Make Same Set

AtCoder

IDarc156_f

Time4000ms

Memory256MB

Difficulty—

You are given three integer sequences of length $N$: $A=(A_1,A_2,\dots,A_N),B=(B_1,B_2,\dots,B_N),C=(C_1,C_2,\dots,C_N)$. Find one set of integers that satisfies the following conditions. * It can be obtained as follows: start with an empty set, and for each $i=1,2,\dots,N$ in this order, add $A_i$ or $B_i$ to the set. * It can be obtained as follows: start with an empty set, and for each $i=1,2,\dots,N$ in this order, add $A_i$ or $C_i$ to the set. * It has the maximum number of elements among the sets that satisfy the two conditions above. ## Constraints * $1 \leq N \leq 5000$ * $1 \leq A_i,B_i,C_i \leq 10000$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\dots$ $A_N$ $B_1$ $B_2$ $\dots$ $B_N$ $C_1$ $C_2$ $\dots$ $C_N$ [samples]

Samples

Input #1

Output #1

3
4 1 2

For the set $\lbrace 1,2,4\rbrace$, we have the following.

*   The first condition is satisfied because you can add $B_1,A_2,B_3$ to an empty set to obtain this set.
*   The second condition is satisfied because you can add $A_1,C_2,C_3$ to an empty set to obtain this set.

Clearly, any set satisfying these conditions has at most $N=3$ elements, so this set also satisfies the third condition.

Input #2

15
1 1 15 11 13 7 7 1 6 1 5 7 4 9 8
11 30 1 18 16 15 19 17 3 27 22 7 21 29 9
24 14 23 17 18 16 9 12 10 5 26 29 20 19 11

Output #2

12
7 9 11 17 19 1 15 4 5 6 29 13

API Response (JSON)

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    "name": "Make Same Set",
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      "content": "You are given three integer sequences of length $N$: $A=(A_1,A_2,\\dots,A_N),B=(B_1,B_2,\\dots,B_N),C=(C_1,C_2,\\dots,C_N)$. Find one set of integers that satisfies the following conditions. *   It can ",
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      "statement_type": "Markdown",
      "content": "You are given three integer sequences of length $N$: $A=(A_1,A_2,\\dots,A_N),B=(B_1,B_2,\\dots,B_N),C=(C_1,C_2,\\dots,C_N)$.\nFind one set of integers that satisfies the following conditions.\n\n*   It can ...",
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