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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;
typedef long long ll;
#define REP(i,n) for (ll i = 0; i < (n); ++i)

int main(){
    ll n;
    cin >> n;
    vector<ll> l(n);
    REP(i, n){
        cin >> l.at(i);
    }
    sort(l.begin(), l.end());
    ll ans = 0;
    REP(bi, n - 1){
        const ll b = l.at(bi);
        ll ci = bi + 1;
        REP(ai, bi){
            const ll a = l.at(ai);
            while(ci < n && l.at(ci) < a + b){ ci++; }
            ans += ci - bi - 1;
        }
    }
    cout << ans << endl;
    return 0;
}