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?

Input

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.

Output

For each testcase, print a single integer — the maximum number of layers Monocarp's morning sandwich can have.

Note

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.

Samples

3
2 1 1
10 1 2
3 7 8

3
7
5