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.

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.

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.

Sample Input 1

3
1 3
2 4
5 6

Sample Output 1

4

If we let x_1=3,x_2=4,x_3=5, we get the dissatisfaction level of 4. We cannot make it 3 or less, so the answer is 4.

Sample Input 2

3
1 1
1 1
1 1

Sample Output 2

0

Sample Input 3

6
1 5
2 4
1 1
4 4
3 6
3 3

Sample Output 3

15

见题面 Input 部分

见题面 Output 部分