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>
#pragma GCC optimize("unroll-loops,no-stack-protector")
#pragma GCC target("sse,sse2,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#define watch(x) cout << (#x) << " is " << (x) << endl

using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;

const int MOD = 1e9 + 7;

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int cnt = 0;
    int n;
    cin >> n;
    vector<int> l(n);
    for(int i = 0; i < n; i++) cin >> l[i];
    sort(l.begin(), l.end());
    for(int i = 0; i < n - 2; i++)
    {
        int k = i + 2;
        for(int j = i + 1; j < n; j++)
        {
            while(k < n && l[i] + l[j] > l[k]) k++;
            if(k > j) cnt += k - j - 1;
        }
    }
    cout << cnt;

    return 0;
}