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The WeeOnes Kindergarten has a strange ceremony as part of its graduation: The children line up with the girls on the left and the boys on the right with a single space between the boys and the girls. By making a sequence of the following four moves, the children are to end up with all the boys on the left and all the girls on the right with a single space between the boys and the girls.
|Slide left (s)||The child to the right of the empty space moves into the empty space.|
|Slide right (S)||The child to the left of the empty space moves into the empty space.|
|Hop left (h)||The child two spaces to the right of the open space leapfrogs over the intervening child to the open space.|
|Hop right (H)||The child two spaces to the left of the open space leapfrogs over the intervening child to the open space.|
In each case, the previous position of the child who moved becomes the new open space.
For example, with two girls and two boys we begin with:
the following moves give the desired result:
The teacher would like this process to end in a reasonable amount of time so the parents can go home (the children are probably willing to do this all day). Write a program which takes as input the numbers of girls and boys (nGirls and nBoys respectively) and finds a sequence of at most (nGirls * nBoys + nGirls + nBoys) moves which takes you from the starting position to the ending position. [Each girl must leapfrog over (or be leapfrogged over by) each boy and, on average, each child must move past the empty space.]
The input begins with the number of problems N, (1 <= N <= 1000), on a line by itself followed by N problem instances each on its own line. A problem instance has the form:
There is at least 1 child and at most 24 children in a class.
For each problem instance, output the number of moves on a line. On following line, output the codes for the required moves in order.
3 2 2 4 0 5 10
8 sHShhSHs 2 HH 65 sHShhsHHHShhhhsHHHHHshhhhhsHHHHHshhhhhsHHHHHshhhhhSHHHHshhhSHHshS
Note: Other solutions are possible; for instance: