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 (1.14.1) (judge verdict: Accepted)

// a,bを決めてcをにぶたんする cを最長とする
// sort.Searchのせいで4時間くらいバグらせた （対処法不明
package main
import (
	"fmt"
	"sort"
)
func main(){
	var N int
	fmt.Scan(&N)
	L := make([]int, N)
	for i:=0; i<N; i++{
		fmt.Scan(&L[i])
	}
	sort.Ints(L)
	ans := 0
	for a:=0; a<N-2; a++{
		for b:=a+1; b<N-1; b++{
			// cを最長とおいたのでb以上（for的にL[b]>=L[a]なので）

			// なぜかうまくいかない 多分以下のせい どこが悪いのか不明 ジャッジかパッケージがバグってるとしか思えない
			// c := sort.Search(N, func(j int)bool{
			// 	if L[a]+L[b] < L[j]{
			// 		return true
			// 	}
			// 	return false
			// })
			l, r := b, N
			for r>l{
				mid := (l+r)/2
				if L[a]+L[b] <= L[mid]{
					r = mid
				}else{
					l = mid+1
				}
			}
			c := l
			if c > b{
				ans += (c-1-b)
			}
		}
	}
	fmt.Println(ans)
}