Drawing Lines

Interview

Time limit1sMemory limit256 MB

Summary

Given N segments on a number line, find the total length of their union, counting overlaps once and printing it as an integer.

Level: Medium4 of 10
Topics: Sorting, Intervals, Greedy, Array
Solved: No attempts yet

Problem

Junyong's nephew Junseop was drawing several line segments parallel to one straight line with a crayon.

Watching Junseop, Junyong became curious about the total length of the segments after projecting every line Junseop drew onto the number line.

You, who need to stay on Junyong's good side, must write a program that answers Junyong's question.

Input

The first line gives $N$ , the number of lines Junseop drew.

Lines 2 through $N+1$ give the start coordinate $X_i$ and the end coordinate $Y_i$ of each line Junseop drew, in that order. $X_i$ and $Y_i$ are integers separated by a space.

$N$ ranges from 1 to 10,000. The start and end coordinates of a line are natural numbers from 1 to 10,000.

Output

Print the total length of the lines projected onto the number line as an integer.

Hint

Sample explanation

Orange lines: the lines Junseop drew
Green lines: the lines projected onto the number line

Examples1

Example 1
Input
```
4
1 3
2 5
4 9
11 13
```
Expected output
```
10
```