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: Time Limit Exceeded)

#include <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;

int main(){
    int N; cin >> N;
    vector<int> L(N);
    vector<vector<int>> plus(N, vector<int>(N));
    vector<vector<int>> minus(N, vector<int>(N));
    ll ans =0;

    rep(i,N){
        cin >> L[i];
    }

    sort(L.begin(), L.end());

    rep(i,N-2){
        for(int j=i+1;j <N-1; j++){
            plus[i][j] = L[i]+L[j];

            rep(k,N){

                if(L[k] > L[i] && L[k] > L[j]){

                    if(L[k] < plus[i][j]){
                        ans++;
                    }
                }

            }
        }
    }

    cout << ans << endl;
}