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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;

int N;
//array<int, 2000> L;
int L[2000];

signed main() {
  cin >> N;
  for(int i=0; i<N; i++) cin >> L[i];
  //sort(L.begin(), L.begin()+N);
  sort(L, L+N);

  int ans = 0;
  for(int i=0; i<N; i++) for(int j=i+1; j<N; j++) {
    int a = L[i], b=L[j];
    auto l = upper_bound(L, L+N, abs(a-b));
    auto r = lower_bound(L, L+N, a+b);
    if(distance(l,r)) {
      ans += distance(l,r);
      if( *l <= a && a <= *(r-1)) ans--;
      if( *l <= b && b <= *(r-1)) ans--;
    }
  }
  cout << ans / 3 << endl;
}