C. Leaving the Bartime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputFor a vector \vec{v} = (x, y), define |v| = \sqrt{x^2 + y^2}.Allen had a bit too much to drink at the bar, which is at the origin. There are n vectors \vec{v_1}, \vec{v_2}, \cdots, \vec{v_n}. Allen will make n moves. As Allen's sense of direction is impaired, during the i-th move he will either move in the direction \vec{v_i} or -\vec{v_i}. In other words, if his position is currently p = (x, y), he will either move to p + \vec{v_i} or p - \vec{v_i}.Allen doesn't want to wander too far from home (which happens to also be the bar). You need to help him figure out a sequence of moves (a sequence of signs for the vectors) such that his final position p satisfies |p| \le 1.5 \cdot 10^6 so that he can stay safe.InputThe first line contains a single integer n (1 \le n \le 10^5) — the number of moves.Each of the following lines contains two space-separated integers x_i and y_i, meaning that \vec{v_i} = (x_i, y_i). We have that |v_i| \le 10^6 for all i.OutputOutput a single line containing n integers c_1, c_2, \cdots, c_n, each of which is either 1 or -1. Your solution is correct if the value of p = \sum_{i = 1}^n c_i \vec{v_i}, satisfies |p| \le 1.5 \cdot 10^6.It can be shown that a solution always exists under the given constraints.ExamplesInput3999999 00 999999999999 0Output1 1 -1 Input1-824590 246031Output1 Input8-67761 603277640586 -39667146147 -122580569609 -2112400 914208131792 309779-850150 -4862935272 721899Output1 1 1 1 1 1 1 -1 
Input3999999 00 999999999999 0
Output1 1 -1 
['brute force', 'data structures', 'geometry', 'greedy', 'math', 'sortings', '*2300']