In this very first task, let us look at a boring mathematics problem. :-)

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

• x + y + z = A
• xyz = B
• x² + y² + z² = C

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

For the Extreme version of this problem, please click here.

Input

The first line of the input file gives the number of test cases 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.

Sample Input

2
1 2 3
6 6 14

Sample Output

No solution.
1 2 3