Minimum Reachable City

AtCoder

IDabc295_g

Time3000ms

Memory256MB

Difficulty—

We have a directed graph $G_S$ with $N$ vertices numbered $1$ to $N$. It has $N-1$ edges. The $i$\-th edge $(1\leq i \leq N-1)$ goes from vertex $p_i\ (1\leq p_i \leq i)$ to vertex $i+1$. We have another directed graph $G$ with $N$ vertices numbered $1$ to $N$. Initially, $G$ equals $G_S$. Process $Q$ queries on $G$ in the order they are given. There are two kinds of queries as follows. * `1 u v` : Add an edge to $G$ that goes from vertex $u$ to vertex $v$. It is guaranteed that the following conditions are satisfied. * $u \neq v$. * On $G_S$, vertex $u$ is reachable from vertex $v$ via some edges. * `2 x` : Print the smallest vertex number of a vertex reachable from vertex $x$ via some edges on $G$ (including vertex $x$). ## Constraints * $2\leq N \leq 2\times 10^5$ * $1\leq Q \leq 2\times 10^5$ * $1\leq p_i\leq i$ * For each query in the first format: * $1\leq u,v \leq N$. * $u \neq v$. * On $G_S$, vertex $u$ is reachable from vertex $v$ via some edges. * For each query in the second format, $1\leq x \leq N$. * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $p_1$ $p_2$ $\dots$ $p_{N-1}$ $Q$ $\mathrm{query}_1$ $\mathrm{query}_2$ $\vdots$ $\mathrm{query}_Q$ Here, $\mathrm{query}_i$ denotes the $i$\-th query and is in one of the following formats: $1$ $u$ $v$ $2$ $x$ [samples]

Samples

Input #1

Output #1

4
2
1

*   At the time of the first query, only vertex $4$ is reachable from vertex $4$ via some edges on $G$.
*   At the time of the third query, vertices $2$, $3$, $4$, and $5$ are reachable from vertex $4$ via some edges on $G$.
*   At the time of the fifth query, vertices $1$, $2$, $3$, $4$, and $5$ are reachable from vertex $4$ via some edges on $G$.

Input #2

7
1 1 2 2 3 3
10
2 5
1 5 2
2 5
1 2 1
1 7 1
1 6 3
2 5
2 6
2 1
1 7 1

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Minimum Reachable City",
    "description": {
      "content": "We have a directed graph $G_S$ with $N$ vertices numbered $1$ to $N$. It has $N-1$ edges. The $i$\\-th edge $(1\\leq i \\leq N-1)$ goes from vertex $p_i\\ (1\\leq p_i \\leq i)$ to vertex $i+1$. We have anot",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc295_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a directed graph $G_S$ with $N$ vertices numbered $1$ to $N$. It has $N-1$ edges. The $i$\\-th edge $(1\\leq i \\leq N-1)$ goes from vertex $p_i\\ (1\\leq p_i \\leq i)$ to vertex $i+1$.\nWe have anot...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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