Your assignment is to find a succession of integers a1,a2,… ,ak with the end goal that: every simulated intelligence is completely more prominent than 1; a1⋅a2⋅… ⋅ak=n (I. e. the result of this grouping is n); ai+1 is separable by
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You are given an integer n (n>1).
Your assignment is to find a succession of integers a1,a2,… ,ak with the end goal that:
every simulated intelligence is completely more prominent than 1;
a1⋅a2⋅… ⋅ak=n (I. e. the result of this grouping is n);
k is the most extreme conceivable (I. e. the length of this grouping is the greatest conceivable).
In case there are a few such groupings, any of them is adequate. It tends to be demonstrated that somewhere around one substantial grouping consistently exists for any integer n>1.
You need to answer t autonomous experiments.
Input
The primary line of the input contains one integer t (1≤t≤5000) — the number of experiments. Then, at that point, t experiments follow.
The main line of the experiment contains one integer n (2≤n≤1010).
It is ensured that the amount of n doesn't surpass 1010 (∑n≤1010).
Output
For each experiment, print the appropriate response: in the main line, print one sure integer k — the greatest conceivable length of a. In the subsequent line, print k integers a1,a2,… ,ak — the grouping of length k fulfilling the conditions from the issue explanation.
In case there are a few replies, you can print any. It tends to be demonstrated that something like one legitimate arrangement consistently exists for any integer n>1.
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