B - Trapezoid Sum

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.

2
1 3
3 5

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 $1+2+3+3+4+5=18$.

3
11 13
17 47
359 44683

998244353

1
1 1000000

500000500000