human
PYTHON solution for "Let's call a set of positive integers a_1, a_2, ..., a_k quadratic if the product of the factorials of its elements is a square of an integer, i. e. ∏_{i=1}^{k} a_i! = m^2, for some integer m.

You are given a positive integer n.

Your task is to find a quadratic subset of a set 1, 2, ..., n of maximum size. If there are multiple answers, print any of them.

Input

A single line contains a single integer n (1 ≤ n ≤ 10^6).

Output

In the first line, print a single integer — the size of the maximum subset. In the second line, print the subset itself in an arbitrary order.

Examples

Input

1

Output

1
1 

Input

4

Output

3
1 3 4 

Input

7

Output

4
1 4 5 6 

Input

9

Output

7
1 2 4 5 6 7 9 ":


 ... Write me a Python program to find a quadratic subset of a set 1, 2,?
assistant
#Here is Python program to find a quadratic subset of a set 1, 2, .
 def T(n):
    return int(n**0.5)**2 == n

def solve(n):
    if n % 4 == 0: return [n//2]
    if n == 1: return []
    if n % 4 == 1: return [n//2, n]
    if n % 4 == 2:
        if T(n + 2): return [n//2 + 1]
        if T(n * (n//2 - 1)): return [n//2 - 2]
        return [n//2, 2]
    else:
        if T(n + 1): return [n//2 + 1, n]
        if T(2*(n//2)*(n//2 - 1)): return [n, n//2 - 2]
        if T((n//2-1) * n): return [n//2 - 2, n-2]
        return [2, n//2, n]

if __name__ == '__main__':
    n = int(input())
    arr = solve(n)
    ans = [i for i in range(1, n+1) if i not in arr]
    print(len(ans))
    print(" ".join(str(i) for i in ans))