One Two Three

AtCoder

IDagc065_e

Time5000ms

Memory256MB

Difficulty—

You are given two sequences of positive integers of length $N$, $A=(A_1,A_2,\dots,A_N)$ and $B=(B_1,B_2,\dots,B_N)$. Find the minimum possible inversion number of a sequence of positive integers $C=(C_1,C_2,\dots,C_N)$ such that the $i$\-th element $C_i$ is $A_i$ or $B_i$. Solve $T$ test cases. ## Constraints * $1 \le T$ * $1 \le N \le 5 \times 10^5$ * $1 \le A_i,B_i \le \color{red}{\boldsymbol{3}}$ * The sum of $N$ for all test cases in a single input is at most $5 \times 10^5$. ## Input The input is given from Standard Input in the following format: $T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$ Here, $\mathrm{case}_i$ represents the $i$\-th test case. Each test case is given in the following format: $N$ $A_1$ $A_2$ $\dots$ $A_N$ $B_1$ $B_2$ $\dots$ $B_N$ [samples]

Samples

Input #1

8
3
2 1 1
3 3 2
5
2 1 3 2 2
1 2 1 2 3
8
2 1 3 3 3 1 2 2
1 2 3 1 2 1 3 2
10
1 3 2 1 1 3 2 2 2 2
2 3 1 1 1 1 3 1 3 3
12
2 1 1 3 3 1 3 3 2 2 2 1
3 1 1 3 3 1 3 2 3 2 1 2
15
1 3 1 3 3 2 2 1 2 3 3 3 1 1 3
3 3 3 2 3 2 1 3 2 1 2 2 3 3 3
18
3 1 1 3 3 2 1 1 2 3 2 1 3 3 3 2 2 3
1 1 3 2 1 3 1 2 1 2 3 2 2 1 3 1 3 3
20
2 2 3 1 1 3 2 3 3 1 3 1 2 1 2 2 1 2 3 2
1 1 1 3 3 1 1 3 2 2 1 1 1 1 1 2 2 2 2 1

Output #1

1
0
6
6
20
9
5
17

For the first test case, an optimal solution is $C=(2,3,2)$ with the inversion number of $1$.
For the second test case, an optimal solution is $C=(1,1,1,2,3)$ with the inversion number of $0$.

API Response (JSON)

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    "name": "One Two Three",
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      "statement_type": "Markdown",
      "content": "You are given two sequences of positive integers of length $N$, $A=(A_1,A_2,\\dots,A_N)$ and $B=(B_1,B_2,\\dots,B_N)$.\nFind the minimum possible inversion number of a sequence of positive integers $C=(C...",
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