Validate a Sudoku

Definition

Sudokus are number-puzzles in which cells in a 9×9 grid must be populated with the numbers 1 to 9.

The following constraints must apply to the 9×9 grid.

• Each digit from 1 to 9 only occurs only once
  • per row
  • per column
  • per block (i.e. 3×3 sub grid)

Goal

Validate, if a given Sudoku is a valid solution.

The Sudoku must comply with the definition above.

Input

A sequence of 81 digits, organized in 9 columns and 9 rows.

The columns of a row are separated by blanks.

Rows are separated by line-breaks.

Output

A boolean value true or false defining the correctness of the input.

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