FJ has installed a beautiful pond for his cows' aesthetic enjoyment
and exercise.

The rectangular pond has been partitioned into square cells of M
rows and N columns (1 <= M <= 30; 1 <= N <= 30). Some of the cells
have astonishingly sturdy lilypads; others have rocks; the remainder
are just beautiful, cool, blue water.

Bessie is practicing her ballet moves by jumping from one lilypad
to another and is currently located at one of the lilypads. She
wants to travel to another lilypad in the pond by jumping from one
lilypad to another.

Surprising only to the uninitiated, Bessie's jumps between lilypads
always appear as a chess-knight's move: one move in one direction
and then two more in the orthogonal direction (or perhaps two in
one direction and then one in the orthogonal direction).

Farmer John is observing Bessie's ballet drill and realizes that
sometimes she might not be able to jump to her destination lilypad
because intermediary lilypads are missing.

Ever thrifty, he wants to place additional lilypads so she can
complete her quest (perhaps quickly, perhaps by using a large number
of intermediate lilypads). Of course, lilypads cannot be placed where
rocks already intrude on a cell.

Help Farmer John determine the minimum number of additional lilypads
he has to place, and in how many ways he can place that minimum
number.

INPUT FORMAT:

* Line 1: Two space-separated integers: M and N

* Lines 2..M+1: Line i+1 describes row i of the pond using N
        space-separated integers with these values: 0 indicates empty
        water; 1 indicates a lilypad in place; 2 indicates rock in
        place; 3 indicates the lilypad Bessie starts on; 4 indicates
        the lilypad Bessie wants to travel to.

SAMPLE INPUT 

4 5
1 0 0 0 0
3 0 0 0 0
0 0 2 0 0
0 0 0 4 0

INPUT DETAILS:

The ponds has 4 rows and 5 columns. Bessie is at row 2 column 1, and she
wants to reach row 4 column 4. A rock and three lilypads are present.

OUTPUT FORMAT:

* Line 1: One integer: the minimum number of additional lilypads
        required. If it is not possible to help Bessie jump to her
        destination, print -1.

* Line 2: One integer: the total number of possible ways the
        additional lilypads can be positioned.  This number is
        guaranteed to fit into a single 64-bit signed integer. Do not
        output this line if line 1 contains -1.


2
3

OUTPUT DETAILS:

Two lilypads are required. There are three ways to place them: row
4 column 2 and row 2 column 3; row 1 column 3 and row 3 column 2;
or row 1 column 3 and row 2 column 5:

          R1C2,R2C3     R1C3,R3C2     R1C3,R2C5
          1 0 0 0 0     1 0 X 0 0     1 0 X 0 0
          3 0 X 0 0     3 0 0 0 0     3 0 0 0 X
          0 0 2 0 0     0 X 2 0 0     0 0 2 0 0
          0 X 0 4 0     0 0 0 4 0     0 0 0 4 0