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: Wrong Answer)

n = int(input())
l = [int(i) for i in input().split(" ")]

def meguru_nibutan(ar,m,key):
    a = m
    b = len(ar)
    while(abs(a-b) > 1):
        c = (a+b)//2
        if (ar[c] > key):
            a = c
        else:
            b = c
    return a

def main():
    cnt = 0
    l.sort(reverse=True)
    for a in range(0,n-2):
        for b in range(a+1,n-1):
            cnt += meguru_nibutan(l,b,l[a]-l[b]) - b

if (__name__ == "__main__"):
    main()