2605：Snake

Snake is a popular game , and I believe most of us had played it . The Original game is that you can control a snake to eat the magic bean and after the snake eat one magic bean , the length of the snake’s body will get longer .But today we are talking about a new game. These are the rules of the new Snake Game :
1. The length of the snake’s body won’t change even though it eat a magic bean.
2. Some pairs of the beans have a relation , that is, one of them can not be eaten until another one had been eaten . We call the latter “the key bean” . For example , if A can’t be eaten until B had been eaten ,we say “B is the key bean of A”. (That means when A can’t be eaten , the snake can not move into the grid where A is.)
3. The snake could not move to a wall or its body.Befor it move,it will chooses an adjacent vacant square of its head,which is neither a stone nor occupied by its body.
Figure 1 and figure2 shows how the snake move

Figure 1

Figure 2

The first line contain a integer T (T <= 10).Followed by T cases. Each case contain five parts.
The first part: six integers ,H,W,L,K,R,N,(H <= 20 , W <= 20 , L <= 8 , K <= 7 ) means the height of the map , the width of the map , the length of the snake’s body, the number of the magic beans . the number of the relations , the number of the wall respectively.
The second part: L lines , each line contain two integer h_i ,w_i, indicating the original position of each block of snake's body, from B₁(h₁,w₁) to B_L(h_L,w_L) orderly, where 1<=h_i<=H, and 1<=w_i<=W,1<=i<=L.
The third part: K lines ,each line contain two integer h_i ,w_i , indicating the position of each magic bean , from MB₁(h₁,w₁) to MB_K(h_K,w_K) orderly, where 1<=h_i<=H, and 1<=w_i<=W,1<=i<=K.
The fourth part : R lines , each line contain two integer A ,B means “A is the key bean of B ”. The A and B may appear several times , but “one bean will have only one key bean”.
The fifth part: N lines , each line contain two integer h_i ,w_i , indicating the position of each wall , from W₁(h₁,w₁) to W_N(h_N,w_N) orderly, where 1<=h_i<=H, and 1<=w_i<=W,1<=i<=N.

For each case , if the snake could eat all the magic beans , output the minimum step it took. If the snake could not , just output “-1” (without the quotation marks) .