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 ll long long
#define ld long double
#define pb push_back
#define mod 1000000007
#define mk make_pair
#define sz size
#define inf 1e9+5
 
 
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    
    ll n;
    cin>>n;
    vector<ll> arr(n);
    for(ll i=0;i<n;i++)cin>>arr[i];
    ll ans=0;
    sort(arr.begin(),arr.end());
    for(ll i=0;i<n;i++){
        for(ll j=i+1;j<n;j++){
            ll temp = arr[i]+arr[j];
            ll pos = lower_bound(arr.begin(),arr.end(),temp) - arr.begin();
            ans+=(pos-j-1);
        }
    }
    cout<<ans;

    return 0;  
}