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

**Example 2:**

Input:n = 1Output:1

**Constraints:**

`1 <= n <= 9`