
ZOJ Problem Set  4091
Let $\mathbb{E} = \{2k  k \in \mathbb{Z}^+\}$, which is the set of all positive even numbers. Define the following concepts:
Given a positive even number $e$, your task is to find an eprime factorization $\mathbb{P}$ of $e!!$, such that $\mathbb{P}$ (the size of $\mathbb{P}$) is as large as possible. In order to make the task easier, you just need to output the value of $\mathbb{P}$. InputThere are multiple test cases. The first line of the input contains an integer $T$ (about 50), indicating the number of test cases. For each test case: The first and only line contains a positive even number $e$ ($2 \le e \le 10^{1000}$), indicating the given number. OutputFor each test case output one integer in one line, indicating the maximum size of the eprime factorization of $e!!$. Sample Input2 2 4 Sample Output1 3 HintFor the first sample test case, as 2!! = 2 is an eprime, the answer is (obviously) 1. For the second sample test case, we can factorize 4!! = 8 into $2 \times 2 \times 2$, which contains 3 eprimes. Author: CHEN, Jingbang Source: The 19th Zhejiang University Programming Contest Sponsored by TuSimple 