Number into Sequence

题意翻译

共 $t (t\le 5000)$ 组数据, 对于每组数据输入一个整数 $n (2 \le n \le 10^{10})$ 请构造一个长度为 $k$ 的数列 $a$, 满足以下条件: - $\forall i \in a : i > 1$; - $\prod_{i=1}^k a_i = n$; - $\forall i \in [2,k] : a_i \bmod a_{i-1} = 0$ ; - $k$ 尽可能大; 对于每组数据第一行输出一个整数 $k$, 第二行输出 $k$ 个整数 $a_i$, 如果有多个数列满足条件任意输出一个.

题目描述

You are given an integer $ n $ ( $ n > 1 $ ). Your task is to find a sequence of integers $ a_1, a_2, \ldots, a_k $ such that: - each $ a_i $ is strictly greater than $ 1 $ ; - $ a_1 \cdot a_2 \cdot \ldots \cdot a_k = n $ (i. e. the product of this sequence is $ n $ ); - $ a_{i + 1} $ is divisible by $ a_i $ for each $ i $ from $ 1 $ to $ k-1 $ ; - $ k $ is the maximum possible (i. e. the length of this sequence is the maximum possible). If there are several such sequences, any of them is acceptable. It can be proven that at least one valid sequence always exists for any integer $ n > 1 $ . You have to answer $ t $ independent test cases.

输入输出格式

输入格式

The first line of the input contains one integer $ t $ ( $ 1 \le t \le 5000 $ ) — the number of test cases. Then $ t $ test cases follow. The only line of the test case contains one integer $ n $ ( $ 2 \le n \le 10^{10} $ ). It is guaranteed that the sum of $ n $ does not exceed $ 10^{10} $ ( $ \sum n \le 10^{10} $ ).

输出格式

For each test case, print the answer: in the first line, print one positive integer $ k $ — the maximum possible length of $ a $ . In the second line, print $ k $ integers $ a_1, a_2, \ldots, a_k $ — the sequence of length $ k $ satisfying the conditions from the problem statement. If there are several answers, you can print any. It can be proven that at least one valid sequence always exists for any integer $ n > 1 $ .

输入输出样例

输入样例 #1

4
2
360
4999999937
4998207083

输出样例 #1

1
2 
3
2 2 90 
1
4999999937 
1
4998207083