Migrated from Lutece 296 Sudoku

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Description

The puzzle game of Sudoku is played on a board of $N^2\times N^2$ cells. The cells are grouped in $N\times N$ squares of $N\times N$ cells each. Each cell is either empty or contains a number between $1$ and $N^2$.

The Sudoku position is correct when numbers in each row, each column and each square are different. The goal of the game is, starting from some correct positions; fill all empty cells so that the final position is still correct. (We call the final position is a solution to the starting position).

This problem is not about to solve a specific Sudoku puzzle, but ask you to find all correct positions that have a unique solution when $N = 2$.

Input

There's no input for this problem.

Output

Output $x$ on a single line where $x$ is the number of correct positions have a unique solution when $N = 2$.

Samples

(There are no sample input)

123456

Note

(The Sudoku description is quoted from problem Sudoku Checker, Northeastern Europe 2005)

The sample output is NOT CORRECT, it just shows how to output your solution.

Resources

2010 ACM-ICPC Multi-University Training Contest 13 Host by UESTC