A city block contains n buildings. Building i is a rectangle standing on the ground: it spans horizontally from left to right (left < right) and has height height. Looking at the block from far away, the buildings form a silhouette (the skyline). A key point is a position where the silhouette's height changes as you scan from left to right; the standard skyline is the minimal list of such points, and it always ends with the point where the silhouette drops back to height 0 on the far right. Report the number of key points in this minimal skyline.

Input format

Line 1: an integer n. Next n lines: three integers left, right, height describing one building.

Output format

A single integer: the number of key points in the skyline.

Constraints

• 1 ≤ n ≤ 100000
• 0 ≤ left < right ≤ 1000000000
• 1 ≤ height ≤ 1000000000

1
2 9 10

2

2
1 5 3
2 7 4

3