There are $9$ clocks, arranged in a $3\times 3$ array. They are labelled:

A B C
D E F
G H I

Each clock is set to either one o'clock, two o'clock, three o'clock, … or twelve o'clock.
There are nine possible moves, numbered from $1$ to $9$. Each move advances a certain set of clocks by $1$ hour. The moves and their corresponding sets of clocks are:

1 ABDE
2 ABC
3 BCEF
4 ADG
5 BDEFH
6 CFI
7 DEGH
8 GHI
9 EFHI

We wish to know the shortest sequence of moves that will restore all the clocks to twelve o'clock.
For example, suppose $A$, $B$, and $C$ are initially set to eleven o'clock, $D$, $E$, and $F$ are set to twelve o'clock, and $G$, $H$, and $I$ are set to ten o'clock. Then, doing move $2$ once and move $8$ twice resets all the clocks.

Input Specification

$9$ lines, containing one integer each, the initial states of clocks $A$, $B$, $C$, $D$, $E$, $F$, $G$, $H$, and $I$, respectively, where $1$ denotes one o'clock, $2$ denotes two o'clock, and so on.

Output Specification

$9$ lines, containing one integer each. Line $n$ should contain the number of times to do move $n$ in the shortest possible sequence of moves.

Sample Input

11
11
11
12
12
12
10
10
10

Sample Output

0
1
0
0
0
0
0
2
0