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"
	"math"
	"os"
	"strconv"
)

var scanner = bufio.NewScanner(os.Stdin)

func nextLine() string {
	scanner.Scan()
	return scanner.Text()
}

func nextInt() int {
	i, e := strconv.Atoi(nextLine())
	if e != nil {
		panic(e)
	}
	return i
}

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

func min(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton min() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Min(float64(res), float64(nums[i])))
	}
	return res
}

func max(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton max() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Max(float64(res), float64(nums[i])))
	}
	return res
}

func sumSlice(nums []int) int {
	sum := 0
	for _, n := range nums {
		sum += n
	}
	return sum
}

func canMakeTriangle(a, b, c int) bool {
	result := true
	if a >= b+c {
		result = false
	}
	if b >= c+a {
		result = false
	}
	if c >= a+b {
		result = false
	}
	return result
}

func main() {
	scanner.Split(bufio.ScanWords) // switch to separating by space
	// scanner.Buffer([]byte{}, 1000000009) // switch to read large size input
	N := nextInt()
	nums := scanNums(N)

	count := 0
	for i, a := range nums[:N-1] {
		for j, b := range nums[i+1 : N-1] {
			for _, c := range nums[i+j+2:] {
				// fmt.Println(a, b, c)
				if canMakeTriangle(a, b, c) {
					count++
				}
			}
		}
	}

	fmt.Println(count)
}