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 numpy as np

L_MAX = 3000 + 7

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

cnt = np.zeros((L_MAX, ), dtype=np.int)
for i in range(N):
  cnt[L[i]] += 1

s = np.cumsum(cnt)

ans = 0
for _i in range(N*N):
  i = _i // N
  j = _i % N

  if i == j: continue

  a = L[i]
  b = L[j]

  c_min = abs(a-b)
  c_max = abs(a+b)

  add = s[c_max-1] - s[c_min]

  if c_min < a < c_max: add -= 1
  if c_min < b < c_max: add -= 1

  ans += add

print(ans // 6)