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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include<iomanip>
#include <string>
#include<vector>
#include<algorithm>
#include<utility>
#include<queue>
#include<math.h>
#include<stack>
#include<set>
#include<map>
#include<ctime>
#include<cstdlib>
#define INF 1001001001001001001
#define MAX 2001001
#define rep(i,n,m) for(int i=n;i<m;i++)

using namespace std;

int main() {
	int n;
	cin >> n;
	vector<int>L(n),fix(n);
	rep(i, 0, n) {
		cin >> L[i];
		fix[i] = L[i];
	}
	sort(fix.begin(), fix.end());

	long int ans = n * (n - 1) * (n - 2) / 6;
	rep(i, 0, n) {
		rep(j, i, n) {
			if (i == j)continue;
			auto count = lower_bound(fix.begin(), fix.end(),fix[i] + fix[j]);
			ans = ans - int(fix.end() - count);
		}
	}
	cout << ans << endl;
}