<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) {
        set<int> st;
        st.insert(1);
        // 1
        // 1 2
        // 1 2 4 3
        // 1 2 3 4 5 6 8 
        // 1 2 3 4 5 6 8 9 10 12 15 16 
        // 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32
        // 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54 60 64
        
        while(st.size()<n){
            int t=st.size();
            auto it = st.begin();
            for(int i = 0;i<t;i++){
                long x = long(*it)*2;
                if(x>INT_MAX)   break;
                st.insert((*it)*2);
                
                // if(st.size()>n) break;
                // cout<<(*it)<<" "<<(*it)*2<<" ";
                it++;
            }
            
            // auto it_end=st.end();
            it=st.begin();
            for(int i = 0;i<t;i++){
                int x = (*it)*3;
                if(x<*prev(st.end()))    st.insert(x);
                else    break;
                it++;
            }
            it=st.begin();
            for(int i = 0;i<t;i++){
                int x = (*it)*5;
                if(x<*prev(st.end()))    st.insert(x);
                else    break;
                it++;
            }
            // for(auto i:st)  cout<<i<<" ";
            // cout<<st.size()<<" "<<*st.end()<<"\n";
        }
        int count=0;
        for(auto i:st){
            count++;
            if(count==n)    return i;
        }
        return n;
        
        
    }
};
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