$^{\text{∗}}$The minimum excluded (MEX) of a collection of integers$c\_1, c\_2, \ldots, c\_k$is defined as the smallest non-negative integer$x$which does not occur in the collection$c$.

For example:

• $\operatorname{mex}([2,2,1])= 0$, since$0$does not belong to the array.
• $\operatorname{mex}([3,1,0,1]) = 2$, since$0$and$1$belong to the array, but$2$does not.
• $\operatorname{mex}([0,3,1,2]) = 4$, since$0$,$1$,$2$, and$3$belong to the array, but$4$ does not.</p>

  Input

  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

  For each test case, output the maximum possible sum of $\operatorname{mex}$ across all rows and columns.

  Note

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

  Samples

  3
  1 1
  2 2
  3 5
  

  2
  3
  6