## 1090 Highest Price in Supply Chiain

A supply chain is a network of retailers（零售商）, distributors（经销商）, and suppliers（供应商）-- everyone involved in moving a product from supplier to customer.

Starting from one root supplier, everyone on the chain buys products from one’s supplier in a price P and sell or distribute them in a price that is r% higher than P. It is assumed that each member in the supply chain has exactly one supplier except the root supplier, and there is no supply cycle.

Now given a supply chain, you are supposed to tell the highest price we can expect from some retailers.

### Input Specification:

Each input file contains one test case. For each case, The first line contains three positive numbers: $$N (≤10^5)$$, the total number of the members in the supply chain (and hence they are numbered from $0$ to $N−1$); $P$, the price given by the root supplier; and $r$, the percentage rate of price increment for each distributor or retailer. Then the next line contains $N$ numbers, each number $S_i$ is the index of the supplier for the $i$-th member. $S_{root}$ for the root supplier is defined to be $$-1$$. All the numbers in a line are separated by a space.

### Output Specification:

For each test case, print in one line the highest price we can expect from some retailers, accurate up to $2$ decimal places, and the number of retailers that sell at the highest price. There must be one space between the two numbers. It is guaranteed that the price will not exceed $10^{10}$.

## 思路

• 记录level数组，表示传销层级
• 记录last数组，记录每个公司的上级
• 对last数组深度优先遍历，更新level

## 思考

• 建议使用第二遍代码，即使用剪枝的深度优先遍历，使用C++来写。
• 这道题目给Python的时间其实比C++要充裕，通过第一二四遍的代码对比可以得出。
• Python始终不对不是因为时间原因。
• 使用错误异常机制定位到，是count_level() 函数里的内容报错。
• 可是函数里的内容，这两种语言写法几乎是一模一样，除了最基础的语法部分。
• 所以我陷入了迷惑。
• 希望读者评论能够点醒我。