Problem Statement

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

Output

Print $k$, the number of elements in the set of integers satisfying the conditions, and $x_i\ (1\leq i \leq k)$, the $k$ elements of the set, in the following format:

k
x_1 x_2 \dots x_k

If multiple sets satisfy the conditions, you may print any of them.