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"
        "os"
        "sort"
        "strconv"
)

func main() {
        scanner := bufio.NewScanner(os.Stdin)
        scanner.Split(bufio.ScanWords)
        writer := bufio.NewWriter(os.Stdout)
        defer writer.Flush()

        scanner.Scan()
        N, _ := strconv.Atoi(scanner.Text())
        L := make([]int, N)
        for i := range L {
                scanner.Scan()
                L[i], _ = strconv.Atoi(scanner.Text())
        }

        cnt := 0
        sort.Ints(L)
        for i := range L {
                a := L[i]
                for j := i + 1; j < len(L); j++ {
                        b := L[j]
                        for k := j + 1; k < len(L); k++ {
                                c := L[k]
                                if a < b+c && b < c+a && c < a+b {
                                        cnt++
                                }
                        }
                }
        }
        writer.WriteString(strconv.Itoa(cnt) + "\n")
}