Problem Statement

$N$ people, numbered $1,2,\ldots ,N$, are going to stand on the number line. Let's denote by $x_i$ the coordinate the Person $i$ stands at. Then, $x_i$ should be an integer satisfying $L_i \leq x_i \leq R_i$. Multiple people can occupy the same coordinate.

We define the dissatisfaction level as the following formula:

$\displaystyle\sum_{i=1}^{N-1}\sum_{j=i+1}^{N}|x_j-x_i|$

Find the minimum possible value of the dissatisfaction level.

Constraints

• $2 \leq N \leq 3 \times 10^5$
• $1 \leq L_i \leq R_i \leq 10^7 \,(1 \leq i \leq N)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
L_1 R_1
L_2 R_2
\vdots
L_N R_N

Output

Print the answer.