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 Ruby (2.3.3) (judge verdict: Accepted)

def bisect_left(arr, target, left = 0, hi = arr.size)
  right = hi - 1

  while left <= right
    middle = (left + right)/2;

    if arr[middle] < target
      left = middle + 1;
    elsif arr[middle] > target
      right = middle - 1;
    else
      i = middle
      while i > 0 && arr[i-1] == arr[middle]
        i -= 1
      end
      return i
    end
  end
  return left
end

n = gets.to_i
ls = gets.split.map(&:to_i)
ls.sort!
last = nil
count = 0

i = 0
while i < ls.size - 2
  j = i + 1
  while j < ls.size - 1
    k = j + 1

    x = bisect_left(ls, ls[i] + ls[j], k)
    count += x - k

    j += 1
  end
  i += 1
end

puts count