One day, the schoolboy Mark misbehaved, so the teacher Sasha called him to the whiteboard.

Sasha gave Mark a table with $$$n$$$ rows and $$$m$$$ columns. His task is to arrange the numbers $$$0, 1, \ldots, n \cdot m - 1$$$ in the table (each number must be used exactly once) in such a way as to maximize the sum of MEX$$$^{\text{∗}}$$$ across all rows and columns. More formally, he needs to maximize $$$$$$\sum\limits_{i = 1}^{n} \operatorname{mex}(\{a_{i,1}, a_{i,2}, \ldots, a_{i,m}\}) + \sum\limits_{j = 1}^{m} \operatorname{mex}(\{a_{1,j}, a_{2,j}, \ldots, a_{n,j}\}),$$$$$$ where $$$a_{i,j}$$$ is the number in the $$$i$$$-th row and $$$j$$$-th column.

Sasha is not interested in how Mark arranges the numbers, so he only asks him to state one number — the maximum sum of MEX across all rows and columns that can be achieved.

Input format:
Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 10^9$$$) — the number of rows and columns in the table, respectively.
Output format:
For each test case, output the maximum possible sum of $$$\operatorname{mex}$$$ across all rows and columns.
Example Input 0:
3
1 1
2 2
3 5

Example Output 0:
2
3
6

Notes:
In the first test case, the only element is $$$0$$$, and the sum of the $$$\operatorname{mex}$$$ of the numbers in the first row and the $$$\operatorname{mex}$$$ of the numbers in the first column is $$$\operatorname{mex}(\{0\}) + \operatorname{mex}(\{0\}) = 1 + 1 = 2$$$.

In the second test case, the optimal table may look as follows:

$$$3$$$$$$0$$$$$$2$$$$$$1$$$

Then $$$\sum\limits_{i = 1}^{n} \operatorname{mex}(\{a_{i,1}, a_{i,2}, \ldots, a_{i,m}\}) + \sum\limits_{j = 1}^{m} \operatorname{mex}(\{a_{1,j}, a_{2,j}, \ldots, a_{n,j}\}) = \operatorname{mex}(\{3, 0\}) + \operatorname{mex}(\{2, 1\})$$$ $$$+ \operatorname{mex}(\{3, 2\}) + \operatorname{mex}(\{0, 1\}) = 1 + 0 + 0 + 2 = 3$$$.

Example input:
3
1 1
2 2
3 5


Example output:
2
3
6