The puzzle game of Sudoku is played on a board of N^2 × N^2 cells. The cells are grouped in N × N squares of N × 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.

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.

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

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