# Expression

Time Limit: 1 Second    Memory Limit: 32768 KB
Special Judge

It is known that Sheffer stroke function (NOT-AND) 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 x|y 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 N-1 (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.
• (x|y) 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).

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.

## Output

Write to the output an expression for calculating overflow bit of the addition of two N-bit 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.

The output format consists of N output blocks. There is a blank line between output blocks.

```1

2
```

## Sample Output

`((A1|B1)|(((A0|B0)|(A0|B0))|((A1|A1)|(B1|B1))))`
Submit

Source: Northeastern Europe 1999