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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        main.solve();
    }
    public void solve() {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int N = scan.nextInt();
        List<Long> l = new ArrayList<>();
        for (int i = 0; i < N; i++) {
            l.add(scan.nextLong());
        }
        l.sort(Comparator.naturalOrder());
        long ans = 0;
        for (int i = 0; i < N; i++) {
            long l_i = l.get(i);
            for (int j = i+1; j < N; j++) {
                long l_j = l.get(j);
                long seek = l_i + l_j;
                int key = ~Collections.binarySearch(l, seek, new LowerBoundComparator<>());
                ans += Math.max(0, key - 1 - j);
            }
        }
        System.out.println(ans);
    }
    class LowerBoundComparator<T extends Comparable<? super T>> implements Comparator<T> {
        public int compare(T x, T y) {
            return (x.compareTo(y) >= 0) ? 1 : -1;
        }
    }
}