PORALIS

AtCoder

IDagc074_c

Time2000ms

Memory256MB

Difficulty—

You are given a positive integer $N$. Output one pair of non-negative integer sequences $P=(P_1, P_2, \dots,P_N), A=(A_1, A_2, \dots,A_N)$ that satisfies all of the following conditions: * $0 \leq P_i < 2^{30}~(1 \leq i \leq N)$ * $0 \leq A_i < 2^{30}~(1 \leq i \leq N)$ * The length of a longest strictly increasing subsequence of $(P_1~\mathrm{OR}~A_i, P_2~\mathrm{OR}~A_i, \dots, P_N~\mathrm{OR}~A_i)$ is $i$. $(1 \leq i \leq N)$ * $\mathrm{OR}$ denotes the bitwise $\mathrm{OR}$ operation. It can be proved that under the constraints of this problem, there exists at least one pair $P, A$ that satisfies the conditions. Solve $T$ test cases per input. What is bitwise $\mathrm{OR}$?The bitwise $\mathrm{OR}$ of non-negative integers $A, B$, denoted $A\ \mathrm{OR}\ B$, is defined as follows: * When $A\ \mathrm{OR}\ B$ is written in binary, the digit at position $2^k$ ($k \geq 0$) is $1$ if at least one of the digits at position $2^k$ in the binary representations of $A$ and $B$ is $1$, and $0$ otherwise. For example, $3\ \mathrm{OR}\ 5 = 7$ (in binary: $011\ \mathrm{OR}\ 101 = 111$). ## Constraints * $1 \leq T$ * $1 \leq N \leq 1024$ * For test cases in a single input, the sum of $N$ is at most $200000$. * For test cases in a single input, the sum of $N^2$ is at most $1024^2$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$ Each case is given in the following format: $N$ [samples]

Samples

Input #1

Output #1

3 14 5
13 2 10
6 902 909 186 684 219 471 248
1023 249 64 0 264 768 778 794
2025
1026

For the first test case, the sample output is $P = (3, 14, 5), A = (13, 2, 10)$.

*   One longest strictly increasing subsequence of $(3~\mathrm{OR}~13, 14~\mathrm{OR}~13, 5~\mathrm{OR}~13) = (15, 15, 13)$ is $(13)$, whose length is $1$.
*   One longest strictly increasing subsequence of $(3~\mathrm{OR}~2, 14~\mathrm{OR}~2, 5~\mathrm{OR}~2) = (3, 14, 7)$ is $(3, 7)$, whose length is $2$.
*   One longest strictly increasing subsequence of $(3~\mathrm{OR}~10, 14~\mathrm{OR}~10, 5~\mathrm{OR}~10) = (11, 14, 15)$ is $(11, 14, 15)$, whose length is $3$.

From the above, it can be confirmed that $P = (3, 14, 5), A = (13, 2, 10)$ satisfies the conditions.

API Response (JSON)

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