P6720 [BalkanOI 2011] decrypt

This is an **interactive IO problem**.

We randomly choose three numbers $R_0, R_1, R_2$, and generate the whole sequence $R$ by the following rule: $$R_n = R_{n-2} \oplus R_{n-1}$$ Here, $\oplus$ denotes the XOR operation. In addition, we have a function $M$, which is a bijection. That is, we guarantee that for $x \not= y$, $M(x) \not= M(y)$. Your goal is to determine $R_0, R_1, R_2, M(0), M(1), \ldots, M(255)$ after making multiple queries. #### Interaction Your program should read from standard input and write to standard output. You may output an integer $A$ to standard output. If this is your $N$-th query, you will read: $$M(A \oplus R_{N-1})$$ If you have obtained all answers, output a line with the string `SOLUTION`, and then output $259$ lines, which are $R_0, R_1, R_2, M(0), M(1), \ldots, M(255)$. **Remember to flush the output buffer after printing each line.**

N/A

# Hint #### Sample (Because the sample testdata is hard to present, it is placed here.) We manually set $R_0 = 0, R_1 = 1, R_2 = 3, M(i) = (i + 1) \bmod 256$. Then $R_3 = 1$. | Output | Input | Explanation | | :-: | :-: | :-: | | $10$ | $11$ | $M(10 \oplus 0) = M(10) = 11$ | | $10$ | $12$ | $M(10 \oplus 1) = M(11) = 12$ | | $11$ | $9$ | $M(11 \oplus 3) = M(8) = 9$ | | $12$ | $14$ | $M(12 \oplus 1) = M(13) = 14$ | | … | | Some outputs are omitted. | | ``SOLUTION`` | | Some outputs are omitted. | #### Constraints and limits For $100\%$ of the testdata, it is guaranteed that the input numbers, output numbers, the array $R$, and both $x$ and $M(x)$ in $M(x)$ are all $\ge 0$ and $\le 255$. #### Scoring policy If the number you output is not within the range above, you will fail. Your number of queries must be less than $320$, otherwise, you will fail. ###

#### Sample (Because the sample testdata is hard to present, it is placed here.) We manually set $R_0 = 0, R_1 = 1, R_2 = 3, M(i) = (i + 1) \bmod 256$. Then $R_3 = 1$. | Output | Input | Explanation | | :-: | :-: | :-: | | $10$ | $11$ | $M(10 \oplus 0) = M(10) = 11$ | | $10$ | $12$ | $M(10 \oplus 1) = M(11) = 12$ | | $11$ | $9$ | $M(11 \oplus 3) = M(8) = 9$ | | $12$ | $14$ | $M(12 \oplus 1) = M(13) = 14$ | | … | | Some outputs are omitted. | | ``SOLUTION`` | | Some outputs are omitted. | #### Constraints and limits For $100\%$ of the testdata, it is guaranteed that the input numbers, output numbers, the array $R$, and both $x$ and $M(x)$ in $M(x)$ are all $\ge 0$ and $\le 255$. #### Scoring policy If the number you output is not within the range above, you will fail. Your number of queries must be less than $320$, otherwise, you will fail. #### Hint How to flush the output buffer: C: ```c printf("%d\n", q); fflush(stdout); ``` C++: ```cpp cout