<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) {
        ll n = 1LL * 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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