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>
using namespace std;

#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))
#define deg_to_rad(deg) (((deg) / 360) * 2 * M_PI)
#define rad_to_deg(rad) (((rad) / 2 / M_PI) * 360)

#define rep(i, n) for (int i = 0; i < (int)(n); i++)

typedef long long ll;

void solve(long long N, std::vector<long long> L)
{
    sort(L.begin(), L.end());
    int ans = 0;
    rep(b, N) rep(a, b)
    {
        int ab = L[a] + L[b];
        int r = lower_bound(L.begin(), L.end(), ab) - L.begin();
        int l = b + 1;
        ans += r - l;
    }
    cout << ans << endl;
}

// Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You
// use the default template now. You can remove this line by using your custom
// template)
int main()
{
    long long N;
    scanf("%lld", &N);
    std::vector<long long> L(N);
    for (int i = 0; i < N; i++)
    {
        scanf("%lld", &L[i]);
    }
    solve(N, std::move(L));
    return 0;
}