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 Python (3.4.3) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
#define rep(i,n) for(int (i)=0;(i)<(n);++(i))
#define all(x) (x).begin(),(x).end()
#define dump(x) cout << #x << " = " << (x) << endl

using namespace std;
using ll = long long;
using P = pair<int, int>;

const int INF = 1001001001;


int main() {
    int n; cin >> n;
    vector<ll> l(n);
    rep(i, n) cin >> l[i];
    sort(all(l));

    ll ans = 0;
    rep(i, n) {
        for (int j=i+1;j<n;++j) {
            int k = lower_bound(all(l), l[i] + l[j]) - l.begin();
            ans += max(k - (j + 1), 0);
        }
    }

    cout << ans << endl;
}