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 rep(i,n) for(ll i=0;i<n;++i)
#define all_map(itr,mp) for(auto itr=mp.begin();itr!=mp.end();itr++)
#define ALL(a) (a).begin(),(a).end()

using namespace std;
using ll  = long long;
using pll = pair<ll, ll>;

const ll MOD  = 1e9+7;
const ll LINF = 1LL << 60;
const int INF = 1e9 + 7;

int main(){
    ll n;
    cin >> n;

    vector<ll> l(n);
    rep(i, n)cin >> l[i];
    
    sort(ALL(l));

    ll ans = 0;
    rep(a, n){
        for(ll b = a+1; b < n; ++b){
            ll r_pos, l_pos;

            if(l[a]+l[b] > l.back())r_pos = n-1;
            else r_pos = lower_bound(ALL(l), l[a]+l[b]) - l.begin(), r_pos--;

            l_pos = upper_bound(ALL(l), l[b]-l[a]) - l.begin();
            l_pos = max(l_pos, b);

            ans += r_pos - l_pos;
        }
    }

    cout << ans << endl;
}