The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other.

Given an integer n, return the number of distinct solutions to the n-queens puzzle.

  Example 1:

Input: n = 4 Output: 2 Explanation: There are two distinct solutions to the 4-queens puzzle as shown.

Example 2:

Input: n = 1 Output: 1

  Constraints:

1 <= n <= 9