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<bits/stdc++.h>
using namespace std;
 
int n,len,a[100005],num[100005];
 
int sum(int a[])
{
    int ans=0;
    int x;
   
     for(int i=0;i<len;i++)
    {
        if(num[a[i]] >= 3)
            ans+=1;
        
        if(num[a[i]]>=2)
        {
            x = lower_bound(a,a+len,2*a[i])-a;
            ans += (x-1);
        }
        for(int j=i+1;j<len;j++)
        {
            x = lower_bound(a+j,a+len,a[i]+a[j])-a;
            ans += (x-j-1);
        }
    }
    return ans;
}
 
int main()
{
    cin>>n;
    
    for(int i=0;i<n;i++)
    {
        cin>>a[i];
        num[a[i]]++;
    }
    sort(a,a+n);
    
    len=unique(a,a+n)-a;
    
    cout<<sum(a)<<endl;
    return 0;
}