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)

import sys
from itertools import combinations
import bisect
import math
n = int(input())
l_ls = [int(i) for i in sys.stdin.readline().split()]
l_ls.sort()
l_dict = { i : j for i, j in enumerate(l_ls)}
_sum_ls = []
cnt = 0
for combi in combinations(l_ls, 2):
    bisect.insort_left(_sum_ls, combi[0] + combi[1])
len_sum_ls = len(_sum_ls)
for l in l_ls:
    ind = bisect.bisect_right(_sum_ls, l)
    cnt += ind
print(int(math.factorial(n) / math.factorial(3) / math.factorial(n-3)) - cnt)