A. Morning Sandwich
implementation; math
Monocarp always starts his morning with a good ol' sandwich. Sandwiches Monocarp makes always consist of bread, cheese and/or ham.A sandwich always follows the formula: a piece of bread a slice of cheese or ham a piece of bread \(\dots\) a slice of cheese or ham a piece of bread So it always has bread on top and at the bottom, and it alternates between bread and filling, where filling is a slice of either cheese or ham. Each piece of bread and each slice of cheese or ham is called a layer.Today Monocarp woke up and discovered that he has \(b\) pieces of bread, \(c\) slices of cheese and \(h\) slices of ham. What is the maximum number of layers his morning sandwich can have?
The first line contains a single integer \(t\) (\(1 \le t \le 1000\)) — the number of testcases.Each testcase consists of three integers \(b, c\) and \(h\) (\(2 \le b \le 100\); \(1 \le c, h \le 100\)) — the number of pieces of bread, slices of cheese and slices of ham, respectively.
For each testcase, print a single integer — the maximum number of layers Monocarp's morning sandwich can have.
In the first testcase, Monocarp can arrange a sandwich with three layers: either a piece of bread, a slice of cheese and another piece of bread, or a piece of bread, a slice of ham and another piece of bread.In the second testcase, Monocarp has a lot of bread, but not too much filling. He can arrange a sandwich with four pieces of bread, one slice of cheese and two slices of ham.In the third testcase, it's the opposite — Monocarp has a lot of filling, but not too much bread. He can arrange a sandwich with three pieces of bread and two slices of cheese, for example.