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