Sum of Fractions

You are given a fraction 4/n.

Your task is to represent it as a sum 1/a + 1/b + 1/c where a > b > c are positive integers.

Input

The input file consists of multiple test cases. The first line of the input le contains one integer number T ≤ 1.5·10^4  the number of test cases. The following T lines contain one integer number 4 ≤ n ≤ 15000 each.

Output

For each test case, write to the output file a separate line with three integer numbers 2^63 > a > b > c > 0 separated by spaces such that 4/n = 1/a + 1/b + 1/c or three zeros, if such representation is impossible.

Examples