<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:
    vector<int>ans={1,2,3,4,5,6,8,9,10,12};
    int i=6,j=4,k=4;
    Solution(){
        while(ans.size()<1690){
            if((2*ans[i])<=(3*ans[j]) and (2*ans[i])<=(5*ans[k])){
                ans.push_back(2*ans[i]);
                if((2*ans[i])==(3*ans[j])){
                    j++;
                }
                if((2*ans[i])==(5*ans[k])){
                    k++;
                }
                i++;
            }
            else if((2*ans[i])>=(3*ans[j]) and (3*ans[j])<=(5*ans[k])){
                ans.push_back(3*ans[j]);
                if((2*ans[i])==(3*ans[j])){
                    i++;
                }
                if((3*ans[j])==(5*ans[k])){
                    k++;
                }
                j++;
            }
            else{
                ans.push_back(5*ans[k]);
                if((2*ans[i])==(5*ans[k])){
                    i++;
                }
                if((3*ans[j])==(5*ans[k])){
                    j++;
                }
                k++;
            }
        }
    }
    int nthUglyNumber(int n) {
        return ans[n-1];    
    }
};
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