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.

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