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 is_ok(a, b, c):
    if a < b + c:
        if b < c + a:
            if c < a + b:
                return True
    return False


def main():
    n = int(input())
    l_list = list(map(int, input().split()))

    ans = 0
    for i, a in enumerate(l_list):
        for j, b in enumerate(l_list[i+1:]):
            for k, c in enumerate(l_list[i+1+j+1:]):
                # if i == j or j == k or k == i:
                #     continue
                if is_ok(a, b, c):
                    ans += 1
    print(ans)


if __name__ == '__main__':
    main()