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>
#define watch(x) cout << (#x) << " is " << (x) << endl
typedef long long ll;
using namespace std;
int static fast = [](){
  ios::sync_with_stdio(false);
  cin.tie(0); cout.tie(0); return 0;
}();

int main() {
    int n;
    cin >> n;
    vector<int> arr(n, 0);
    for(auto& val: arr)
        cin >> val;
    sort(arr.begin(), arr.end());
    int ans = 0;
    for(int i = 0; i < n; i++) {
        for(int j = i+1; j < n; j++) {
            auto it = lower_bound(arr.begin()+j+1, arr.end(), arr[i]+arr[j]);
            int idx = prev(it) - arr.begin();
            ans += max(idx-j, 0);
        }
    }
    cout << ans << endl;
    return 0;
}