/**

* Difficulty:

* Hard

*

* Desc:

* Follow up for N-Queens problem.

* Now, instead outputting board configurations, return the total number of distinct solutions

*

* 还是 n 皇后问题，只是相对于上一题，这次只需要求出解的数目即可

*/

var getQueues = function(n) {

var results = 0;

var getQueue = function(row, notAvaliableColumn, finishedRowCount) {

if (row > n) return true;

var result = false;

for (var i = 0; i < n; i += 1) {

if (notAvaliableColumn.has(`c${i}`) || notAvaliableColumn.has(`s${row + i}`) || notAvaliableColumn.has(`d${row - i}`)) continue;

var notAvaliable = new Set([...notAvaliableColumn]);

notAvaliable.add(`c${i}`);

notAvaliable.add(`d${row - i}`);

notAvaliable.add(`s${row + i}`);

var qRow = new Array(n).fill('.');

qRow[i] = 'Q';

if (getQueue(row + 1, notAvaliable, finishedRowCount + 1)) {

if (finishedRowCount >= n) {

result = true;

results += 1;

break;

}

} else {

notAvaliable.delete(`c${i}`);

notAvaliable.delete(`d${row - i}`);

notAvaliable.delete(`s${row + i}`);

}

}

return result;

};

getQueue(1, new Set(), 1);

return results;

};

/**

* @param {number} n

* @return {number}

*/

var totalNQueens = function(n) {

if (n === 1) return 1;

if (n <= 3) return 0;

var results = getQueues(n);

return results;

};