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: Time Limit Exceeded)

#include <bits/stdc++.h>
#include <stdio.h>

#define ll long long
#define int ll
#define pii pair<int, int>
#define pb push_back
#define INF 1e18
#define REP(i, n) for (int i=0; i<n; i++)
#define FOR(i, a, b) for (int i=a; i<b; i++)
#define REPD(i, n) for (int i=n-1; i>=0; i--)
#define FORD(i, a, b) for (int i=a; i>=b; i--)
#define vi vector<int>
#define all(v) v.begin(), v.end()
#define print(x) cout << x << endl
#define debug(x) cout << #x << " = "<< x << endl

const double PI=3.141592653589793238462643383279502884197169399375105820974944;

using namespace std;

void solve() {
    int N;
    cin >> N;

    vector<int> L(N);
    REP(i, N) cin >> L[i];

    sort(L.begin(), L.end());

    int ok = 0;
    REP(i, N) {
        REP(j, N) {
            if (i >= j) continue; 
            REP(k, N) {
                if (j >= k) continue;
                if ((L[i] < L[j] + L[k]) && (L[j] < L[i] + L[k]) && (L[k] < L[i] + L[j])) ok += 1;
            }
        }
    }
    print(ok);
}

signed main() {
    solve();
}