<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) {
        vector <long long> primes={2,3,5};
        vector <long long> mulIdx(3,1);
        vector <long long> dp(n+1,0);
        dp[1]=1;
        for (int i=2;i<=n;i++) {
            long long mini=INT_MAX;
            for (int j=0;j<3;j++) {
                long long temp = primes[j] * (dp[mulIdx[j]]);
                if (temp<mini) {
                    mini=temp;
                }
            }
            dp[i]=mini;
            for (int j=0;j<3;j++) {
                long long temp = primes[j] * (dp[mulIdx[j]]);
                if (temp==mini) {
                    mulIdx[j]++;
                }
            }
        }
        return dp[n];
    }
};
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