Nearest vectors

Description:

Input:

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, x² + y² > 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).

Output:

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.

Sample Input:

4
-1 0
0 -1
1 0
1 1

Sample Output:

3 4

Sample Input:

6
-1 0
0 -1
1 0
1 1
-4 -5
-4 -6

Sample Output:

6 5