N-Queens

## Problem 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. Two queens attack each other if they are in the same row, column, or diagonal. ## Examples **Example 1:** ``` Input: n = 4 Output: 2 Explanation: There are two distinct solutions to the 4-queens puzzle. ``` **Example 2:** ``` Input: n = 1 Output: 1 ``` **Example 3:** ``` Input: n = 5 Output: 10 ``` ## Approach Hints Use backtracking. Place queens row by row. For each row, try every column and check if the placement is safe (no conflict in column, main diagonal, or anti-diagonal). Use sets to track occupied columns and diagonals for O(1) conflict checks.