<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>

class Solution {
public:
    int nthUglyNumber(int n) {
        // priority_queue<int,vector<int>,greater<int>>pq;
        // pq.push(1);
        set<long long>s;
        s.insert(1ll);
        vector<long long>vec(n+1);
        vec[1] = 1;
        int idx = 1;
        while(idx<=n){

            // int t = pq.top();
            // pq.pop();
            auto ptr = s.begin();
            
            long long t = (long long)(*ptr);
            s.erase(ptr);

            vec[idx] = t;
            idx++;
            if(idx==n+1) break;
            s.insert(t*2ll);
            s.insert(t*3ll);
            s.insert(t*5ll);

        }
        // for(auto val:vec){
        //     cout<<val<<" ";
        // }
        return vec[n];
    }
};
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