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: Wrong Answer)

package main

import (
	"fmt"
	"sort"
)

func main() {
	var N int
	fmt.Scan(&N)

	inputs := scanNums(N)
	sort.Sort(sort.Reverse(sort.IntSlice(inputs)))
	res := 0
	for i := 0; i < N; i++ {
		for j := i + 1; j < N; j++ {
			if inputs[i] >= 2*inputs[j] {
				break
			}
			if inputs[i] == inputs[j] {
				continue
			}
			for k := j + 1; k < N; k++ {

				a := inputs[i]
				b := inputs[j]
				c := inputs[k]
				if a >= b+c {
					break
				}
				// if a >= b+c {
				// 	continue
				// }
				// if b >= a+c {
				// 	continue
				// }
				// if c >= a+b {
				// 	continue
				// }
				res++
			}
		}
	}

	fmt.Println(res)

}

func scanNums(len int) (nums []int) {
	var num int
	for i := 0; i < len; i++ {
		fmt.Scan(&num)
		nums = append(nums, num)
	}
	return
}