First player picks a digit d between 1 and 9. N is replaced by N - d. Second player does the same thing, but has to choose a key which is adjacent to the last one (but not the same one, you cannot repeat the digit select by the opponent). Repeat until one player gets a negative number. He lost !

For example, we start with N = 20.

7 8 9

4 5 6

1 2 3

First player can pick any digit and hits 8. N becomes 12.

7 x 9

4 5 6

* * *

Second player can pick 4, 5, 6, 7 or 9. He picks 9 N becomes 3.

* 8 x

* 5 6

* * *

First player can pick 5, 6 or 8. He picks 5. N becomes -2. First player has lost this game.

Your job is to find all winning moves in a starting situation.

Examples: - if N = 1, then 1 is the only winning move (getting to 0 makes the other player lose since he will have to make N negative on his turn). - if N = 8, then 5 is NOT a winning move (since second player can reply with 3).

Note: detailed specification of what is "near".

When 1 was selected, then 2, 4 or 5 can be selected. When 2 was selected, then 1, 3, 4, 5 or 6 can be selected. When 3 was selected, then 2, 5 or 6 can be selected. When 4 was selected, then 1, 2, 5, 7, or 8 can be selected. When 5 was selected, then 1, 2, 3, 4, 6, 7, 8 or 9 can be selected. When 6 was selected, then 2, 3, 5, 8 or 9 can be selected. When 7 was selected, then 4, 5 or 8 can be selected. When 8 was selected, then 4, 5, 6, 7 or 9 can be selected. When 9 was selected, then 5, 6, or 8 can be selected.

Input

Line 1 : An int N : the starting number

Output

Line 1 : 0 to 9 ints, separated with spaces, from lowest to highest. These are the winning moves when playing first and N is the starting number