Curling 2.0

Description

On Planet MM-21, after their Olympic games this year, curling is getting
popular. But the rules are somewhat different from ours. The game is played on
an ice game board on which a square mesh is marked. They use only a single
stone. The purpose of the game is to lead the stone from the start to the goal
with the minimum number of moves.

Fig. 1 shows an example of a game board. Some squares may be occupied with
blocks. There are two special squares namely the start and the goal, which are
not occupied with blocks. (These two squares are distinct.) Once the stone
begins to move, it will proceed until it hits a block. In order to bring the
stone to the goal, you may have to stop the stone by hitting it against a block,
and throw again.

Fig. 1:
Example of board (S: start, G: goal)

The movement of the stone obeys the following rules:

• At the beginning, the stone stands still at the start square.


• The movements of the stone are restricted to x and y directions. Diagonal
  moves are prohibited.


• When the stone stands still, you can make it moving by throwing it. You
  may throw it to any direction unless it is blocked immediately(Fig. 2(a)).


• Once thrown, the stone keeps moving to the same direction until one of the
  following occurs:
  
  • The stone hits a block (Fig. 2(b), (c)).
    
    • The stone stops at the square next to the block it hit.
    
    
    • The block disappears.
  
  
  • The stone gets out of the board.
    
    • The game ends in failure.
  
  
  • The stone reaches the goal square.
    
    • The stone stops there and the game ends in success.


• You cannot throw the stone more than 10 times in a game. If the stone does
  not reach the goal in 10 moves, the game ends in failure.

Fig. 2:
Stone movements

Under the rules, we would like to know whether the stone at the start can
reach the goal and, if yes, the minimum number of moves required.

With the initial configuration shown in Fig. 1, 4 moves are required to
bring the stone from the start to the goal. The route is shown in Fig. 3(a).
Notice when the stone reaches the goal, the board configuration has changed as
in Fig. 3(b).

Fig. 3:
The solution for Fig. D-1 and the final board configuration

Input

The input is a sequence of datasets. The end of the input is indicated by a
line containing two zeros separated by a space. The number of datasets never
exceeds 100.

Each dataset is formatted as follows.

the width(=w) and the height(=h) of the board
First row of
the board
...
h-th row of the board

The width and the height of the board satisfy: 2 <= w <= 20, 1
<= h <= 20.

Each line consists of w decimal numbers delimited by a space. The
number describes the status of the corresponding square.

0	vacant square
1	block
2	start position
3	goal position

The dataset for Fig. D-1 is as follows:

6 6
1 0 0 2 1 0
1 1 0 0 0 0
0 0 0 0 0 3
0 0 0 0 0 0
1 0
0 0 0 1
0 1 1 1 1 1

Output

For each dataset, print a line having a decimal integer indicating the
minimum number of moves along a route from the start to the goal. If there are
no such routes, print -1 instead. Each line should not have any character other
than this number.

Sample Input

2 1

3 2

6 6

1 0 0 2 1 0

1 1 0 0 0 0

0 0 0 0 0 3

0 0 0 0 0 0

1 0 0 0 0 1

0 1 1 1 1 1

6 1

1 1 2 1 1 3

6 1

1 0 2 1 1 3

12 1

2 0 1 1 1 1 1 1 1 1 1 3

13 1

2 0 1 1 1 1 1 1 1 1 1 1 3

0 0

Sample Output

1

4

-1

4

10

-1