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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;

int main(){
    int n;
    cin>>n;
    vector<int> l(n);
    for(int i=0;i<n;i++){
        cin>>l[i];
    }
    sort(l.begin(),l.end());
    int ans=0;
    for(int i=0;i<n;i++){
        for(int j=i+1;j<n;j++){
            int a=lower_bound(l.begin(),l.end(),l[i]+l[j])-l.begin();
            int b=j+1;
            ans+=a-b;
        }
    }
    cout<<ans<<endl;
}