public class Solution {
    public static int sum;
    public int totalNQueens(int n) {
        sum = 0;
        int[] usedColumns = new int[n];
        placeQueen(usedColumns, 0);
        return sum;
    }
    public void placeQueen(int[] usedColumns, int row) {
        int n = usedColumns.length;

        if (row == n) {
            sum ++;
            return;
        }

        for (int i = 0; i < n; i++) {
            if (isValid(usedColumns, row, i)) {
                usedColumns[row] = i;
                placeQueen(usedColumns, row + 1);
            }
        }
    }
    public boolean isValid(int[] usedColumns, int row, int col) {
        for (int i = 0; i < row; i++) {
            if (usedColumns[i] == col) {
                return false;
            }
            if ((row - i) == Math.abs(col-usedColumns[i])) {
                return false;
            }
        }
        return true;
    }
}