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 (
	"bufio"
	"fmt"
	"strconv"
	"strings"
    "os"
)

func main() {
	var N int

	var ln []int

	fmt.Scanf("%d", &N)
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Scan()
	dn := scanner.Text()
	dn = strings.TrimSpace(dn)

	dnn := strings.Fields(dn)

	for j := range dnn {
		var iparam int
		iparam, _ = strconv.Atoi(dnn[j])
		ln = append(ln, iparam)
	}

	sum := 0

	for i:=0; i<(N-2); i++ {
		for j:=i+1; j<(N-1); j++ {
			for k:=j+1; k<N; k++ {
				if( ln[i] < ln[j] + ln[k] &&
					ln[j] < ln[i] + ln[k] &&
					ln[k] < ln[i] + ln[j]) {
						sum++
				}
			}
		}
	}
	fmt.Printf("%d\n", sum)
}