Shift It!

There is a square box 6 × 6 in size. It contains 36 chips 1 × 1 in size. Those chips contain 36 different characters — "0"-"9" and "A"-"Z". There is exactly one chip with each character.

You are allowed to make the following operations: you may choose one of 6 rows or one of 6 columns and cyclically shift the chips there to one position to the left or to the right (for the row) or upwards or downwards (for the column). Those operations are allowed to perform several times.

To solve the puzzle is to shift the chips using the above described operations so that they were written in the increasing order (exactly equal to the right picture). An example of solving the puzzle is shown on a picture below.

Write a program that finds the sequence of operations that solves the puzzle. That sequence should not necessarily be shortest, but you should not exceed the limit of 10000 operations. It is guaranteed that the solution always exists.

Input

The input data are represented by 6 lines containing 6 characters each. They are the puzzle's initial position. Those lines contain each character from the string "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ" exactly once.

Output

On the first line print number n, which is the number of operations. On the next n lines print the sequence of operations one per line. An operation is described by a word consisting of two characters. The first character shows the direction where the row or the column will be shifted. The possible directions are "L", "R" (to the left, to the right correspondingly, we shift a row), "U", "D" (upwards, downwards correspondingly, we shift a column). The second character is the number of the row (or the column), it is an integer from "1" to "6". The rows are numbered from the top to the bottom, the columns are numbered from the left to the right.

The number of operations should not exceed 104. If there are several solutions, print any of them.

Examples

Input

01W345 729AB6 CD8FGH IJELMN OPKRST UVQXYZ

Output

2 R2 U3

inputFormat

Input

The input data are represented by 6 lines containing 6 characters each. They are the puzzle's initial position. Those lines contain each character from the string "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ" exactly once.

outputFormat

Output

On the first line print number n, which is the number of operations. On the next n lines print the sequence of operations one per line. An operation is described by a word consisting of two characters. The first character shows the direction where the row or the column will be shifted. The possible directions are "L", "R" (to the left, to the right correspondingly, we shift a row), "U", "D" (upwards, downwards correspondingly, we shift a column). The second character is the number of the row (or the column), it is an integer from "1" to "6". The rows are numbered from the top to the bottom, the columns are numbered from the left to the right.

The number of operations should not exceed 104. If there are several solutions, print any of them.

Examples

Input

01W345 729AB6 CD8FGH IJELMN OPKRST UVQXYZ

Output

2 R2 U3

样例

01W345
729AB6
CD8FGH
IJELMN
OPKRST
UVQXYZ

260
D3
R2
D3
L2
D3
R2
D3
L2
D3
R2
D3
L2
D3
R2
D3
R2
U3
R2
D3
R2
U3
R2
D3
R2
U3
R2
D6
R2
D6
L2
D6
R2
D6
L2
D6
R2
D6
L2
D6
D5
R2
D5
L2
D5
R2
D5
L2
D5
R2
D5
L2
D5
D4
R2
D4
L2
D4
R2
D4
L2
D4
R2
D4
L2
D4
D3
R2
D3
L2
D3
R2
D3
L2
D3
R2
D3
L2
D3
D2
R2
D2
L2
D2
R2
D2
L2
D2
R2
D2
L2
D2
R3
D3
R3
U3
R3
D3
R3
U3
R3
D3
R3
U3
R3
D4
R3
D4
L3
D4
R3
D4
L3
D4
R3
D4
L3
D4
R3
D4
R3
U4
R3
D4
R3
U4
R3
D4
R3
U4
R3
R4
D3
R4
U3
R4
D3
R4
U3
R4
D3
R4
U3
R4
D4
R4
D4
L4
D4
R4
D4
L4
D4
R4
D4
L4
D4
R4
D4
R4
U4
R4
D4
R4
U4
R4
D4
R4
U4
R4
R5
D3
R5
U3
R5
D3
R5
U3
R5
D3
R5
U3
R5
D4
R5
D4
L5
D4
R5
D4
L5
D4
R5
D4
L5
D4
R5
D4
R5
U4
R5
D4
R5
U4
R5
D4
R5
U4
R5
R6
D3
R6
U3
R6
D3
R6
U3
R6
D3
R6
U3
R6
D4
R6
D4
L6
D4
R6
D4
L6
D4
R6
D4
L6
D4
R6
D4
R6
U4
R6
D4
R6
U4
R6
D4
R6
U4
R6
D4
R6
D4
L6
D4
R6
D4
L6
D4
R6
D4
L6
D4

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