shunfurh 于 2017.09.07 18:14 提问
 Expression

It is known that Sheffer stroke function (NOTAND) can be used to construct any Boolean function. The truth table for this function is given below:
Truth table for Sheffer stroke function
x y xy
0 0 1
0 1 1
1 0 1
1 1 0
Consider the problem of adding two binary numbers A and B, each containing N bits. The individual bits of A and B are numbered from 0 (the least significant) to N1 (the most significant). The sum of A and B can always be represented by N+1 bits. Let's call most significant bit of the sum (bit number N) the overflow bit.Your task is to construct a logical expression using the Sheffer stroke function that computes the value of the overflow bit for arbitrary values of A and B. Your expression shall be constructed according to the following rules:
Ai is an expression that denotes value of ith bit of number A.
Bi is an expression that denotes value of ith bit of number B.
(xy) is an expression that denotes the result of Sheffer stroke function for x and y, where x and y are expressions.
When writing the index, i, for bits in A and B, the index shall be written as a decimal number without leading zeros. For example, bit number 12 of A must be written as A12. The expression should be completely parenthesized (according to the 3rd rule). No blanks are allowed inside the expression.Input
The input contains a single integer N (1 <= N <= 100).
Output
Write to the output an expression for calculating overflow bit of the addition of two Nbit numbers A and B according to the rules given in the problem statement.
Note: The stroke symbol (  ) is an ASCII character with code 124 (decimal).
The output file shall not exceed 50*N bytes.
This problem contains multiple test cases!
The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.
The output format consists of N output blocks. There is a blank line between output blocks.
Sample Input
1
2
Sample Output
((A1B1)(((A0B0)(A0B0))((A1A1)(B1B1))))