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)

def ri(): return int(input())
def rli(): return list(map(int, input().split()))

cnt=0
n=ri()
lu=rli()
lu.sort()
if n<=2:
  print(0)
else:
  for i in range(n-2):
    for j in range(i+1,n-1):
      r=n
      l=j
      if lu[-1]<lu[i]+lu[j]:
        cnt+=n-1-j
        continue
      if lu[j+1]>lu[j]+lu[i]:
        continue
      
      while r-l>1 :
        mid=(r+l)//2
        if lu[i]+lu[j]>lu[mid]:
          l=mid
        else:
          r=mid
      cnt+=l-j
  print(cnt)