#描述#
You are given n closed, integer intervals [ai, bi] and n integers c1, ..., cn.

Write a program that:

reads the number of intervals, their endpoints and integers c1, ..., cn from the standard input,

computes the minimal size of a set Z of integers which has at least ci common elements with interval [ai, bi], for each i = 1, 2, ..., n,

writes the answer to the standard output.

#格式#
##输入格式##
The first line of the input contains an integer n (1 &lt= n &lt= 50 000) - the number of intervals. The following n lines describe the intervals. The i+1-th line of the input contains three integers ai, bi and ci separated by single spaces and such that 0 &lt= ai &lt= bi &lt= 50 000 and 1 &lt= ci &lt= bi - ai + 1.

Process to the end of file.

##输出格式##
The output contains exactly one integer equal to the minimal size of set Z sharing at least ci elements with interval [ai, bi], for each i = 1, 2, ..., n.

#样例1#
##样例输入1##

5
3 7 3
8 10 3
6 8 1
1 3 1
10 11 1

##样例输出1##

6

#限制#
1000ms
32768KB

#提示#

#来源#