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>
#include <iostream>
#include <cmath>
#include <algorithm>
#include <utility>
#include <numeric>
#define REP(i, n) for(int i=0;i<int(n);++i)
using namespace std;
template<class A>void pr(A a){cout << (a) << endl;}
template<class A,class B>void pr(A a,B b){cout << a << " "  ;pr(b);}
template<class A,class B,class C>void pr(A a,B b,C c){cout << a << " " ;pr(b,c);}
template<class A,class B,class C,class D>void pr(A a,B b,C c,D d){cout << a << " " ;pr(b,c,d);}

int main(void) {
  int N;
  int L[2010];
  cin >> N;
  REP(i,N) cin >> L[i];
  long long ans=0;
  REP(i,N) {
    for(int j=i+1;j<N;++j) {
      for(int k=j+1;k<N;++k) {
        // if (L[i]<L[j]+L[k]&&
        //     L[j]<L[i]+L[k]&&
        //     L[k]<L[i]+L[j]) {
          ans++;
        // }
      }
    }
  }
  pr(ans);
  return 0;
}