<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>

// naive apply ugly number 1 for each number
class Solution {
public:
    int nthUglyNumber(int n) {
        priority_queue<long long, vector<long long>, greater<long long>> pq;
        unordered_set<long long> set;
        pq.push(1);
        int count = 0;
        long long ans = 1;
        while (count < n) {
            long long val = pq.top();
            pq.pop();
            ans = val;
            long long first=ans*2;
            long long second=ans*3;
            long long third=ans*5;
            if(set.find(first)==set.end()){
                set.insert(first);
                pq.push(first);
            }
            if(set.find(second)==set.end()){
                set.insert(second);
                pq.push(second);
            }
            if(set.find(third)==set.end()){
                set.insert(third);
                pq.push(third);
            }

            count++;
        }
        return ans;
    }
};
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