) (0,7)(9,7) (0,8)(9,8) (0,9)(9,9)

(0.5,0.5)4 (1.5,0.5)7 (2.5,0.5)5 (3.5,0.5)6 (4.5,0.5)8 (5.5,0.5)9 (6.5,0.5)1 (7.5,0.5)3 (8.5,0.5)2

(0,1) (0.5,0.5)9 (1.5,0.5)2 (2.5,0.5)9 (3.5,0.5)1 (4.5,0.5)4 (5.5,0.5)3 (6.5,0.5)6 (7.5,0.5)7 (8.5,0.5)5

(0,2) (0.5,0.5)6 (1.5,0.5)3 (2.5,0.5)1 (3.5,0.5)2 (4.5,0.5)7 (5.5,0.5)5 (6.5,0.5)9 (7.5,0.5)4 (8.5,0.5)8

(0,3) (0.5,0.5)5 (1.5,0.5)1 (2.5,0.5)6 (3.5,0.5)4 (4.5,0.5)2 (5.5,0.5)8 (6.5,0.5)7 (7.5,0.5)9 (8.5,0.5)3

(0,4) (0.5,0.5)2 (1.5,0.5)4 (2.5,0.5)8 (3.5,0.5)3 (4.5,0.5)9 (5.5,0.5)7 (6.5,0.5)5 (7.5,0.5)6 (8.5,0.5)1

(0,5) (0.5,0.5)7 (1.5,0.5)9 (2.5,0.5)3 (3.5,0.5)5 (4.5,0.5)6 (5.5,0.5)1 (6.5,0.5)8 (7.5,0.5)2 (8.5,0.5)4

(0,6) (0.5,0.5)1 (1.5,0.5)5 (2.5,0.5)7 (3.5,0.5)9 (4.5,0.5)3 (5.5,0.5)4 (6.5,0.5)2 (7.5,0.5)8 (8.5,0.5)6

(0,7) (0.5,0.5)3 (1.5,0.5)8 (2.5,0.5)2 (3.5,0.5)7 (4.5,0.5)1 (5.5,0.5)6 (6.5,0.5)4 (7.5,0.5)5 (8.5,0.5)9

(0,8) (0.5,0.5)9 (1.5,0.5)6 (2.5,0.5)4 (3.5,0.5)8 (4.5,0.5)5 (5.5,0.5)2 (6.5,0.5)3 (7.5,0.5)1 (8.5,0.5)7

In this problem we do not ask you to solve any Sudoku, just to check that every given matrix can be the solution of a Sudoku.

Input

Input consists of a number nn, followed by nn cases. Every case has 9 rows, each one with 9 numbers between 1 and 9.

Output

For every case, print “yes” or “no” depending on whether the given matrix follows the rules of the solutions of Sudokus.

Public test cases

  • Input

    2

1 2 3 4 5 6 7 8 9
4 5 6 7 8 9 1 2 3
7 8 9 1 2 3 4 5 6
2 3 1 6 7 4 8 9 5
8 7 5 9 1 2 3 6 4
6 9 4 5 3 8 2 1 7
3 1 7 2 6 5 9 4 8
5 4 2 8 9 7 6 3 1
9 6 8 3 4 1 5 7 2

1 2 3 4 5 6 7 8 9
4 5 6 7 8 9 1 2 3
7 8 9 1 2 3 4 5 6
2 3 1 6 7 4 8 9 5
8 7 5 9 1 2 3 6 4
6 9 4 5 3 8 2 1 7
3 1 7 2 6 5 9 4 8
5 4 2 8 9 7 6 2 1
9 6 8 3 4 1 5 7 3

    Output

    yes
no
    • Information
    Author
    Salvador Roura
    Language
    English
    Translator
    Salvador Roura
    Original language
    Catalan
    Other languages
    Catalan
    Official solutions
    C++ Python
    User solutions
    C++ Java Python