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.util.*;

public class Main {

    public static int lowerBound(int[] array, int value) {
        int left = -1;
        int right = array.length;
        while (right - left > 1) {
            int middle = (right + left) / 2;
            if (array[middle] >= value) {
                right = middle;
            } else {
                left = middle;
            }
        }
        return right;
    }

    public static int upperBound(int[] array, int value) {
        int left = -1;
        int right = array.length;
        while (right - left > 1) {
            int middle = (right + left) / 2;
            if (array[middle] > value) {
                right = middle;
            } else {
                left = middle;
            }
        }
        return right;
    }

    int count(int[] array, int i, int j) {
        int lower = array[j] - array[i];
        int upper = array[j] + array[i] - 1;

        int lowerIdx = Math.max(lowerBound(array, lower), j);
        int upperIdx = upperBound(array, upper);
//        debug(lower, upper, lowerIdx, upperIdx);
        int count = upperIdx - lowerIdx - 1;
//        debug(count);
        return count;
    }

    void run() {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] arr = new int[n];

        for (int i = 0; i < n; i++) {
            arr[i] = sc.nextInt();
        }

        Arrays.sort(arr);
//        debug(arr);
        int count = 0;
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                count += count(arr, i, j);
            }
        }
        System.out.println(count);
    }


    void debug(Object... os) {
        System.err.println(Arrays.deepToString(os));
    }

    public static void main(String[] args) {
        new Main().run();
    }
}