{"raw_statement":[{"iden":"problem statement","content":"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.\n\n*   $S$ and $T$ contain the same number of `0`s.\n*   $S$ and $T$ contain the same number of `1`s.\n\nParticularly, for a good string pair $(S, T)$, $S$ and $T$ have the same length.\nFor a good string pair $(S, T)$, we define an undirected graph $G(S, T)$ as follows.\n\n*   Let $L$ be the length of $S$. Create a graph $g$ with vertices $1, 2, \\cdots, L$.\n*   Let $n$ be the number of `0`s in $S$. Let the indices of `0`s in $S$ be $1 \\leq a_1 < a_2 < \\cdots < a_n \\leq L$. Let the indices of `0`s 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 $g$.\n*   Let $m$ be the number of `1`s in $S$. Let the indices of `1`s in $S$ be $1 \\leq c_1 < c_2 < \\cdots < c_m \\leq L$. Let the indices of `1`s 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 $g$.\n*   The graph $g$ obtained through the above steps is $G(S, T)$.\n\nYou 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.\n\n*   Let $L$ be the length of $S$. It satisfies $N \\leq L \\leq 10^5$.\n*   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 $A_i = A_j$.\n\nIt can be proved that a solution always exists under the constraints of this problem."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 100$\n*   $1 \\leq A_i \\leq N$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $\\cdots$ $A_N$"},{"iden":"sample input 1","content":"3\n1 2 1"},{"iden":"sample output 1","content":"4\n0011\n1100\n\nFor the $S$ and $T$ in the sample output, we obtain $G(S, T)$ as follows:\n\n*   Prepare a graph $g$ with $4$ vertices.\n*   The indices of `0`s in $S$ are $(1, 2)$, and the indices of `0`s in $T$ are $(3, 4)$. Add edges $(1, 3)$ and $(2, 4)$ to $g$.\n*   The indices of `1`s in $S$ are $(3, 4)$, and the indices of `1`s in $T$ are $(1, 2)$. Add edges $(3, 1)$ and $(4, 2)$ to $g$.\n*   Let $G(S, T) = g$.\n\n$G(S, T)$ has a connected component with vertices $(1, 3)$ and another with vertices $(2, 4)$. This satisfies all the conditions, so this $(S, T)$ is a valid output."},{"iden":"sample input 2","content":"5\n1 2 3 4 5"},{"iden":"sample output 2","content":"5\n01010\n01010"},{"iden":"sample input 3","content":"6\n1 1 1 1 1 1"},{"iden":"sample output 3","content":"6\n011111\n111110"},{"iden":"sample input 4","content":"10\n1 2 3 2 4 3 4 4 5 6"},{"iden":"sample output 4","content":"21\n000101010111100011011\n011010000010101111110"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}