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 <bits/stdc++.h>
using namespace std;
int main()
{
    int n;
    cin >> n;
    vector <int> a(n);
    for (int i = 0; i < n; ++i)
        cin >> a[i];
    sort(a.begin(), a.end());
    long long ans = 0;
    for (int i = 0; i < n; ++i)
        for (int j = i + 1; j < n; ++j)
        {
            int l = upper_bound(a.begin(), a.end(), a[j] - a[i]) - a.begin();
            int r = lower_bound(a.begin(), a.end(), a[j] + a[i]) - a.begin() - 1;
            ans += max(0, r - l + 1 - (l <= i && i <= r) - (l <= j && j <= r));
        }
    cout << ans / 3;
}