Problem:
Score : 400 points

Problem Statement

Takahashi has N sticks that are distinguishable from each other. The length of the i-th stick is L_i.

He is going to form a triangle using three of these sticks. Let a, b, and c be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:

a < b + c

b < c + a

c < a + b

How many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.

Constraints

All values in input are integers.

3 \leq N \leq 2 \times 10^3

1 \leq L_i \leq 10^3

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Constraints

Print the number of different triangles that can be formed.

Sample Input 1

4
3 4 2 1

Sample Output 1

1

Only one triangle can be formed: the triangle formed by the first, second, and third sticks.

Sample Input 2

3
1 1000 1

Sample Output 2

0

No triangles can be formed.

Sample Input 3

7
218 786 704 233 645 728 389

Sample Output 3

23

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
int main()
{
    int x,y,z,n,i,j,count=0,k;
    scanf ("%d",&n);
    int a[n];
    for (i=0;i<n;i++)
{
    scanf ("%d",&a[i]);
}
for (i=0;i<n-2;i++)
 {
for (j=i+1;j<n-1;j++)
{
 x=a[i];y=a[j];z=a[j+1];
 if ((x<y+z)&&(y<x+z)&&(z<y+x))
 {
     count++;
 }
}
for (j=i+2;j<n-2;j=j+1)
{
 x=a[i];y=a[j];z=a[j+2];
 if ((x<y+z)&&(y<x+z)&&(z<y+x))
 {
     count++;
 }
}
for (j=i+3;j<n-3;j=j+1)
{
 x=a[i];y=a[j];z=a[j+3];
 if ((x<y+z)&&(y<x+z)&&(z<y+x))
 {
     count++;
 }
}


}
printf ("%d",count);
}