Mancunian is in a committed relationship with his girlfriend Nancy. His idea of a date is for them to have a romantic candlelight dinner and then play graph games. This time they are using a graph of $$N$$ nodes and $$E$$ edges. Mancunian is located at vertex $$M_1$$ and wants to move to $$M_2$$. Nancy wants to move from vertex $$N_1$$ to $$N_2$$. Anyone can move at any time, till both have reached their respective destinations. But there is a catch. Nancy can't bear to be too far away from her true love, Mancunian and hence the shortest distance between them at any point in time should never exceed a specified parameter $$K$$.
You are given several possible pairs of $$N_1$$, $$N_2$$ for Nancy. Count the number of such pairs which will make a valid game (where both Mancunian and Nancy can reach their respective destinations without violating the distance condition).
The first line contains three integers $$N$$, $$E$$ and $$K$$ denoting the number of vertices, number of edges in the graph and the maximum allowed distance between the two lovers respectively.
The following E lines contain two integers $$A$$ and $$B$$, denoting an undirected edge between those two vertices. There will be no self-loops or multiple edges in the graph.
Next line contains two integers $$M_1$$ and $$M_2$$ denoting the source and destination for Mancunian.
Next line contains a single integer $$Q$$ denoting the number of games.
Each of the next $$Q$$ lines contains two integers $$N_1$$ and $$N_2$$ denoting the source and destination for Nancy, for that game.
Print a single integer, denoting the number of valid games.
The game may proceed in the following manner. Mancunian moves to vertex $$3$$ and then Nancy also moves to $$3$$. Mancunian moves to $$4$$, and then $$5$$. Nancy moves to vertex $$6$$.