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.*;
import java.util.*;

class Main {
    static Scanner scanner = new Scanner();
    static long mod = 1000000007;
    static int inf = 0x7ffffff;

    public static void main(String[]$) throws Exception {
        int n = scanner.nextInt();
        int[] l = scanner.nextIntArray(n);
        Arrays.sort(l);
        long count = 0;
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                int b = lowerBound(l, l[j] + l[i]);
                count += b - j - 1;
            }
        }
        System.out.println(count);
    }

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

    static class System {
        static PrintWriter out = new PrintWriter(java.lang.System.out);

        static {
            Runtime.getRuntime().addShutdownHook(new Thread(System.out::flush));
        }
    }

    static class Scanner {
        BufferedReader reader = new BufferedReader(new InputStreamReader(java.lang.System.in), 1 << 15);
        StringTokenizer tokenizer;

        String next() {
            try {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    tokenizer = new StringTokenizer(reader.readLine());
                }
            } catch (IOException ignored) {
            }
            return tokenizer.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        char[][] nextCharArray(int n, int m) {
            char[][] a = new char[n][m];
            for (int i = 0; i < n; i++) {
                a[i] = next().toCharArray();
            }
            return a;
        }

        int[] nextIntArray(int n, java.util.function.IntUnaryOperator op) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = op.applyAsInt(nextInt());
            }
            return a;
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }

        long[] nextLongArray(int n, java.util.function.LongUnaryOperator op) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = op.applyAsLong(nextLong());
            }
            return a;
        }
    }
}