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;
typedef long long ll;
typedef pair<ll, ll> l_l;
typedef pair<int, int> P;
#define rep(i,n) for(int i=0;i<n;++i)


int main(){
  int n;
  cin>>n;
  vector<int>l(n);
  rep(i,n){cin>>l[i];}
  sort(l.begin(),l.end());
  int ans=0;
  for(int i=0;i<n-2;i++){
    for(int j=i+1;j<n-1;j++){
      int k=l[i]+l[j];
      int id=lower_bound(l.begin(),l.end(),k)-l.begin();
    //  cout<<id<<' '<<i<<'i'<<j<<'j'<<endl;
      ans+=max(0,id-j-1);
    }
  }
  cout<<ans;
  }