<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[2000];
        a[0] = 1;
        int q = 0, w = 0, e = 0;
        unordered_map<int ,int> ma;
        ma[1] = 1;
        for (int i=1; i<n; i++) {
            if (a[q]*2 <= a[w]*3 && a[q]*2 <= a[e]*5) {
                a[i] = a[q]*2;
                q++;
            } else if (a[w]*3 <= a[q]*2 && a[w]*3 <= a[e]*5) {
                a[i] = a[w]*3;
                w++;
            } else {
                a[i] = a[e]*5;
                e++;
            }
            if (ma[a[i]] == 0)
              ma[a[i]] = 1;
            else i--;
        }
        return a[n-1];
    }
};
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