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 <vector>
#include <algorithm>
using namespace std;
#define LL long long

void _143() {
    int n;
    cin >> n;

    vector<int> L;
    int tmp;
    for (int i = 0; i < n; ++i) {
        cin >> tmp;
        L.push_back(tmp);
    }
    sort(L.begin(), L.end());

    LL count = 0;
    for (int i = 0; i < n - 2; ++i) {
        for (int j = i + 1; j < n - 1; ++j) {
            for (int k = j + 1; k < n; ++k) {
                if (L[i] + L[j] <= L[k]) {
                    break;
                } 
                count++;
            }
        }
    }

    cout << count << endl;
}

int main()
{
    _143();
    return 0;
}