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 (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)
 
var sc = bufio.NewScanner(os.Stdin)
 
func next() string {
	sc.Scan()
	return sc.Text()
}
 
func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func main() {
    sc.Split(bufio.ScanWords)
 
	N := nextInt()
	L := make([]int, N)
	for i := 0; i < N; i++ {
		L[i] = nextInt()
	}
 
    fmt.Println(solver(N,L))
}

func solver(N int, L []int) int {
    var ans int
    ans = 0
    sort.Sort(sort.Reverse(sort.IntSlice(L)))
    for i := 0; i < N-2; i++ {
        for j := i+1; j < N-1; j++ {
            for k := j+1; k < N; k++ {
                if L[i] < L[j] + L[k] && 
                   L[j] < L[i] + L[k] &&
                   L[k] < L[j] + L[i] {
                    ans++
                    continue
                }
                break
            }
        }
    }
    return ans
}