Problem Statement

A pair of strings $(S, T)$ consisting of 0 and 1 is called good if and only if all of the following conditions are satisfied.

• $S$ and $T$ contain the same number of 0s.
• $S$ and $T$ contain the same number of 1s.

Particularly, for a good string pair $(S, T)$, $S$ and $T$ have the same length.

For a good string pair $(S, T)$, we define an undirected graph $G(S, T)$ as follows.

• Let $L$ be the length of $S$. Create a graph $g$ with vertices $1, 2, \cdots, L$.
• Let $n$ be the number of 0s in $S$. Let the indices of 0s in $S$ be $1 \leq a_1 < a_2 < \cdots < a_n \leq L$. Let the indices of 0s in $T$ be $1 \leq b_1 < b_2 < \cdots < b_n \leq L$. For each $1 \leq i \leq n$, add an edge between vertices $a_i$ and $b_i$ to $g$.
• Let $m$ be the number of 1s in $S$. Let the indices of 1s in $S$ be $1 \leq c_1 < c_2 < \cdots < c_m \leq L$. Let the indices of 1s in $T$ be $1 \leq d_1 < d_2 < \cdots < d_m \leq L$. For each $1 \leq i \leq m$, add an edge between vertices $c_i$ and $d_i$ to $g$.
• The graph $g$ obtained through the above steps is $G(S, T)$.

You are given an integer sequence $A = (A_1, A_2, \cdots, A_N)$ of length $N$. Find one good string pair $(S, T)$ satisfying all of the following conditions.

• Let $L$ be the length of $S$. It satisfies $N \leq L \leq 10^5$.
• For each pair $1 \leq i, j \leq N$, vertices $i$ and $j$ belong to the same connected component in $G(S, T)$ if and only if $A_i = A_j$.

It can be proved that a solution always exists under the constraints of this problem.

Constraints

• $1 \leq N \leq 100$
• $1 \leq A_i \leq N$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

Print a solution in the following format:

L
S
T

Here, $L$ is the length of $S$ and $T$. If multiple solutions exist, any of them will be accepted.