Overlapping Segments

There are N line segments on a one-dimensional coordinate line. Find the maximum number of segments that overlap at the same point.

If two segments meet only at an endpoint, that contact is not counted as an overlap.

The first line contains the number of segments N. (1 ≤ N ≤ 1,000,000)

Each of the next N lines contains two integers s and e, the start and end coordinates of a segment. It is always true that s < e. Every coordinate is an integer whose absolute value is at most 1,000,000,000.

Print the maximum number of segments that overlap.