Problem Statement

Yukiko-chan is playing a puzzle called the "15 puzzle".
The rules of the 15 puzzle are shown below.

Pieces with the numbers from 1 to 15 written on them are placed in order on a 4×4 board (see the figure below).
You repeatedly slide a piece adjacent to the empty square (above, below, left, or right of it) into the empty square.
You succeed if you can create the target arrangement of pieces.



Yukiko-chan has grown bored of the usual way of playing the 15 puzzle.
So she decided to play with the following new rule added.

Rule: A piece that has been slid once cannot be slid again

Given a target arrangement of pieces, determine whether that arrangement can be created.

Input

$a_{11}$ $a_{12}$ $a_{13}$ $a_{14}$
$a_{21}$ $a_{22}$ $a_{23}$ $a_{24}$
$a_{31}$ $a_{32}$ $a_{33}$ $a_{34}$
$a_{41}$ $a_{42}$ $a_{43}$ $a_{44}$

The target arrangement of pieces is given.
$a_{ij}$ are distinct integers from 0 to 15.
Here, 0 represents the empty square.
For example, the initial arrangement is input as in Sample 1.

Output

Print Yes if the target arrangement of pieces can be created, and No otherwise.
Print a newline at the end.

Sample

1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 0

Yes

1 2 3 4
5 6 7 8
9 10 12 0
13 14 11 15

Yes

1 2 3 4
5 6 7 8
9 10 12 15
13 14 11 0

No