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>

using namespace std;

int main(){
 
int n; cin >> n;

vector<int> l(n);

for (int i = 0; i < n; i++)
{
    cin >> l[i];
}

sort(l.begin(),l.end());

int min,max,lf,ri,mid,lans,hans,cnt=0;
for (int i = 0; i < n-1; ++i)
{
   for (int j = i+1; j < n; ++j)
   {  
       
       lf=j;ri=n;
       max = l[i]+l[j];
      
       while(lf+1<ri){
        mid = (lf+ri)/2;
        if (l[mid]<max) {lf=mid;}
        else ri=mid;      
       }
       hans = lf;
       cnt+=hans-j;
       
   }
}

cout << cnt;
return 0;
}