Once upon a time, three girls — Winnie, Grace and Bonnie — owned a large number of pearls. However, each of them only had a single color of pearls. Winnie had white pearls, Grace had grey pearls and Bonnie had black pearls. One day, after a long discussion, they decided to make necklaces using the pearls. They are interested in knowing how many patterns can be formed using a certain number of pearls of each color, and have asked you to solve this problem for them. Note that rotating or flipping over a necklace cannot produce a different kind of necklace. i.e. The following figure shows three equivalent necklaces. The following figure shows all possible necklaces formed by 3 white pearls, 2 grey pearls and 1 black pearl. Input The input begins with an integer N (≤ 2500) which indicates the number of test cases followed. Each of the following test cases consists of three non-negative integers a, b, c, where 3 ≤ a + b + c ≤ 40. Output For each test case, print out the number of different necklaces that formed by a white pearls, b grey pearls and c black pearls in a single line.
2/2 Sample Input 2 321 222 Sample Output 6 11