Intervals

Time Limit: 10 Seconds
Memory Limit: 32768 KB

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.

**Input**

The first line of the input contains an integer n (1 <= n <= 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 <= ai <= bi <= 50 000 and 1 <= ci <= bi
- ai + 1.

Process to the end of file.

**Output**

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.

**Sample Input**

5

3 7 3

8 10 3

6 8 1

1 3 1

10 11 1

**Sample Output**

6

Source:

**Southwestern Europe 2002**
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