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 FOR(i,n) for(int i=0;i<(n);i++)
#define MOD 1000000007
#define all(n) (n).begin(),(n).end()
typedef long long ll;
template <class T> inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}else{return 0;}}
template <class T> inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}else{return 0;}}
template <class T> inline T GCD(T a,T b){T c;while(b!=0){c=a%b;a=b;b=c;}return a;}
template <class T> inline T LCM(T a,T b){return a*b/GCD(a,b);}

int main(){
	ll n;
	vector<ll> l;
	cin >> n;
	ll x;
	FOR(i,n){cin >> x;l.push_back(x);};

	sort(all(l));
	int ans=0;

	FOR(i,n-1){
		for(int j=i+1;j<n;j++){
			int p=lower_bound(all(l),l[i]+l[j])-l.begin();
			ans+=max(p-j-1,0);
			
			
		}	
	}
	cout << ans << endl;
}