Morris' Blog 我在摸索我存在的意義、生命的意義、內涵及價值。 沒有真正神手般的厲害，套用模式是大部分的情況。 沒那麼厲害的我存在的意義為何，襯托出神的存在？ 有時候不能怪別人不給我機會，我已經開始省思， 為什麼我沒有給別人機會的原因，而是全要靠別人。 有時候我認為我與眾不同，那是因為我做不到很多人能辦到的事情。 我聽不到、玩不起來、說得不夠明瞭、理解得不夠多， 我缺少的語文能力，就是一切一切無能的判定。 為此，我不曉得能做些對別人有幫助的事情。 我知道我自己是個不服輸的性格，但現在我不得不認輸。 我沒有能力，因此我必須認輸。 我到底來這世界作什麼？處處充滿不確定性， 而我總是無法出類拔萃，想當個一般人似乎也回不了頭了。 越強大的挑戰需要越強力的支持，而我的支持是什麼？ 最近嘗試與人談話，但都是失敗的結局，沒人能接受， 不需要言語，不需要溝通，一切所想都表達不出來。

49愛的鼓勵 6訂閱站台

Problem B
"Expression"

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 i^th bit of number A.
2. Bi is an expression that denotes value of i^th 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 first line of the input contains an integer indicating the number of test cases in the input. After that there is a blank line and the test cases separated by a blank line. Each test case consists of a single integer N (1 ≤ N ≤ 100) on a line by itself.

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. Print a blank line between test cases.

Note: The stroke symbol ( | ) is an ASCII character with code 124 (decimal).

The output file size shall not exceed 50*N bytes.

Sample input

1

2

Sample output for the sample input

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

---

NAND 全加器 的 carry 表示 cin 跟 cout

ai, bi, cin, cout
cout = (ai|bi)|(cin)|(ai or bi)
ai or bi = (ai|ai)|(bi|bi)


#include <stdio.h>
char s[105][5005];
int main() {
    sprintf(s[0], "((A0|B0)|(A0|B0))");
    int i, t;
    for(i = 1; i <= 100; i++) {
        sprintf(s[i], "((A%d|B%d)|(%s|((A%d|A%d)|(B%d|B%d))))", i, i, s[i-1], i, i, i, i);
    }
    scanf("%d", &t);
    while(t--) {
        scanf("%d", &i);
        puts(s[i-1]);
        if(t)   puts("");
    }
    return 0;
}