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"
)

func main() {
	var n, l, out int
	fmt.Scanf("%d", &n)
	L := make([]int, n)
	for i := 0; i < n; i++ {
		fmt.Scanf("%d", &l)
		L[i] = l
	}
	btmp := true
	for i := 0; i < n-2; i++ {
		for ii := i + 1; ii < n-1; ii++ {
			btmp = true
			for iii := ii + 1; btmp && iii < n; iii++ {
				fmt.Printf("a:%d\n", L[i])
				fmt.Printf("b:%d\n", L[ii])
				fmt.Printf("c:%d\n", L[iii])
				if L[ii] <= L[i] {
					if L[iii] > L[i]-L[ii] {
						out++
						fmt.Println("OK")
					}
				} else {
					if L[iii] > L[ii]-L[i] {
						out++
						fmt.Println("OK")
					}
				}
				if L[iii] >= L[i]+L[ii] {
					btmp = false
				}
			}
		}
	}
	fmt.Println("答え：")
	fmt.Println(out)
}