Points
Description
You are given N points on a plane. Write a program which will find the sum of squares of distances between all pairs of points.
The first line of input contains one integer number N (1 ≤ N ≤ 100 000) — the number of points. Each of the following N lines contain two integer numbers X and Y ( - 10 000 ≤ X, Y ≤ 10 000) — the coordinates of points. Two or more points may coincide.
The only line of output should contain the required sum of squares of distances between all pairs of points.
Input
The first line of input contains one integer number N (1 ≤ N ≤ 100 000) — the number of points. Each of the following N lines contain two integer numbers X and Y ( - 10 000 ≤ X, Y ≤ 10 000) — the coordinates of points. Two or more points may coincide.
Output
The only line of output should contain the required sum of squares of distances between all pairs of points.
Samples
4
1 1
-1 -1
1 -1
-1 1
32