{"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\u003eMusicians of a popular band \"Flayer\" have announced that they are going to \"make their exit\" with a world tour. Of course, they will visit Berland as well.\u003c/p\u003e\u003cp\u003eThere are \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e cities in Berland. People can travel between cities using two-directional train routes; there are exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e routes, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th route can be used to go from city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e to city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (and from \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e), and it costs \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e coins to use this route.\u003c/p\u003e\u003cp\u003eEach city will be visited by \"Flayer\", and the cost of the concert ticket in \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th city is \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 coins.\u003c/p\u003e\u003cp\u003eYou have friends in every city of Berland, and they, knowing about your programming skills, asked you to calculate the minimum possible number of coins they have to pay to visit the concert. For every city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e you have to compute the minimum number of coins a person from city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e has to spend to travel to some city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ej\u003c/i\u003e\u003c/span\u003e (or possibly stay in city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e), attend a concert there, and return to city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e (if \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ej\u003c/i\u003e ≠ \u003ci\u003ei\u003c/i\u003e\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eFormally, for every \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/f35cd9483b275a4118d7014f714fb814?v\u003d1719752331\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e you have to calculate \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/94683cdcd15025880d4eea9b601e5623?v\u003d1719752331\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e, where \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e(\u003ci\u003ei\u003c/i\u003e, \u003ci\u003ej\u003c/i\u003e)\u003c/span\u003e is the minimum number of coins you have to spend to travel from city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e to city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ej\u003c/i\u003e\u003c/span\u003e. If there is no way to reach city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ej\u003c/i\u003e\u003c/span\u003e from city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e, then we consider \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e(\u003ci\u003ei\u003c/i\u003e, \u003ci\u003ej\u003c/i\u003e)\u003c/span\u003e to be infinitely large.\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\u003em\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e2 ≤ \u003ci\u003en\u003c/i\u003e ≤ 2·10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003em\u003c/i\u003e ≤ 2·10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThen \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e lines follow, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th contains three integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ev\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003eu\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ \u003ci\u003en\u003c/i\u003e, \u003ci\u003ev\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≠ \u003ci\u003eu\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e12\u003c/sup\u003e\u003c/span\u003e) denoting \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th train route. There are no multiple train routes connecting the same pair of cities, that is, for each \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ev\u003c/i\u003e, \u003ci\u003eu\u003c/i\u003e)\u003c/span\u003e neither extra \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ev\u003c/i\u003e, \u003ci\u003eu\u003c/i\u003e)\u003c/span\u003e nor \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003eu\u003c/i\u003e, \u003ci\u003ev\u003c/i\u003e)\u003c/span\u003e present in input.\u003c/p\u003e\u003cp\u003eThe next line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e 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\u003ek\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e12\u003c/sup\u003e\u003c/span\u003e) — price to attend the concert in \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th city.\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. \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th of them must be equal to the minimum number of coins a person from city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e has to spend to travel to some city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ej\u003c/i\u003e\u003c/span\u003e (or possibly stay in city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e), attend a concert there, and return to city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e (if \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ej\u003c/i\u003e ≠ \u003ci\u003ei\u003c/i\u003e\u003c/span\u003e).\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 2\n1 2 4\n2 3 7\n6 20 1 25\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e6 14 1 25 \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 3\n1 2 1\n2 3 1\n1 3 1\n30 10 20\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e12 10 12 \n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}