﻿ ABC181 B - Trapezoid Sum - Atcoder

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Score : $200$ points

### Problem Statement

We have a blackboard with nothing written on it. Takahashi will do $N$ operations to write integers on it.

In the $i$-th operation, he will write each integer from $A_i$ through $B_i$ once, for a total of $B_i - A_i + 1$ integers.

Find the sum of the integers written on the blackboard after the $N$ operations.

### Constraints

• All values in input are integers.
• $1 \leq N \leq 10^5$
• $1 \leq A_i \leq B_i \leq 10^6$

### Input

Input is given from Standard Input in the following format:

$N$
$A_1$ $B_1$
$\vdots$
$A_N$ $B_N$


### Output

Print the sum of the integers written on the blackboard after the $N$ operations.

### Sample Input 1

2
1 3
3 5


### Sample Output 1

18


In the $1$-st operation, he will write $1$, $2$, and $3$ on the blackboard.

In the $2$-nd operation, he will write $3$, $4$, and $5$ on the blackboard.

The sum of the integers written is $1+2+3+3+4+5=18$.

### Sample Input 2

3
11 13
17 47
359 44683


### Sample Output 2

998244353


### Sample Input 3

1
1 1000000


### Sample Output 3

500000500000