2284. Expression

Time Limit: 1.0 Seconds Memory Limit: 65536K Multiple test files

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:

1. `Ai` is an expression that denotes value of ith bit of number A.
2. `Bi` is an expression that denotes value of ith bit of number B.
3. `(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 file contains a single integer N (1 ≤ N ≤ 100).

### Output

Write to the output file 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 size shall not exceed 50*N bytes.

No special judge, make your output exactly the same with sample output, please.

### Sample input

`

    2

`

### Sample output for the sample input

`

    ((A1|B1)|(((A0|B0)|(A0|B0))|((A1|A1)|(B1|B1))))

`
Source: Northeastern European 1999

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