{"problem":{"name":"Linear Approximation","description":{"content":"Snuke has an integer sequence $A$ of length $N$. He will freely choose an integer $b$. Here, he will get sad if $A_i$ and $b+i$ are far from each other. More specifically, the _sadness_ of Snuke is ca","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc100_a"},"statements":[{"statement_type":"Markdown","content":"Snuke has an integer sequence $A$ of length $N$.\nHe will freely choose an integer $b$. Here, he will get sad if $A_i$ and $b+i$ are far from each other. More specifically, the _sadness_ of Snuke is calculated as follows:\n\n*   $abs(A_1 - (b+1)) + abs(A_2 - (b+2)) + ... + abs(A_N - (b+N))$\n\nHere, $abs(x)$ is a function that returns the absolute value of $x$.\nFind the minimum possible sadness of Snuke.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq A_i \\leq 10^9$\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\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc100_a","tags":[],"sample_group":[["5\n2 2 3 5 5","2\n\nIf we choose $b=0$, the sadness of Snuke would be $abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2$. Any choice of $b$ does not make the sadness of Snuke less than $2$, so the answer is $2$."],["9\n1 2 3 4 5 6 7 8 9","0"],["6\n6 5 4 3 2 1","18"],["7\n1 1 1 1 2 3 4","6"]],"created_at":"2026-03-03 11:01:13"}}