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 fi first
#define se second
#define all(x) x.begin(), x.end()
using namespace std;
using ull = unsigned long long;
using ll = long long;
constexpr int I_INF = INT_MAX;
constexpr ll L_INF = LLONG_MAX;

struct __INIT {
    __INIT() {
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
    }
} __init;

int main() {
    int N;
    cin >> N;
    vector<int> L(N);
    for(int i = 0; i < N; i++) cin >> L[i];
    sort(all(L));
    ll sum = 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]) sum++;
                else break;
            }
        }
    }
    cout << sum << endl;
}