{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027$$$$$$\u0027, right: \u0027$$$$$$\u0027, display: true},\n {left: \u0027$$$\u0027, right: \u0027$$$\u0027, display: false},\n {left: \u0027$$\u0027, right: \u0027$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003ePolycarp likes arithmetic progressions. A sequence $$$[a_1, a_2, \\dots, a_n]$$$ is called an arithmetic progression if for each $$$i$$$ ($$$1 \\le i \u0026lt; n$$$) the value $$$a_{i+1} - a_i$$$ is the same. For example, the sequences $$$[42]$$$, $$$[5, 5, 5]$$$, $$$[2, 11, 20, 29]$$$ and $$$[3, 2, 1, 0]$$$ are arithmetic progressions, but $$$[1, 0, 1]$$$, $$$[1, 3, 9]$$$ and $$$[2, 3, 1]$$$ are not.\u003c/p\u003e\u003cp\u003eIt follows from the definition that any sequence of length one or two is an arithmetic progression.\u003c/p\u003e\u003cp\u003ePolycarp found some sequence of positive integers $$$[b_1, b_2, \\dots, b_n]$$$. He agrees to change each element by at most one. In the other words, for each element there are exactly three options: an element can be decreased by $$$1$$$, an element can be increased by $$$1$$$, an element can be left unchanged.\u003c/p\u003e\u003cp\u003eDetermine a minimum possible number of elements in $$$b$$$ which can be changed (by exactly one), so that the sequence $$$b$$$ becomes an arithmetic progression, or report that it is impossible.\u003c/p\u003e\u003cp\u003eIt is possible that the resulting sequence contains element equals $$$0$$$.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains a single integer $$$n$$$ $$$(1 \\le n \\le 100\\,000)$$$ — the number of elements in $$$b$$$.\u003c/p\u003e\u003cp\u003eThe second line contains a sequence $$$b_1, b_2, \\dots, b_n$$$ $$$(1 \\le b_i \\le 10^{9})$$$.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIf it is impossible to make an arithmetic progression with described operations, print \u003cspan class\u003d\"tex-font-style-tt\"\u003e-1\u003c/span\u003e. In the other case, print non-negative integer — the minimum number of elements to change to make the given sequence becomes an arithmetic progression. The only allowed operation is to add/to subtract one from an element (can\u0027t use operation twice to the same position).\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e4\n24 21 14 10\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e2\n500 500\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\n14 5 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e-1\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e5\n1 3 6 9 12\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eIn the first example Polycarp should increase the first number on $$$1$$$, decrease the second number on $$$1$$$, increase the third number on $$$1$$$, and the fourth number should left unchanged. So, after Polycarp changed three elements by one, his sequence became equals to $$$[25, 20, 15, 10]$$$, which is an arithmetic progression.\u003c/p\u003e\u003cp\u003eIn the second example Polycarp should not change anything, because his sequence is an arithmetic progression.\u003c/p\u003e\u003cp\u003eIn the third example it is impossible to make an arithmetic progression.\u003c/p\u003e\u003cp\u003eIn the fourth example Polycarp should change only the first element, he should decrease it on one. After that his sequence will looks like $$$[0, 3, 6, 9, 12]$$$, which is an arithmetic progression.\u003c/p\u003e"}}]}