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;
#define REP(i,a,n) for(int i=(a); i<(int)(n); i++)
#define rep(i,n) REP(i,0,n)
#define FOR(it,c) for(__typeof((c).begin()) it=(c).begin(); it!=(c).end(); ++it)
#define ALLOF(c) (c).begin(), (c).end()
typedef long long ll;
typedef unsigned long long ull;


int main(){
  int N;
  cin >> N;
  vector<int> v;
  rep(i,N){
    int a;
    cin >> a;
    v.push_back(a);
  }
  sort(ALLOF(v));

  ll ret = 0;
  rep(i,N){
    REP(j,i+1,N){
      int b = v[i];
      int a = v[j];

      // a-b < c < a+b
      // => a-b < a < c < a+b
      auto high = lower_bound(ALLOF(v), a+b);
      int dist = high - v.begin();
      //cout << b << " " << a << " " << dist << " " << dist-1-j << endl;
      ret += dist-1 - j;
    }
  }

  cout << ret << endl;
  
  return 0;
}