LogiQuest

11. N-Queens Count

HardBacktracking

Count the ways to place n queens on an n × n chessboard so that no two attack each other.

Input format

A single integer n.

Output format

The number of solutions.

Example 1

Input

4

Output

2

Example 2

Input

1

Output

1

Constraints

1 ≤ n ≤ 9

Read input from standard input and print the answer to standard output. Your code is judged against 6 test cases, most of them hidden.

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