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: Wrong Answer)

#include<iostream>
#include<vector>
#include<string>
#include<cmath>
#include<algorithm>
#include <numeric>
#include<map>
#include<unordered_map>
#include <queue>
 
using namespace std;
using ll=long long;
#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()
 
int main(){
    ll n;
    cin >> n;
    vector<ll> l(n);
    rep(i, n)cin >> l[i];
    ll ans = 0;
    for(ll  a=0; a<l.size(); ++a){
        for(ll b=a+1; b<l.size(); ++b){
            ll low = upper_bound(l.begin()+b, l.end(), l[b]-l[a])-l.begin();
            ll high = lower_bound(l.begin()+b, l.end(), l[b]+l[a])-l.begin()-1;
            ll plus = high-low+1;
            if(a<=high&&a>=low)plus--;
            if(b<=high&&b>=low)plus--;
            ans += max(plus, (ll)0);
        }
    }
    cout << ans << endl;
}