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 lli long long int
#define mod 1000000007

int main() {
    int n;
    cin>>n;
    int a[n];
    for(int i=0;i<n;i++)cin>>a[i];
    sort(a, a+n);
    lli ans = 0;
    for(int i=0;i<n;i++){
        for(int j=i+1;j<n;j++){
            int p = a[i] + a[j];
            int l=j+1,r=n-1,val=-1,mid;
            while(l<=r){
                mid = (l+r)/2;
                if(a[mid] >= p){
                    r = mid - 1;
                }else{
                    val = mid;
                    l = mid + 1;
                }
            }
            if(val != -1){
                ans += (val-j);
            }
        }
    }
    cout<<ans<<"\n";
    return 0;
}