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 (
	"bufio"
	"fmt"
	"math"
	"os"
	"sort"
	"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 binarySearch(idxB, idxC int, nums []int) int {
	c := nums[idxC]
	b := nums[idxB]
	minLength := c - b + 1

	left := 0
	right := idxB
	list := nums[:idxB]
	mid := (left + right) / 2

	for {
		if list[mid] < minLength {
			left = mid + 1
		} else {
			right = mid - 1
		}
		mid = (left + right) / 2
		if left >= right {
			break
		}
	}
	total := idxB - mid
	return total
}

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)
	sort.Ints(nums)

	idxC := 0
	idxB := 0
	total := 0

	for i := 0; i < N-2; i++ {
		idxC = N - i - 1
		for j := i + 1; j < N-1; j++ {
			idxB = N - j - 1
			total += binarySearch(idxB, idxC, nums)
		}
	}

	fmt.Println(total)
}