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: Accepted)

#include<stdio.h>
int c[2002];
int merge(int *L,int a,int b){
  if(a!=b){
    merge(L,a,(a+b)/2);
    merge(L,(a+b)/2+1,b);
    int i=a,j=(a+b)/2+1,num=a;
    while(i<(a+b)/2+1 && j<=b){
      if(L[i]>L[j]){
        c[num]=L[j];
        j++;
      }
      else{
        c[num]=L[i];
        i++;
      }
      num++;
    }
    while(i<(a+b)/2+1){
      c[num]=L[i];
      i++;
      num++;
    }
    while(j<=b){
      c[num]=L[j];
      j++;
      num++;
    }
    for(i=a;i<=b;i++)
        L[i]=c[i];
  }
}

int main(){
  int n,i,j,k,count=0;
  scanf("%d",&n);
  int L[n+1];
  for(i=0;i<n;i++)
    scanf("%d",&L[i]);
  merge(L,0,n-1);
  for(i=0;i<n-2;i++){
    for(j=i+1;j<n-1;j++){
      k=j+1;
      while(L[i]+L[j]>L[k] && k<n){
        count++;
        k++;
      }
    }
  }
  printf("%d\n",count);
  return 0;
}