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: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func readInt() int {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}
	return i
}

func readString() string {
	sc.Scan()
	return sc.Text()
}

func readInt64() int64 {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}
	return int64(i)
}

func readfloat64() float64 {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}
	return float64(i)
}

func abs(a int) int {
	if a < 0 {
		return a * -1
	}
	return a
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func main() {
	sc.Split(bufio.ScanWords)

	n := readInt()
	l := make([]int, n)
	for i := 0; i < n; i++ {
		l[i] = readInt()
	}

	sort.Sort(sort.IntSlice(l))

	ans := 0
	for i := 0; i < n-2; i++ {
		for j := i + 1; j < n-1; j++ {
			right := n
			left := j
			for right-left > 1 {
				middle := (right + left) / 2
				a, b, c := l[i], l[j], l[middle]
				if check(a, b, c) && check(b, c, a) && check(c, a, b) {
					left = middle
				} else {
					right = middle
				}
			}
			if left != j {
				ans += left - j
			}
		}
	}
	fmt.Println(ans)
}

func check(a, b, c int) bool {
	return a < b+c
}