Problem A: Pouring Water-I guess that everybody can play this game: There are two buckets(水桶). Bucket 1 has the capacity X and bucket 2 has Y liters(升). Then you are asked to measure Z liters of water in one of the two buckets, using the three operations:



　　　 1. F(i), which means fill the bucket i(1<=i<=2) with water



　　　 2. E(i), which means make the bucket i empty



　　　 3. P(i, j), which means pour water from bucket i to bucket j　After this operation either the bucket j is full or the bucket i is empty.



　　　 Duncan is so curious about this problem. He analyses this problem: First he check if the aim is achieved, if not, each time we need to choose one from these six operations from left to right:



　　　 F(1), F(2), E(1), E(2), P(1, 2), P(2, 1).



　　　 Duncan decides to search the answer by the order given in the upper.



So, you should help him find the shortest possible sequence of these operations that will measure exactly Z liters of water.





Input

The first line i