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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main

import "fmt"

func main() {
	var n, v int
	var sticks []int
	fmt.Scan(&n)
	for i := 0; i < n; i++ {
		fmt.Scan(&v)
		sticks = append(sticks, v)
	}
	count := 0
	for indexA, a := range sticks {
		for indexB, b := range sticks[indexA+1:] {
			for _, c := range sticks[indexA+indexB+2:] {
				if makeTriangle(a, b, c) {
					count++
				}
			}
		}
	}
	fmt.Println(count)
}

func makeTriangle(a, b, c int) bool {
	if a < b+c && b < c+a && c < b+a {
		return true
	}
	return false
}