This is an extreme version of Problem A of our contest. If your code solves this problem, it will also get "Accepted" for Problem A.

Let us recall the scenario: 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.

Input

The first line of the input file gives the number of test cases N (< 250). Each of the following N lines gives the values of A, B and C (1 ≤ A, B, C ≤ 6 × 10¹⁸ = 6000000000000000000).

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