E869120 is initially standing at the origin (0, 0) in a two-dimensional plane. He has N engines, which can be used as follows:

• When E869120 uses the i-th engine, his X- and Y-coordinate change by x_i and y_i, respectively. In other words, if E869120 uses the i-th engine from coordinates (X, Y), he will move to the coordinates (X + x_i, Y + y_i).
• E869120 can use these engines in any order, but each engine can be used at most once. He may also choose not to use some of the engines. He wants to go as far as possible from the origin. Let (X, Y) be his final coordinates. Find the maximum possible value of \sqrt{X^2 + Y^2}, the distance from the origin.

-----Constraints-----

• 1 \leq N \leq 100
• -1 \ 000 \ 000 \leq x_i \leq 1 \ 000 \ 000
• -1 \ 000 \ 000 \leq y_i \leq 1 \ 000 \ 000
• All values in input are integers.

-----Input----- Input is given from Standard Input in the following format: N x_1 y_1 x_2 y_2 : : x_N y_N

-----Output----- Print the maximum possible final distance from the origin, as a real value. Your output is considered correct when the relative or absolute error from the true answer is at most 10^{-10}.

-----Sample Input----- 3 0 10 5 -5 -5 -5

-----Sample Output----- 10.000000000000000000000000000000000000000000000000

The final distance from the origin can be 10 if we use the engines in one of the following three ways:

• Use Engine 1 to move to (0, 10).
• Use Engine 2 to move to (5, -5), and then use Engine 3 to move to (0, -10).
• Use Engine 3 to move to (-5, -5), and then use Engine 2 to move to (0, -10). The distance cannot be greater than 10, so the maximum possible distance is 10.