{"problem":{"name":"Snuke's Subway Trip","description":{"content":"Snuke's town has a subway system, consisting of $N$ stations and $M$ railway lines. The stations are numbered $1$ through $N$. Each line is operated by a company. Each company has an identification nu","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc061_c"},"statements":[{"statement_type":"Markdown","content":"Snuke's town has a subway system, consisting of $N$ stations and $M$ railway lines. The stations are numbered $1$ through $N$. Each line is operated by a company. Each company has an identification number.\nThe $i$\\-th ( $1 \\leq i \\leq M$ ) line connects station $p_i$ and $q_i$ bidirectionally. There is no intermediate station. This line is operated by company $c_i$.\nYou can change trains at a station where multiple lines are available.\nThe fare system used in this subway system is a bit strange. When a passenger only uses lines that are operated by the same company, the fare is $1$ yen (the currency of Japan). Whenever a passenger changes to a line that is operated by a different company from the current line, the passenger is charged an additional fare of $1$ yen. In a case where a passenger who changed from some company A's line to another company's line changes to company A's line again, the additional fare is incurred again.\nSnuke is now at station $1$ and wants to travel to station $N$ by subway. Find the minimum required fare.\n\n## Constraints\n\n*   $2 \\leq N \\leq 10^5$\n*   $0 \\leq M \\leq 2×10^5$\n*   $1 \\leq p_i \\leq N$ $(1 \\leq i \\leq M)$\n*   $1 \\leq q_i \\leq N$ $(1 \\leq i \\leq M)$\n*   $1 \\leq c_i \\leq 10^6$ $(1 \\leq i \\leq M)$\n*   $p_i \\neq q_i$ $(1 \\leq i \\leq M)$\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $M$\n$p_1$ $q_1$ $c_1$\n:\n$p_M$ $q_M$ $c_M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc061_c","tags":[],"sample_group":[["3 3\n1 2 1\n2 3 1\n3 1 2","1\n\nUse company $1$'s lines: $1$ → $2$ → $3$. The fare is $1$ yen."],["8 11\n1 3 1\n1 4 2\n2 3 1\n2 5 1\n3 4 3\n3 6 3\n3 7 3\n4 8 4\n5 6 1\n6 7 5\n7 8 5","2\n\nFirst, use company $1$'s lines: $1$ → $3$ → $2$ → $5$ → $6$. Then, use company $5$'s lines: $6$ → $7$ → $8$. The fare is $2$ yen."],["2 0","\\-1"]],"created_at":"2026-03-03 11:01:14"}}