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`