Nearest points

Limits: 2 sec., 256 MiB

This statement was translated automatically from Ukrainian.

There are \(n\) points on the plane numbered from \(1\) to \(n\) with coordinates \((x_i, y_i)\).

The distance between points with indices \(i\) and \(j\) is defined as \(dist(i, j) = min(|x_i-x_j|, |y_i-y_j|)\).

Find a pair of points with the smallest possible distance.

Input

The first line contains \(n\) — the number of points on the plane. The next \(n\) lines each contain 2 integers \(x_i\) and \(y_i\) — the coordinates of the \(i\)-th point.

Output

In a single line, print two integers separated by a space \(i\) and \(j\) — the indices of the points with the minimum distance.

If there is more than one such pair of points, find the pair that minimizes \(i + j\).

If there are still multiple such pairs, find the pair with the minimum \(i\).

Constraints

\(2 \le n \le 100000\),

\(-10^9 \le x_i, y_i \le 10^9\).

Samples