B"Find the minimum height of a rooted tree ^{ dagger} with a+b+c vertices that satisfies the following conditions: The tree above is rooted at the top vertex, and each vertex is labeled with the number of children it has. Here a=2 , b=1 , c=3 , and the height is 2 . ^{ dagger} A rooted tree is a connected graph without cycles, with a special vertex called the root. In a rooted tree, among any two vertices connected by an edge, one vertex is a parent (the one closer to the root), and the other one is a child. The distance between two vertices in a tree is the number of edges in the shortest path between them. The height of a rooted tree is the maximum distance from a vertex to the root. The first line contains an integer t ( 1 <= q t <= q 10^4 ) -- the number of test cases. The only line of each test case contains three integers a , b , and c ( 0 <= q a, b, c <= q 10^5 ; 1 <= q a + b + c ). The sum of a + b + c over all test cases does not exceed 3 cdot 10^5 . For each test case, if no such tree exists, output -1 . Otherwise, output one integer -- the minimum height of a tree satisfying the conditions in the statement. The first test case is pictured in the statement. It can be proven that you can't get a height smaller than 2 . In the second test case, you can form a tree with a single vertex and no edges. It has height 0 , which is clearly optimal. In the third test case, you can form a tree with two vertices joined by a single edge. It has height 1 , which is clearly optimal. "...