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 (
	"fmt"
	"sort"
)

func main() {
	var n, r int
	fmt.Scan(&n)
	l := make([]int, n)
	for i := 0; i < n; i++ {
		fmt.Scan(&l[i])
	}
	sort.Sort(sort.IntSlice(l))
	for i := 0; i < n-2; i++ {
		for j := i + 1; j < n-1; j++ {
			t := l[j+1:]
			sum := l[i] + l[j]
			w := sort.Search(len(t), func(i int) bool { return t[i] > sum })
			for k := 0; k < w; k++ {
				if l[i] < l[j]+t[k] && l[j] < t[k]+l[i] && t[k] < l[i]+l[j] {
					r++
				}
			}
		}
	}
	fmt.Println(r)
}