{"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\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eThere are times you recall a good old friend and everything you\u0027ve come through together. Luckily there are social networks\u0026nbsp;— they store all your message history making it easy to know what you argued over 10 years ago.\u003c/p\u003e\u003cp\u003eMore formal, your message history is a sequence of messages ordered by time sent numbered from \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e where \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e is the total number of messages in the chat.\u003c/p\u003e\u003cp\u003eEach message might contain a link to an earlier message which it is a reply to. When opening a message \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e or getting a link to it, the dialogue is shown in such a way that \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e previous messages, message \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e next messages are visible (with respect to message \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e). In case there are less than \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e messages somewhere, they are yet all shown.\u003c/p\u003e\u003cp\u003eDigging deep into your message history, you always read all visible messages and then go by the link in the current message \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e (if there is one) and continue reading in the same manner.\u003c/p\u003e\u003cp\u003eDetermine the number of messages you\u0027ll read if your start from message number \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003c/span\u003e for all \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003c/span\u003e from \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e. Calculate these numbers independently. If you start with message \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e, the initial configuration is \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e itself, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e previous and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e next messages. Messages read multiple times are considered as one.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains two integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003en\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e0 ≤ \u003ci\u003ek\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e) — the total amount of messages and the number of previous and next messages visible.\u003c/p\u003e\u003cp\u003eThe second line features a sequence of integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e0 ≤ \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e \u0026lt; \u003ci\u003ei\u003c/i\u003e\u003c/span\u003e), where \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e denotes the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th message link destination or zero, if there\u0027s no link from \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e. All messages are listed in chronological order. It\u0027s guaranteed that the link from message \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e goes to message with number strictly less than \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e integers with \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th denoting the number of distinct messages you can read starting from message \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e and traversing the links while possible.\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\u003e6 0\n0 1 1 2 3 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1 2 2 3 3 3 \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\u003e10 1\n0 1 0 3 4 5 2 3 7 0\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2 3 3 4 5 6 6 6 8 2 \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 2\n0 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2 2 \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\u003eConsider \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e \u003d 6\u003c/span\u003e in sample case one. You will read message \u003cspan class\u003d\"tex-span\"\u003e6\u003c/span\u003e, then \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e, then \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e and then there will be no link to go.\u003c/p\u003e\u003cp\u003eIn the second sample case \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e \u003d 6\u003c/span\u003e gives you messages \u003cspan class\u003d\"tex-span\"\u003e5, 6, 7\u003c/span\u003e since \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e \u003d 1\u003c/span\u003e, then \u003cspan class\u003d\"tex-span\"\u003e4, 5, 6\u003c/span\u003e, then \u003cspan class\u003d\"tex-span\"\u003e2, 3, 4\u003c/span\u003e and then the link sequence breaks. The number of distinct messages here is equal to \u003cspan class\u003d\"tex-span\"\u003e6\u003c/span\u003e.\u003c/p\u003e"}}]}