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: Time Limit Exceeded)

//***___*********___*****___****___***___*********//
/*  |   \  |   | |   |   |   \  |     |     |   |  **
/*  |   |  |   | |___|   |   _  |__   |___  |___|  **
/*  |   |  |   | |   \   |  | | |         | |   |  **
/*  |___/  |___| |    \  |__| | |___  ____| |   |  **
//*************************************************/
#include <iostream>
#include <bits/stdc++.h>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <queue>
#include <deque>
#include <bitset>
#include <iterator>
#include <list>
#include <stack>
#include <map>
#include <set>
#include <functional>
#include <numeric>
#include <utility>
#include <limits>
#include <time.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <assert.h>
#define ff double
#define endl "\n"
#define M 1000000007
#define forever while(1)
#define ll long long
#define pb push_back
#define vi vector<long long>
#define mii map<int,int>
#define pii pair<int,int>
#define test ll t;cin>>t;while(t--)
#define REP(i,n) for(int i=0;i<(n);i++)
#define FOR(i,a,b) for(int i=(a);i<=(b);i++)
#define IOS ios_base::sync_with_stdio(false);cin.tie(NULL);
#define buffer cin.ignore(numeric_limits<streamsize>::max(),'\n');
using namespace std;
void fastscan(int &x)
{
        bool neg=false;
        register int c;
        x =0;
        c=getchar();
        if(c=='-')
        {
            neg = true;
            c=getchar();
        }
        for(;(c>47 && c<58);c=getchar())
            x = (x<<1) + (x<<3) +c -48;
        if(neg)
            x *=-1;
}
int main()
{
    ll n;
    cin>>n;
    ll arr[n];
    REP(i,n)
    cin>>arr[i];
    ll ans=0;
    for(int i=0;i<n;i++)
    {
        for(int j=i+1;j<n;j++)
        {
            for(int k=j+1;k<n;k++)
            {
                if((arr[i]<arr[j]+arr[k])&&(arr[j]<arr[i]+arr[k])&&(arr[k]<arr[j]+arr[i]))
                    ans++;
            }
        }
    }
    cout<<ans<<endl;

     return 0;


}