A shuttle serves n passenger trips along one route. Trip i boards riders passengers at position board who leave at position alight, occupying the shuttle over the half-open stretch [board, alight) (a passenger leaving at position x is not aboard at x). Report the minimum seat capacity the shuttle must have so that it never runs out of seats at any point of the route.
Input format
Line 1: an integer n.
Next n lines: three integers board alight riders (with board < alight).
Output format
A single integer: the peak number of passengers aboard at once, i.e. the minimum required capacity.
Constraints
- 1 ≤ n ≤ 100000
- 0 ≤ board < alight ≤ 1000000
- 1 ≤ riders ≤ 1000000