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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<bits/stdc++.h>
#define INF 2147483647
#define inf 1000000007
#define SYOU(x) setprecision(x+1)
#define abs(x,y) (max(x,y)-min(x,y))
#define lol long long
#define mp make_pair
#define fi first
#define se second
using namespace std;
lol a,b;
lol i[3000];
signed main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  lol c=1,d=1,e=0,f=0,g=0,h=0;
  cin >>a;
  for(int n=0;n<a;n++) cin >>i[n];
  for(int n=0;n<a-2;n++){
      for(int m=n+1;m<a-1;m++){
	  for(int nm=m+1;nm<a;nm++){
	      if(i[n]<i[m]+i[nm]&&i[m]<i[n]+i[nm]&&i[nm]<i[n]+i[m]) e++;
	  }
      }
  }
  cout <<e<<'\n';
  return (0);
}