{"problem":{"name":"High Elements","description":{"content":"You are given $P$, a permutation of $(1,\\ 2,\\ ...\\ N)$. A string $S$ of length $N$ consisting of `0` and `1` is a _good string_ when it meets the following criterion: *   The sequences $X$ and $Y$ ar","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc028_e"},"statements":[{"statement_type":"Markdown","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.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq P_i \\leq N$\n*   $P_1,\\ P_2,\\ ...\\ P_N$ are all distinct.\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$P_1$ $P_2$ $...$ $P_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc028_e","tags":[],"sample_group":[["6\n3 1 4 6 2 5","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`."],["5\n1 2 3 4 5","\\-1"],["7\n1 3 2 5 6 4 7","0001101"],["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","000000000001100101010010011101"]],"created_at":"2026-03-03 11:01:13"}}