<p>An <strong>ugly number</strong> is a positive integer whose prime factors are limited to <code>2</code>, <code>3</code>, and <code>5</code>.</p>

<p>Given an integer <code>n</code>, return <em>the</em> <code>n<sup>th</sup></code> <em><strong>ugly number</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 10
<strong>Output:</strong> 12
<strong>Explanation:</strong> [1, 2, 3, 4, 5, 6, 8, 9, 10, 12] is the sequence of the first 10 ugly numbers.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 1
<strong>Explanation:</strong> 1 has no prime factors, therefore all of its prime factors are limited to 2, 3, and 5.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 1690</code></li>
</ul>

#define i64 long long
class Solution {
public:
    void rec(int n,priority_queue<i64>& q,vector<int>&chk,long long val,i64 ind){
        if(ind>3 || val>=INT_MAX){
            return;
        }
        if(q.size()<=n){
            q.push(val);
        }
        if(q.size()>n){
            q.pop();
        }
        for(int j=ind;j<3;j++){
            rec(n,q,chk,val*chk[j],j);
        }
    }
    int nthUglyNumber(int n) {
        priority_queue<i64> q;
        vector<int> chk(3);
        chk[0]=2,chk[1]=3,chk[2]=5;
        rec(n,q,chk,1,0);
        return (int)q.top();
    }
};
16228