Write a program to find the n-th ugly number.

Ugly numbers are positive numbers whose prime factors only include 2, 3, 5. For example, 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 is the sequence of the first 10 ugly numbers.

Note that 1 is typically treated as an ugly number.

Hint:

1. The naive approach is to call isUgly
   for every number until you reach the n^th one. Most numbers are not ugly. Try to focus your effort on generating only the ugly ones.
2. An ugly number must be multiplied by either 2, 3, or 5 from a smaller ugly number.
3. The key is how to maintain the order of the ugly numbers. Try a similar approach of merging from three sorted lists: L₁
   , L₂, and L₃.
4. Assume you have U_k, the k^th ugly number. Then U_k+1 must be Min(L₁ * 2, L₂ * 3, L₃ * 5).

這道題是之前那道Ugly Number 醜陋數的延伸，這裡讓我們找到第n個醜陋數，還好題目中給了很多提示，基本上相當於告訴我們解法了，根據提示中的資訊，我們知道醜陋數序列可以拆分為下面3個子列表：

仔細觀察上述三個列表，我們可以發現每個子列表都是一個醜陋數分別乘以2,3,5，而要求的醜陋數就是從已經生成的序列中取出來的，我們每次都從三個列表中取出當前最小的那個加入序列，請參見程式碼如下：

class Solution {
public:
    int nthUglyNumber(int n) {
        vector<int> res(1, 1);
        int i2 = 0, i3 = 0, i5 = 0;
        while (res.size() < n) {
            int m2 = res[i2] * 2, m3 = res[i3] * 3, m5 = res[i5] * 5;
            int mn = min(m2, min(m3, m5));
            if (mn == m2) ++i2;
            if (mn == m3) ++i3;
            if (mn == m5) ++i5;
            res.push_back(mn);
        }
        return res.back();
    }
};