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<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<string>
using namespace std;
typedef long long ll;
vector<ll> node;
int main(){
  int n;
  cin>>n;
  for(int i=0;i<n;i++){
    ll lk;
    cin>>lk;
    node.push_back(lk);
  }
  sort(node.begin(),node.end());
  ll ans=0;
  for(int i=0;i<n-2;i++){
    for(int j=i+1;j<n-1;j++){
      int left=j;
      int right=lower_bound(node.begin(),node.end(),node[i]+node[j])-node.begin();
      ans+=max(right-left-1,0);
      //if(right>left) cout<<i<<" "<<j<<" "<<left<<" "<<right<<endl;
    }
  }
  cout<<ans<<endl;
}