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A. Robot Program

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere 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 $$$(0, 0)$$$?

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.

Example

Input

5 5 5 3 4 7 1 0 0 2 0

Output

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.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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