Snuke's Subway Trip

AtCoder

IDarc061_c

Time3000ms

Memory256MB

Difficulty—

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. The $i$\-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 $c_i$. You can change trains at a station where multiple lines are available. The 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. Snuke is now at station $1$ and wants to travel to station $N$ by subway. Find the minimum required fare. ## Constraints * $2 \leq N \leq 10^5$ * $0 \leq M \leq 2×10^5$ * $1 \leq p_i \leq N$ $(1 \leq i \leq M)$ * $1 \leq q_i \leq N$ $(1 \leq i \leq M)$ * $1 \leq c_i \leq 10^6$ $(1 \leq i \leq M)$ * $p_i \neq q_i$ $(1 \leq i \leq M)$ ## Input The input is given from Standard Input in the following format: $N$ $M$ $p_1$ $q_1$ $c_1$ : $p_M$ $q_M$ $c_M$ [samples]

Samples

Input #1

Output #1

1

Use company $1$'s lines: $1$ → $2$ → $3$. The fare is $1$ yen.

Input #2

Output #2

2

First, use company $1$'s lines: $1$ → $3$ → $2$ → $5$ → $6$. Then, use company $5$'s lines: $6$ → $7$ → $8$. The fare is $2$ yen.

Input #3

2 0

Output #3

\-1

API Response (JSON)

{
  "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 nu...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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