{"problem":{"name":"Swap and Flip","description":{"content":"We have $N$ cards numbered $1, 2, ..., N$. Card $i$ ($1 \\leq i \\leq N$) has an integer $A_i$ written in red ink on one side and an integer $B_i$ written in blue ink on the other side. Initially, these","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"keyence2020_d"},"statements":[{"statement_type":"Markdown","content":"We have $N$ cards numbered $1, 2, ..., N$. Card $i$ ($1 \\leq i \\leq N$) has an integer $A_i$ written in red ink on one side and an integer $B_i$ written in blue ink on the other side. Initially, these cards are arranged from left to right in the order from Card $1$ to Card $N$, with the red numbers facing up.\nDetermine whether it is possible to have a non-decreasing sequence facing up from left to right (that is, for each $i$ ($1 \\leq i \\leq N - 1$), the integer facing up on the $(i+1)$\\-th card from the left is not less than the integer facing up on the $i$\\-th card from the left) by repeating the operation below. If the answer is yes, find the minimum number of operations required to achieve it.\n\n*   Choose an integer $i$ ($1 \\leq i \\leq N - 1$). Swap the $i$\\-th and $(i+1)$\\-th cards from the left, then flip these two cards.\n\n## Constraints\n\n*   $1 \\leq N \\leq 18$\n*   $1 \\leq A_i, B_i \\leq 50$ ($1 \\leq i \\leq N$)\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$A_1$ $A_2$ $...$ $A_N$\n$B_1$ $B_2$ $...$ $B_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"keyence2020_d","tags":[],"sample_group":[["3\n3 4 3\n3 2 3","1\n\nBy doing the operation once with $i = 1$, we have a sequence $[2, 3, 3]$ facing up, which is non-decreasing."],["2\n2 1\n1 2","\\-1\n\nAfter any number of operations, we have the sequence $[2, 1]$ facing up, which is not non-decreasing."],["4\n1 2 3 4\n5 6 7 8","0\n\nNo operation may be required."],["5\n28 15 22 43 31\n20 22 43 33 32","\\-1"],["5\n4 46 6 38 43\n33 15 18 27 37","3"]],"created_at":"2026-03-03 11:01:14"}}