Water Containers Moves

There are two water containers: container A has volume a and container B has volume b. Your want to measure x units of water using the containers. Initially both containers are empty. On each move, you can fill a container, empty a container or move water from a container to another container. When you move water, you must always fill or empty at least one container. After the moves, container A must have x units of water. Find a sequence of moves where the total amount of moved water is minimum or state that it is impossible to measure the water.

Input

The only line has three integers a, b and x.

Output

First print two integers n and m: the number of moves and the total amount of water moved. After that print a sequence of n moves. Each move must move at least one unit of water and be one of the following:

FILL A: fill container A

FILL B: fill container B

EMPTY A: empty container A

EMPTY B: empty container B

MOVE A B: move water from container A to container B

MOVE B A: move water from container B to container A

If it is not possible to measure the water, only print -1.

Constraints

$1 \le a, b, x \le 1000$

Example

Input

5 3 4

Output

6 19
FILL A
MOVE A B
EMPTY B
MOVE A B
FILL A
MOVE A B