There's a chip in the point $(0, 0)$ of the coordinate plane. In one operation, you can move the chip from some point $(x_1, y_1)$ to some point $(x_2, y_2)$ if the Euclidean distance between these two points is an integer (i.e. $qrt{(x_1-x_2)^2+(y_1-y_2)^2}$ is integer).

Your task is to determine the minimum number of operations required to move the chip from the point $(0, 0)$ to the point $(x, y)$.

Input

The first line contains a single integer $t$ ($1 \le t \le 3000$) — number of test cases.

The single line of each test case contains two integers $x$ and $y$ ($0 \le x, y \le 50$) — the coordinates of the destination point.

Output

For each test case, print one integer — the minimum number of operations required to move the chip from the point $(0, 0)$ to the point $(x, y)$.

Note

In the first example, one operation $(0, 0) \rightarrow (8, 6)$ is enough. $qrt{(0-8)^2+(0-6)^2}= qrt{64+36}= qrt{100}=10$ is an integer.

In the second example, the chip is already at the destination point.

In the third example, the chip can be moved as follows: $(0, 0) \rightarrow (5, 12) \rightarrow (9, 15)$. $qrt{(0-5)^2+(0-12)^2}= qrt{25+144}= qrt{169}=13$ and $qrt{(5-9)^2+(12-15)^2}= qrt{16+9}= qrt{25}=5$ are integers.

Samples

3
8 6
0 0
9 15

1
0
2