A. Integer Moves
brute force; math
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. \(\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\) 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 \((x, y)\).
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.
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 \((x, y)\).
In the first example, one operation \((0, 0) \rightarrow (8, 6)\) is enough. \(\sqrt{(0-8)^2+(0-6)^2}=\sqrt{64+36}=\sqrt{100}=10\) 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: \((0, 0) \rightarrow (5, 12) \rightarrow (9, 15)\). \(\sqrt{(0-5)^2+(0-12)^2}=\sqrt{25+144}=\sqrt{169}=13\) and \(\sqrt{(5-9)^2+(12-15)^2}=\sqrt{16+9}=\sqrt{25}=5\) are integers.