CF995C.Leaving the Bar

For 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.

对于向量 $\vec{v} = (x, y)$，定义其模长为 $|v| = \sqrt{x^2 + y^2}$。

Allen 在位于原点的酒吧喝得有点多。现有 $n$ 个向量 $\vec{v_1}, \vec{v_2}, \cdots, \vec{v_n}$。Allen 将进行 $n$ 次移动。由于他的方向感受损，在第 $i$ 次移动时，他将沿 $\vec{v_i}$ 或 $-\vec{v_i}$ 方向移动。换言之，若他当前的位置为 $p = (x, y)$，则他将移动至 $p + \vec{v_i}$ 或 $p - \vec{v_i}$。

Allen 不希望离家（恰好也在酒吧处）太远。你需要帮他确定一个移动序列（即为各向量选定正负号），使得其最终位置 $p$ 满足 $|p| \le 1.5 \cdot 10^6$，从而保证安全。

The 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 $i$.

第一行包含一个整数 $n$（$1 \le n \le 10^5$）—— 表示移动次数。

接下来的每一行包含两个以空格分隔的整数 $x_i$ 和 $y_i$，表示向量 $\vec{v_i} = (x_i, y_i)$。对所有 $i$，满足 $|v_i| \le 10^6$。

Output 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.

输出一行，包含 $n$ 个整数 $c_1, c_2, \cdots, c_n$，每个数为 $1$ 或 $-1$。若向量 $p = \sum_{i = 1}^n c_i \vec{v_i}$ 的模长满足 $|p| \le 1.5 \cdot 10^6$，则你的解是正确的。

可以证明：在给定约束条件下，解总是存在的。