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)

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#include<iostream>
#include<algorithm>
#include<cmath>
#include<iomanip>
#include<set>
#include<map>
#include<queue>
#include<vector>
using namespace std;
typedef long long ll;
const int MOD=1e9+7;
const double pi=3.14159265358979323846;
const int inf=2e9;
const ll INF=9e18;
typedef pair<int,int> P;
int main() {
  cin.tie(0),cout.tie(0);
  ios::sync_with_stdio(false);
  ll n,l[2005]={},ans=0;
  cin >> n;
  for(int i=0; i<n; i++) {
    cin >> l[i];
  }
  sort(l,l+n);
  for(int i=0; i<n; i++) {
    for(int j=i+1; j<n; j++) {
      int x=l[i],y=l[j];
      int itr=lower_bound(l,l+n,x+y)-l-1;
      ans+=itr-j;
    }
  }
  cout << ans << endl;
}