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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

n = int(input())
li = sorted(list(map(int, input().split())))

def ta(li):
  b1 = li[0] < li[1]+li[2]
  b2 = li[1] < li[2]+li[0]
  b3 = li[2] < li[0]+li[1]
  if b1:
    if b2:
      if b3:
        return li
  return -1

all_l = []
count = 0
for i in range(n):
  for j in range(i+1, n):
    for k in range(j+1, n):
      t = [li[i], li[j], li[k]]
      r = ta(t)
      if r!=-1 and r not in all_l:
        all_l.append(r)
        count += 1

print(count)