Ways to Arrange Balls Problem

You are given 'a' balls of type 'A', 'b' balls of type 'B', and 'c' balls of type 'C'. Determine the total number of ways to arrange these balls in a straight line so that no two adjacent balls are of the same type.

Input:

The first line of input consists of an integer 'T', which represents the number of test cases.
 For each test case, there is a single line containing three space-separated positive integers: a, b, c.

Output:

For each test case, output a single integer denoting the total number of valid arrangements of balls where no two adjacent balls are of the same type.

Example:

Input:

2
2 1 1
1 0 1

Output:

6
0

Explanation:

For the first test case, there are 6 ways to arrange: ABCA, ABAC, ACBA, ACAB, BACA, CABA.
For the second test case, there is no valid arrangement, hence the output is 0.

Constraints:

• 1 ≤ T ≤ 100
• 0 ≤ a, b, c ≤ 15
• Time limit: 1 sec