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 BinarySearch(lis, i, j):
    low, high = 0, len(lis)
    border = j-i
    while low < high:
        key = (low+high)//2
        value = lis[key]
        if value <= border:
            low = min([key, low]) + 1
        else:
            high = max([key, high]) - 1
    return low

n = int(input())
l = list(int(x) for x in input().split())
l.sort()
ans = 0
for i in range(n):
    for j in range(i+1, n):
        key = i-BinarySearch(l, l[i], l[j])
        ans += max([key, 0])
print(ans)