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)

import bisect

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

Lsorted = sorted(L,reverse=True)
Lrev = Lsorted[::-1]

ret = 0
cnt = 0
for i in range(N):
  a = Lsorted[i]
  x = a / 2
  b_max_idx = bisect.bisect_left(Lrev, x)
  for j in range(i+1,N-b_max_idx):
    b = Lsorted[j]
    x = a - b
    c_max_idx = bisect.bisect_left(Lrev, x)

    for k in range(j+1, N-c_max_idx):
      
      c = Lsorted[k]
#      print(a,b,c)
#      cnt += 1
      
      if c >= (a + b):
        break
      if b >= (a + c):
        break
      if a >= (b + c):
        break
      
      ret += 1
print(ret)
#print(cnt)