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: Runtime Error)

package main;

import (
    "fmt"
    "sort"
    "os"
)

func main() {
    var N int
    fmt.Scan(&N)

    var L []int;
    for i := 0; i < N; i++ {
		fmt.Scan(&L[i])
    }
    fmt.Println(solver(N,L))
}

func solver(N int, L []int) int {
    var ans int
    ans = 0
    sort.Sort(sort.Reverse(sort.IntSlice(L)))
    var i, j, k int
    i = 0;
    j = 0
    k = 0
    for {
        fmt.Fprintf(os.Stdout, "i:%s,j:%s,k:%s\n", i, j, k)
        if i >= N-2 {
            break
        }
        if j == 0 {
            j = i + 1
        }
        if k == 0 {
            k = j + 1
        }
        if k >= N {
            j++
            k = j + 1
            if k >= N {
                j = 0
                k = 0
                i++
                continue
            }
        }
        if L[i] < L[j] + L[k] &&
           L[j] < L[i] + L[k] &&
           L[k] < L[j] + L[i] {
            ans++
            if k == N-1 {
                j = 0
                k = 0
                i++
                continue
            }
            k++
            continue
        }
        j = 0
        k = 0
    }
    return ans
}