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<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll n,a,b,s[1001],t[2000],ans;
int main(void){
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>t[i];
        s[t[i]]++;
    }
    for(int i=0;i<1000;i++){
        s[i+1]+=s[i];
    }
    for(int i=0;i<n-1;i++){
        for(int j=i+1;j<n;j++){
            a=max(t[i],t[j]);
            b=min(t[i],t[j]);
            //cout<<a<<b<<" "<<s[min(1000LL,a+b-1)]-s[a-b]<<endl;
            ans+=s[min(1000LL,a+b-1)]-s[a-b];
            if(a-2*b<0)ans--;
            ans--;
        }
    }
    cout<<ans/3<<endl;
}