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;

int main(void){
    int n;
    cin >> n;
    vector<int> L(n);
    for(int i=0;i<n;i++){
        cin >> L[i];
    }
    sort(L.begin(),L.end());
    int a,b,i,j,ok,ng,mid;
    long long ans=0;
    for(i=0;i<n-2;i++){
        for(j=i+1;j<n-1;j++){
            a=L[i];b=L[j];
            ok=j;ng=n;
            while(ng-ok>1){
                mid=(ok+ng)/2;
                if(L[mid] < a+b) ok=mid;
                else ng=mid;
            }
            ans+=(ok-j);
        }
    }
    cout << ans << endl;
    return 0;
}