### Cat and Mouse

Time Limit: 1000 ms
Memory Limit: 10000 KiB

#### Problem Description

In a house with many rooms live a cat and a mouse. The cat and the

mouse each have chosen one room as their "home". From their "home"

they regularly walk through the house. A cat can go from room A to

room B if and only if there is a cat door from room A to room B. Cat

doors can only be used in one direction. Similarly a mouse can go from

room A to room B if and only if there is a mouse door from room A to

room B . Also mouse doors can be used in only one direction.

Furthermore, cat doors cannot be used by a mouse, and mouse doors

cannot be used by a cat.

Given a map of the house you are asked to write a program that finds

out

1. if there exist walks for the cat and mouse where they meet each

other in some room, and

2.

3. if the mouse can make a walk through at least two rooms, end in

its "home" room again, and along the way cannot ever meet the cat.

(Here, the mouse may not ever meet the cat, whatever the cat

does.)

[INLINE]

For example, in the map, the cat can meet the mouse in rooms 0, 1, and

2. Also, the mouse can make a walk through two rooms without ever

meeting the cat, viz., a round trip from room 4 to 3 and back.

#### Input

The input consists of integers and defines the configuration of the

house. The first line has three integers separated by blanks: the

first integer defines the number of rooms, the second the initial room

of the cat (the cat's "home"), and the third integer defines the

initial room of the mouse (the mouse's "home"). Next there are zero or

more lines, each with two positive integers separated by a blank.

These lines are followed by a line with two _1's separated by a blank.

The pairs of positive integers define the cat doors. The pair A B

represents the presence of a cat door from room A to room B . Finally

there are zero or more lines, each with two positive integers

separated by a blank. These pairs of integers define the mouse doors.

Here, the pair A B represents the presence of a mouse door from room A

to room B .

The number of rooms is at least one and at most 100. All rooms are

numbered consecutively starting at 0. You may assume that all positive

integers in the input are legal room numbers.

#### Output

The output consists of two characters separated by a blank and ended

by a new-line character. The first character is Y if there exist walks

for the cat and mouse where they meet each other in some room.

Otherwise, it is N. The second character is Y if the mouse can make a

walk through at least two rooms, end in its "home" room again, and

along the way cannot ever meet the cat. Otherwise, it is N.

#### Sample Input

5 2 4 0 1 1 0 2 0 3 2 4 1 -1 -1 0 2 1 4 2 3 3 0 3 1 3 4 4 3

#### Sample Output

Y Y