<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:
    void func(int pt1, int pt2, int pt3, vector<int>& ans, int n) {
        if (ans.size() == n)
            return;

        int op1 = ans[pt1] * 2;
        int op2 = ans[pt2] * 3;
        int op3 = ans[pt3] * 5;
        int mini = min({op1, op2, op3});

        ans.push_back(mini);

        if (mini == op1)
            pt1++;
        if (mini == op2)
            pt2++;
        if (mini == op3)
            pt3++;

        func(pt1, pt2, pt3, ans, n);
    }

    int nthUglyNumber(int n) {
        vector<int> ans;
        ans.push_back(1); // First ugly number is 1
        func(0, 0, 0, ans, n);
        return ans[n - 1];
    }
};

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