Robot Program
Description
There is an infinite 2-dimensional grid. The robot stands in cell $(0, 0)$ and wants to reach cell $(x, y)$. Here is a list of possible commands the robot can execute:
- move north from cell $(i, j)$ to $(i, j + 1)$;
- move east from cell $(i, j)$ to $(i + 1, j)$;
- move south from cell $(i, j)$ to $(i, j - 1)$;
- move west from cell $(i, j)$ to $(i - 1, j)$;
- stay in cell $(i, j)$.
The robot wants to reach cell $(x, y)$ in as few commands as possible. However, he can't execute the same command two or more times in a row.
What is the minimum number of commands required to reach $(x, y)$ from $(0, 0)$?
The first line contains a single integer $t$ ($1 \le t \le 100$) — the number of testcases.
Each of the next $t$ lines contains two integers $x$ and $y$ ($0 \le x, y \le 10^4$) — the destination coordinates of the robot.
For each testcase print a single integer — the minimum number of commands required for the robot to reach $(x, y)$ from $(0, 0)$ if no command is allowed to be executed two or more times in a row.
Input
The first line contains a single integer $t$ ($1 \le t \le 100$) — the number of testcases.
Each of the next $t$ lines contains two integers $x$ and $y$ ($0 \le x, y \le 10^4$) — the destination coordinates of the robot.
Output
For each testcase print a single integer — the minimum number of commands required for the robot to reach $(x, y)$ from $(0, 0)$ if no command is allowed to be executed two or more times in a row.
Samples
5
5 5
3 4
7 1
0 0
2 0
10
7
13
0
3
Note
The explanations for the example test:
We use characters N, E, S, W and 0 to denote going north, going east, going south, going west and staying in the current cell, respectively.
In the first test case, the robot can use the following sequence: NENENENENE.
In the second test case, the robot can use the following sequence: NENENEN.
In the third test case, the robot can use the following sequence: ESENENE0ENESE.
In the fourth test case, the robot doesn't need to go anywhere at all.
In the fifth test case, the robot can use the following sequence: E0E.