{"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\u003eBizon the Champion isn\u0027t just a bison. He also is a favorite of the \"Bizons\" team.\u003c/p\u003e\u003cp\u003eAt a competition the \"Bizons\" got the following problem: \"You are given two distinct words (strings of English letters), \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003es\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003c/span\u003e. You need to transform word \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003es\u003c/i\u003e\u003c/span\u003e into word \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003c/span\u003e\". The task looked simple to the guys because they know the suffix data structures well. Bizon Senior loves suffix automaton. By applying it once to a string, he can remove from this string any single character. Bizon Middle knows suffix array well. By applying it once to a string, he can swap any two characters of this string. The guys do not know anything about the suffix tree, but it can help them do much more. \u003c/p\u003e\u003cp\u003eBizon the Champion wonders whether the \"Bizons\" can solve the problem. Perhaps, the solution do not require both data structures. Find out whether the guys can solve the problem and if they can, how do they do it? Can they solve it either only with use of suffix automaton or only with use of suffix array or they need both structures? Note that any structure may be used an unlimited number of times, the structures may be used in any order.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains a non-empty word \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003es\u003c/i\u003e\u003c/span\u003e. The second line contains a non-empty word \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003c/span\u003e. Words \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003es\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003c/span\u003e are different. Each word consists only of lowercase English letters. Each word contains at most 100 letters.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIn the single line print the answer to the problem. Print \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eneed tree\u003c/span\u003e\" (without the quotes) if word \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003es\u003c/i\u003e\u003c/span\u003e cannot be transformed into word \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003c/span\u003e even with use of both suffix array and suffix automaton. Print \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eautomaton\u003c/span\u003e\" (without the quotes) if you need only the suffix automaton to solve the problem. Print \"\u003cspan class\u003d\"tex-font-style-tt\"\u003earray\u003c/span\u003e\" (without the quotes) if you need only the suffix array to solve the problem. Print \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eboth\u003c/span\u003e\" (without the quotes), if you need both data structures to solve the problem.\u003c/p\u003e\u003cp\u003eIt\u0027s guaranteed that if you can solve the problem only with use of suffix array, then it is impossible to solve it only with use of suffix automaton. This is also true for suffix automaton.\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\u003eautomaton\ntomat\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eautomaton\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\u003earray\narary\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003earray\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\u003eboth\nhot\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eboth\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\u003eneed\ntree\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eneed tree\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 third sample you can act like that: first transform \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eboth\u003c/span\u003e\" into \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eoth\u003c/span\u003e\" by removing the first character using the suffix automaton and then make two swaps of the string using the suffix array and get \"\u003cspan class\u003d\"tex-font-style-tt\"\u003ehot\u003c/span\u003e\".\u003c/p\u003e"}}]}