Jelly Raid

The boarders at Adephagia School For Boys have a thin time of it after dinner. Savings have cut pudding down to a single biscuit, while the masters finish every meal with raspberry jelly. A custard cream or a bourbon is not a bad biscuit, but the children want the jelly, so they have planned a midnight raid.

One child has to get from a bed in the dormitory across the school to the fridge in the kitchen without being seen by the patrolling masters.

The school is a grid of $r$ rows and $c$ columns, and every cell is either walkable or blocked. Time runs in turns numbered from $0$. On turn $0$ the child stands on the bed and every master stands on the first coordinate of its route.

On each later turn the child either stays where it is or steps to a walkable cell that shares an edge with the current one. At the same time every master takes one step along its route. A master walks its route from the first coordinate to the last, then turns around and walks back to the first, and repeats that forever. A master whose route holds a single coordinate never moves.

A master looks along its own row and its own column. The child is caught if at the end of a turn the child and some master share a row or a column and every cell strictly between them is walkable. A master standing on the child's own cell also catches the child. One master never blocks the view of another, only a blocked cell does. The same check applies on turn $0$.

The raid ends the moment the child stands on the fridge. Being seen on that same turn does not matter, because the child either sneaks back to bed unseen or gets caught full of jelly and does not care. The first sample case works out that way: the child reaches the fridge on turn 26 and a master spots it right then.

The first line has two integers $r$ and $c$ ($1 < r, c \le 60$), the number of rows and the number of columns.

The second line has two coordinates, the bed in the dormitory first and the fridge in the kitchen second. A coordinate is a row number and a column number inside parentheses, for example (2 5).

Each of the next $r$ lines has $c$ characters:

• . walkable area
• # blocked area

The next line has one integer $p$ ($1 \le p \le 200$), the number of patrolling masters.

Each of the next $p$ lines describes one patrol route: an integer $k$ ($1 \le k \le 7$) followed by $k$ coordinates. Two coordinates next to each other on a route are equal or share an edge.

The bed, the fridge and every route coordinate are walkable.

Print the minimum number of turns the child needs to reach the fridge. If the child cannot reach the fridge, print IMPOSSIBLE.