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<iostream>
#include<algorithm>
#include<vector>
#include<string>
#include<utility>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<functional>
#include<math.h>
using namespace std;
#define N (1000000000+7)
#define M (998244353)
#define INF 1e16
typedef long long ll;
typedef pair<int,int> P;



int main(){
    ll ans = 0;
    ll n;
    cin>>n;
    vector<int>l(n);
    for(ll i=0;i<n;i++)cin>>l[i];
    sort(l.begin(),l.end());
    for(ll i=0;i<n;i++){
        for(ll j=i+1;j<n;j++){
            ll Lower = l[j]-l[i];
            ll Upper = l[i]+l[j];
            auto itr1 = lower_bound(l.begin()+j+1,l.end(),Upper);
            auto itr2 = upper_bound(l.begin()+j+1,l.end(),Lower);
            ll index1 =itr1-l.begin();
            ll index2 =itr2-l.begin();
            index1--;
            //cout<<i<<" "<<j<<endl;
            //cout<<index2<<" "<<index1<<endl;
            ans+=index1-index2+1;
            //cout<<ans<<endl;
        }
    }

    cout<<ans<<endl;
}