CF598C.Nearest vectors

You are given the set of vectors on the plane, each of them starting at the origin. Your task is to find a pair of vectors with the minimal non-oriented angle between them.

Non-oriented angle is non-negative value, minimal between clockwise and counterclockwise direction angles. Non-oriented angle is always between 0 and π. For example, opposite directions vectors have angle equals to π.

给你平面上的一组向量，每个向量均以原点为起点。你的任务是找出夹角（无向角）最小的一对向量。

无向角是一个非负值，定义为顺时针与逆时针两个方向所成角度中的较小者。无向角的取值范围恒为 $[0, \pi]$。例如，方向相反的两个向量之间的无向角等于 $\pi$。

First line of the input contains a single integer n (2 ≤ n ≤ 100 000) — the number of vectors.

The i-th of the following n lines contains two integers x__i and y__i (|x|, |y| ≤ 10 000, _x_2 + _y_2 > 0) — the coordinates of the i-th vector. Vectors are numbered from 1 to n in order of appearing in the input. It is guaranteed that no two vectors in the input share the same direction (but they still can have opposite directions).

输入的第一行包含一个整数 $n$（$2 \leq n \leq 100\,000$）—— 向量的个数。

接下来的 $n$ 行中，第 $i$ 行包含两个整数 $x_i$ 和 $y_i$（$|x|, |y| \leq 10\,000$，且 $x^2 + y^2 > 0$）—— 第 $i$ 个向量的坐标。向量按输入顺序编号为 $1$ 至 $n$。保证输入中任意两个向量的方向均不相同（但它们仍可能互为反向）。

Print two integer numbers a and b (a ≠ b) — a pair of indices of vectors with the minimal non-oriented angle. You can print the numbers in any order. If there are many possible answers, print any.

输出两个整数 $a$ 和 $b$（$a \neq b$）—— 即夹角（无向角）最小的一对向量的下标。你可以以任意顺序输出这两个数。若存在多个可能的答案，输出任意一个即可。