<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 ll long long
class Solution {
    priority_queue<int, vector<int>, greater<int>> pq;
private:
    void preComp(int N){
    int n = N;
        for(ll p=0; p<=n/2 + 1; p++){
            for(ll q=0; q<=n/3 + 1; q++){
                for(ll r=0; r<=n/5 + 1; r++){
                    if(1LL*pow(2LL,p)*pow(3LL,q)*pow(5LL,r)>=INT_MAX){
                        break;
                    }
                    long long val = 1LL*pow(2LL,p)*pow(3LL,q)*pow(5LL,r);
                    pq.push(val);
                }
            }
        }
    }
public:
    int nthUglyNumber(int n) {
        // 2^p * 3^q * 5^r
        preComp(n);
        for(int i=0; i<n-1; i++){
            pq.pop();
        }
        return pq.top();
    }
};
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