We have three different integers, x, y and z, which satisfy the following three relations:

x + y + z = A

xyz = B

x^{2} + y^{2} + z^{2} = C

You are asked to write a program that solves for x, y and z for given values of A, B and C.

Input

The first line of the input file gives the number of test cases N (N < 20). Each of the following N lines gives the values of A, B and C (1 ≤ A, B, C ≤ 10000).

Output

For each test case, output the corresponding values of x, y and z. If there are many possible answers, choose the one with the least value of x. If there is a tie, output the one with the least value of y.

If there is no solution, output the line 'No solution.' instead.