<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> getVec(int n){
        long long num=1;
        vector<int> vec;
        while(num<=INT_MAX){
            vec.push_back(num);
            num*=n;
        }
        return vec;
    }
    int nthUglyNumber(int n) {
        if(n==1){
            return 1;
        }
        vector<int> a=getVec(2);
        vector<int> b=getVec(3);
        vector<int> c=getVec(5);
        vector<int> ans;
        for(int i=0;i<a.size();i++){
            for(int j=0;j<b.size();j++){
                for(int k=0;k<c.size();k++){
                    long long x=a[i];
                    long long y=b[j];
                    long long z=c[k];
                    if(x*y<=INT_MAX && y*z<=INT_MAX && z*x<=INT_MAX && x*y*z<=INT_MAX) {
                        ans.push_back(x*y*z);
                    }
                }
            }
        }
    
        sort(ans.begin(),ans.end());
        // cout<<ans.back();
        cout<<ans.size();
        return ans[n-1];

    }
};
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