Positive integer x is called composite if it has strictly more than two positive integer divisors. For example, integers 4, 30 and 111 are composite, while 1, 7 and 239 are not.

Integer sequence p = \langle p_1, p_2, \ldots , p_n \rangle is called a permutation of length n if it contains every integer between 1 and n, inclusive, exactly once.

We’ll call permutation p = \langle p_1, p_2, \ldots , p_n \rangle highly composite if for every i between 1 and n, inclusive, the sum of the first i elements of p (that is, p_1 + p_2 + \ldots + p_i) is composite.

Given a single integer n, find a highly composite permutation of length n.

Input

The only line of the input contains a single integer n.

Output

If no highly composite permutation of length n exists, output a single integer -1. Otherwise, output n integers p_1, p_2, \ldots, p_n such that p = \langle p_1, p_2, \ldots , p_n \rangle is a highly composite permutation.

If there are multiple highly composite permutations of length n, you may output any of them.

Constraints

• 1 \le n \le 100

Examples

Input:

13

Output:

9 13 6 5 3 2 8 4 1 12 11 10 7

Input:

2

Output:

-1