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;
using ll = long long;

template <class T> ostream &operator<<(ostream &os, vector<T> &v) {
  for (auto i = v.begin(); i != v.end(); i++) {
    os << *i << " ";
  }
  return os;
}


void solve(long long N, std::vector<long long> L){
  ll ans=0;
  sort(L.begin(), L.end());
  for(int i=0; i<N-2; i++) {
    for(int j=i+1; j<N-1; j++) {
      // std::cout << L[i]<<", "<<L[j] << std::endl;
      // std::cout << "c num: " << lower_bound(L.begin(), L.end(), L[i]+L[j])-L.begin() << std::endl;
      // std::cout << (lower_bound(L.begin(), L.end(), L[i]+L[j])-(L.begin()+j+1)) << std::endl;
      ans+= max(0, (int)(lower_bound(L.begin(), L.end(), L[i]+L[j])-(L.begin()+j+1)));
    }
  }
  std::cout << ans << std::endl;
}

int main(){
  long long N;
  scanf("%lld",&N);
  std::vector<long long> L(N);
  for(int i = 0 ; i < N ; i++){
    scanf("%lld",&L[i]);
  }
  solve(N, std::move(L));
  return 0;
}