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)

#define _LIBCPP_DEBUG 0
#include<bits/stdc++.h>
using namespace std;
typedef long long int ll;
ll MOD = 1e9+7;

int main(void) {

    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-2; ++i) {
        for (int j = i+1; j < N-1; ++j) {
            int syu = L[i]+L[j];
            auto it = upper_bound(L.begin()+j+1, L.end(), syu-1);
            int kyori =  distance(L.begin()+j+1, it);
            ans += kyori;
        }
    }

    cout<<ans<<endl;

    return 0;
}