Zig Zag
-------

In Leutonia, the number 3 is associated with very bad luck.  So is the number 7.  In fact, they are so bad that any multiples of 3 or 7 are considered very unlucky too.  So, when speaking, Leutonians never mention multiples of three or seven.  Instead, they use the euphemisms "zig" and "zag".  This makes life very confusing in Leutonia, because nobody can distinguish between the numbers 3, 6, 9, etc.  It also explains why you have never heard of any great Leutonian mathematicians.

Your task is to write a programme that counts from 1 to a given number n in Leutonian.

Input
-----

The input will be a single number n.

Output
------

The numbers 1 to n, with multiples of three replaced by zig, multiples of seven replaced by zag, and numbers that are multiples of both three and seven replaced by zigzag.  Each number should appear on a separate line.

Sample Input
------------

22

Sample Output
-------------

1
2
zig
4
5
zig
zag
8
zig
10
11
zig
13
zag
zig
16
17
zig
19
20
zigzag
22