Sudoku verifier

Definition

Sudokus are logic number puzzles in which cells in a 9×9 grid must be populated with the digits 1 to 9 in a way that each digit occurrs only once in each unit (that is column, row or block = 3×3 sub grid).

Goal

Validate if a given solution for a Sudoku is valid, by checking that the digit 1 to 9 appear only once in column, in each row and in each of the 9 sub grids.

Input

a sequence of 81 digits, organized in 9 columns and 9 rows

Output

A boolean value, if the grid is valid.

Constraints

1 <= digit <= 9

Examples

Input:

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

Output: true