A14732 | Anti Light's Cell Guessing

You are playing a game on a $n \times m$ grid, in which the computer has selected some cell $(x, y)$ of the grid, and you have to determine which one.

To do so, you will choose some $k$ and some $k$ cells $(x_1, y_1),\, (x_2, y_2), \ldots, (x_k, y_k)$ , and give them to the computer. In response, you will get $k$ numbers $b_1,\, b_2, \ldots b_k$ , where $b_i$ is the manhattan distance from $(x_i, y_i)$ to the hidden cell $(x, y)$ (so you know which distance corresponds to which of $k$ input cells).

After receiving these $b_1,\, b_2, \ldots, b_k$ , you have to be able to determine the hidden cell. What is the smallest $k$ for which is it possible to always guess the hidden cell correctly, no matter what cell computer chooses?

As a reminder, the manhattan distance between cells $(a_1, b_1)$ and $(a_2, b_2)$ is equal to $|a_1-a_2|+|b_1-b_2|$ .

The first line of the input contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. The description of test cases follows.

The single line of each test case contains two integers $n$ and $m$ ( $1 \le n, m \le 10^9$ ) — the number of rows and the number of columns in the grid.

For each test case print a single integer — the minimum $k$ for that test case.