D. Number into Sequencetime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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}).OutputFor 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.ExampleInput
4
2
360
4999999937
4998207083
Output
1
2 
3
2 2 90 
1
4999999937 
1
4998207083 

4
2
360
4999999937
4998207083

1 2  3 2 2 90  1 4999999937  1 4998207083  
['constructive algorithms', 'math', 'number theory', '*1300']