MIT 1st Team Contest 2007

There are N horizontal line segments in the plane. The ith segment has some height h_i (which may be negative) and runs from x = a_i to x = b_i (a_i < b_i). Segments do not contain their endpoints. You must draw a set of vertical lines (note lines and not line segments) so that every given horizontal segment is intersected at least once and at most R times by vertical lines in such a way that R is minimized.

Input

The first line of the input is N (1 ≤ N ≤ 400), the number of horizontal line segments. N lines then follow, where the ith line is "a_i b_i h_i". Each of a_i,b_i,h_i are 32-bit signed integers. Horizontal segments may overlap.

Output

Your output should consist of a single integer, the smallest value of R that is achievable, followed by a newline.

Example

Input:
3
0 1 5
0 2 -2
1 2 7

Output:
2