**C – Buddy Functions**

**Problem**

A buddy function on variable x is an expression constructed according to the following grammar:

E ::= ( E ) | E + E | E –
E | E * E | x | *num*

Here *num* represents an integer. Two buddy functions are equivalent
if they yield the same result for all values of the argument x. Write a program that given two buddy
functions determines if they are equivalent. The operators have the usual
arithmetical meaning.

**Input**

The input of your program consists of a single line containing an integer N, followed by a sequence of N pairs of text lines. Each such line contains a buddy function with up to 120 non-blank characters of length.

**Output **

The output of your program
consists a sequence of N text lines. Each line contains either the character **Y** (if the buddy functions in the i^{th}
pair are equivalent) or **N** (if
the buddy functions in the i^{th} pair are not equivalent).

**Sample Input**

**2**

**(4+x)*(4-x)**

**16-x*x**

**x*x*x*x**

**x*x+x*x**

**Sample Output**

**Y**

**N**