On an n x n chessboard, place n queens so that no two attack each
other (no two queens share a row, column, or diagonal). Read the positive
natural number n. Determine and print the total number of valid
arrangements.
Mobile coding works. A laptop is faster for long sessions.
Problem
Input format
Input
input.txt
The program reads from standard input a single natural number, `n`. - `1 <= n <= 8` - For `n = 2` and `n = 3` the answer is `0`.
Output format
Output
output.txt
The program prints a single natural number followed by a newline: the number of valid arrangements.
Example
input
4
output
2
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Sample cases (from the problem)
Sample Case 1
Input
4
Expected output
2
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