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: Wrong Answer)

package main

import (
  "fmt"
  "sort"
)

func main() {
  var N, ans, a, b, c int
  fmt.Scan(&N)
  L := make([]int, N)
  for i := range L {
    fmt.Scan(&L[i])
  }
  sort.Ints(L)
  for a = N-1; a >= 2 && L[a]<L[a-1]+L[a-2]; a--{
    for b = a-1; b >= 1 && L[a]<L[b]+L[b-1]; b--{
      for c = b-1; c >= 0 && L[a]<L[b]+L[c] && L[b]<L[c]+L[a] &&L[c]<L[a]+L[b]; c--{
        ans++
      }
      if c != -1 {
        break
      }
    }
  }
  fmt.Println(ans)
}