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())
L = list(map(int,input().split()))
L.sort()

ans = 0
for i in range(1,n-1):
  for j in range(i):
    if L[n-1] - L[i]-L[j] < 0:
      ans += (n-1) - (i+1) + 1
      continue
    elif L[i+1] - L[i]-L[j] >= 0:
      continue
    l = i+1
    r = n-1
    while abs(r-l) > 1:
      mid = (l+r)//2
      if L[i]+L[j] - L[mid]> 0:
        l = mid
      else:
        r= mid
    ans += l-(i+1)+ 1
print(ans)