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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

n = int(input())
l = list(map(int, input().split()))
l.sort(reverse=True)

dp = [[-1 for i in range(1001)] for j in range(n)]

cnt = 0
for i in range(n-2):
  for j in range(i+1,n-1):
    tgt = l[i] - l[j]
    if dp[j+1][tgt] != -1:
      cnt += dp[j+1][tgt]
    else:
      cptr = ((n-1) + (j+1)) // 2
      fixed = [-1] * n
      while fixed[cptr] == -1:
        if l[cptr] > tgt:
          fixed[cptr] = 0
          cptr = ((n-1) + (cptr+1)) // 2
        else:
          fixed[cptr] = 1
          cptr = ((cptr) + (j+1)) // 2
      inc = cptr - j - fixed[cptr]
      cnt += inc
      dp[j+1][tgt] = inc
#      print('J='+str(j)+', CPTR='+str(cptr)+', CNT='+str(cnt))

print(cnt)