<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) {
        int a=1,b=1,c=1;
        // long long a=1,b=1,c=1;
        int ca=1,cb=1,cc=1;
        vector<int> dp(n+1,1);
        for(int i=2;i<=n;i++)
        {
            vector<int> v={a*2,b*3,c*5};
            sort(begin(v),end(v));
            dp[i]=v[0];
            // dp[i]=min( a*2, min(b*3,c*5) );
            if( dp[i]==a*2 ) a=dp[++ca];
             if( dp[i]== b*3 ) b=dp[++cb];
             if( dp[i]== c*5 ) c=dp[++cc];
            cout<<dp[i];
            cout<<" a = "<<a<<" b = "<<b<<" c = "<<c<<endl;
        }
        return dp[n];
    }
};
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