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: Accepted)

#include <bits/stdc++.h>
#define ll long long

using namespace std;

int main()
{
    ll n;
    cin>>n;
    ll a[n];
    ll i,j,k,c=0;
    for(i=0;i<n;i++)
      cin>>a[i];
    sort(a,a+n);
   // map<pair<ll,ll>,ll>m;
    for(i=0;i<n-2;i++)
    {
       for(j=i+1;j<n-1;j++)
       {
          for(k=j+1;k<n;k++)
          {

             if(a[k]>(a[i]+a[j]))
               break;
             else if(a[i]<(a[j]+a[k])&&a[j]<(a[i]+a[k])&&a[k]<(a[i]+a[j]))
             {
                 c++;
             }
          }
       }
    }
    cout<<c;
    return 0;
}