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: Time Limit Exceeded)

N, *LS = $stdin.read.split.map(&:to_i) 
LS.sort!
ans = 0
for i in 0..(N-2)
  a = LS[i]
  for j in (i+1)...N
    b = LS[j]
    sum = a+b
    abs = (a-b).abs
    for k in 0...N
      #p i: i, j: j, k: k
      next if k == i || k == j
      c = LS[k]
      next if c <= abs
      break if c >= sum
      #p [i, j, k, a, b, c]
      ans += 1
    end
  end
end
p ans/3