<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:
#define ll long long
    int nthUglyNumber(int n) {
        vector<int>primes{2,3,5};
         int p=primes.size();
        ll inf=LLONG_MAX;
        vector<ll>vpidx(p,0);
        vector<ll>val(n);
        val[0]=1;
        for(int i=1;i<n;i++){
          ll v=inf;
          ll idx;
          for(int j=0;j<p;j++){
if(v>(val[vpidx[j]]*primes[j]) && (val[vpidx[j]]*primes[j])>val[i-1] ){
    v=(val[vpidx[j]]*primes[j]); 
}}
         for(int j=0;j<p;j++){
if(v==(val[vpidx[j]]*primes[j]) ){
    vpidx[j]++;
}
          }
        //   cout<<i<<" "<<v<<" "<<endl;
          val[i]=v;
         
        //   for(int ti=0;ti<p;ti++){cout<<vpidx[ti]<<" ";} cout<<endl;
        }
        
        return val[n-1];
    }
};
10884