Prime Factors

Given a natural number N. Lay it on the prime factors.

Input

The first line of input contains the number of T (1 ≤ T ≤ 10000) of natural numbers to be decomposed into prime factors. Each of the next T lines contains a single integer N (2 ≤ N ≤ 10 000 000).

Output

For each number N of the input data in a single line through the gap carry him the prime factors in the format shown in the examples.

Do not put extra spaces, otherwise you will get a "Wrong Answer". For example, if N is 4, you need to remove "2 * 2" (no space after the second two).

Examples