{"raw_statement":[{"iden":"problem statement","content":"You are given $P$, a permutation of $(1,\\ 2,\\ ...\\ N)$.\nA string $S$ of length $N$ consisting of `0` and `1` is a _good string_ when it meets the following criterion:\n\n*   The sequences $X$ and $Y$ are constructed as follows:\n    *   First, let $X$ and $Y$ be empty sequences.\n    *   For each $i=1,\\ 2,\\ ...\\ N$, in this order, append $P_i$ to the end of $X$ if $S_i=$ `0`, and append it to the end of $Y$ if $S_i=$ `1`.\n*   If $X$ and $Y$ have the same number of _high_ elements, $S$ is a good string. Here, the $i$\\-th element of a sequence is called _high_ when that element is the largest among the elements from the $1$\\-st to $i$\\-th element in the sequence.\n\nDetermine if there exists a good string. If it exists, find the lexicographically smallest such string."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq P_i \\leq N$\n*   $P_1,\\ P_2,\\ ...\\ P_N$ are all distinct.\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$P_1$ $P_2$ $...$ $P_N$"},{"iden":"sample input 1","content":"6\n3 1 4 6 2 5"},{"iden":"sample output 1","content":"001001\n\nLet $S=$ `001001`. Then, $X=(3,\\ 1,\\ 6,\\ 2)$ and $Y=(4,\\ 5)$. The high elements in $X$ is the first and third elements, and the high elements in $Y$ is the first and second elements. As they have the same number of high elements, `001001` is a good string. There is no good string that is lexicographically smaller than this, so the answer is `001001`."},{"iden":"sample input 2","content":"5\n1 2 3 4 5"},{"iden":"sample output 2","content":"\\-1"},{"iden":"sample input 3","content":"7\n1 3 2 5 6 4 7"},{"iden":"sample output 3","content":"0001101"},{"iden":"sample input 4","content":"30\n1 2 6 3 5 7 9 8 11 12 10 13 16 23 15 18 14 24 22 26 19 21 28 17 4 27 29 25 20 30"},{"iden":"sample output 4","content":"000000000001100101010010011101"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}