**Time limit:**1.00 s**Memory limit:**512 MB

*Klotski*puzzle consists of a board of size $5 \times 4$ and $10$ blocks:

- $4$ blocks of size $2 \times 1$ (A, B, C, D)

- $1$ block of size $1 \times 2$ (E)

- $4$ blocks of size $1 \times 1$ (F, G, H, I)

- $1$ block of size $2 \times 2$ (X)

Your goal is to move the $2 \times 2$ block to the position from which it can escape the board. What is the minimum number of moves needed for this?

**Input**

The input consists of five lines, each of which contains four characters. Each character is a letter (there is a block) or a dot (empty cell).

**Output**

Print one integer: the minimum number of moves needed to solve the puzzle. If the puzzle is unsolvable, output $-1$.

**Example**

Input:

`AXXC`

AXXC

BEED

BGHD

F..I

Output:

`116`