Based on the geometric mean problem from the last Internet Olympiad.

All crew members have to complete a bunch of tasks in order to win against the impostors, but sometimes the tasks are too difficult, and the crew members are too tired after completing all the short and medium tasks, so they ask you for help.

The current task is as follows: the device has three positive integer parameters a, b and c, which have been reset to factory settings to the values x = g( a, b), y = g(a, c) and z = g( b, c) respectively, where g is the geometric mean rounded down, i.e.

Please help to determine any appropriate a, b and c (if they exist) from the current values of x, y and z so that the crew member was able to properly set up the device and complete the task. Since there are a lot of crew members, and everyone is adjusting their device, you need to solve the problem several times in a row!

Input

The first line contains one integer n (1 ≤ n ≤ 105) the number of crew members to help.

The next n lines contain three integers x, y and z (1 ≤ x, y, * z* ≤ 109) each.

Output

For each triple of numbers x, y, z print the appropriate numbers a, b and c. If there are several suitable answers, print any one. If there is no answer, print three numbers 0.