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: Time Limit Exceeded)

#include <iostream>
#include <vector>
#include <algorithm>
#define rep(i,n) for(int i = 0; i < (n); i++)
#define rrep(i,n) for(int i = 1; i <= (n); i++)
using ll = long long;

using namespace std;



int main() {
    int n;
    cin >> n;
    vector<int> l(n);
    rep(i,n) cin >> l[i];
    sort(l.begin(), l.end());
    int ans = 0;
    rep(i,n) {
        for(int j = i+1; j < n; j++) {
            for(int k = j+1; k < n; k++) {
                if(l[i]<l[j]+l[k] && l[j]<l[k]+l[i] && l[k]<l[i]+l[j]) ans++;
                if(l[k] >= l[i]+l[j]) break;
            }
        }
    }
    cout << ans << endl;

    return 0;
}