There are three types of 2D blocks: T-shaped, H-shaped, and U-shaped. Their exact shapes are shown in the figure below: You are given three non-negative integers (c_T), (c_H), and (c_U), representing the numbers of T-shaped, H-shaped, and U-shaped blocks, respectively. Your task is to pack all ((c_T + c_H + c_U)) blocks into an (n \times 3) grid, following these rules: Every block must be placed entirely inside the grid; No two blocks may overlap (i.e., no unit cell can be covered by more than one block); Blocks can be rotated by any multiple of (90^{\circ}), but their edges must remain parallel to the grid borders. You have to find the minimum possible value of (n) for which such a packing exists. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The only line of each test case contains three integers (c_T), (c_H), and (c_U) ((0\le c_T,c_H,c_U\le 10^9), (c_T+c_H+c_U \gt 0)) — the numbers of T-shaped, H-shaped, and U-shaped blocks, respectively. For each test case, output a single integer — the minimum possible value of (n). The optimal solutions for the first three test cases are listed below: