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: Runtime Error)

# Atcoder 2019/10/19
"""
# A
A, B = map(int, input().split())

ans = A - 2 * B

if ans >= 0:
    print(ans)
else:
    print(0)
"""

"""
# B
import sys
n = int(input())
d = list(map(int, sys.stdin.readline().strip().split()))

ans = 0

for i in range(n - 1):
    for j in range(i + 1, n):
        ans += d[i] * d[j]

print(ans)
"""

"""
# C
n = int(input())
s = input()

count = 1

for i in range(len(s) - 1):
    if s[i] != s[i + 1]:
        count += 1

print(count)
"""

# D
import sys

def main():
    n = int(input())
    l = list(map(int, sys.stdin.readline().strip().split()))

    global big_ans
    big_ans = []

    def angle(l, count, ans, i, n):
        if len(ans) == 3:
            big_ans.append(ans)
            return ans

        if i == n:
            # print('i end')
            return

        if len(ans) + n - i < 3:
            return

        passa = ans.copy()
        angle(l, count, passa, i + 1, n)
        ans.append(l[i])
        passb = ans.copy()
        angle(l, count + 1, passb, i + 1, n)

    angle(l, 0, [], 0, len(l))

    ans_count = 0

    for i in big_ans:
        if sum(i) - 2 * max(i) > 0:
            ans_count += 1

    print(ans_count)


if __name__ == '__main__':
    main()