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 (
	"fmt"
	"log"
	"math"
	"sort"
)

func main() {
	log.SetFlags(log.Lshortfile)
	var n int
	fmt.Scan(&n)
	l := make([]int, n)
	for i := 0; i < n; i++ {
		fmt.Scan(&l[i])
	}
	var cnt int
	sort.Ints(l)
	for i := 0; i < n-2; i++ {
		for j := i + 1; j < n-1; j++ {
			a := l[i]
			b := l[j]
			k := lower_bound(l, a+b)
			cnt += k - j - 1
		}
	}
	fmt.Println(cnt)
}

func lower_bound(a []int, x int) int {
	var ok, ng, mid int
	ng = -1
	ok = len(a)
	for ok-ng > 1 {
		mid = (ok + ng) / 2
		if a[mid] >= x {
			ok = mid
		} else {
			ng = mid
		}
	}
	return ok
}

var dy = []int{0, 1, 0, -1}
var dx = []int{1, 0, -1, 0}
var inf = int(1e9)

func pow(a, b int) int {
	return int(math.Pow(float64(a), float64(b)))
}

func lcm(a, b int) int {
	return a * b / gcd(a, b)
}
func gcd(a, b int) int {
	if a < b {
		a, b = b, a
	}
	for b != 0 {
		a, b = b, a%b
	}
	return a
}
func max(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r < a[i] {
			r = a[i]
		}
	}
	return r
}
func min(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r > a[i] {
			r = a[i]
		}
	}
	return r
}
func sum(a []int) (r int) {
	for i := range a {
		r += a[i]
	}
	return r
}
func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

type pair struct {
	a, b int
}

type pairs []pair

func (p pairs) Len() int {
	return len(p)
}
func (p pairs) Swap(i, j int) {
	p[i], p[j] = p[j], p[i]
}

func (p pairs) Less(i, j int) bool {
	if p[i].a == p[j].a {
		return p[i].b < p[j].b
	}
	return p[i].a < p[j].a
}