Grafting

AtCoder

IDagc027_f

Time5000ms

Memory256MB

Difficulty—

Snuke has found two trees $A$ and $B$, each with $N$ vertices numbered $1$ to $N$. The $i$\-th edge of $A$ connects Vertex $a_i$ and $b_i$, and the $j$\-th edge of $B$ connects Vertex $c_j$ and $d_j$. Also, all vertices of $A$ are initially painted white. Snuke would like to perform the following operation on $A$ zero or more times so that $A$ coincides with $B$: * Choose a leaf vertex that is painted white. (Let this vertex be $v$.) * Remove the edge incident to $v$, and add a new edge that connects $v$ to another vertex. * Paint $v$ black. Determine if $A$ can be made to coincide with $B$, ignoring color. If the answer is yes, find the minimum number of operations required. You are given $T$ cases of this kind. Find the answer for each of them. ## Constraints * $1 \leq T \leq 20$ * $3 \leq N \leq 50$ * $1 \leq a_i,b_i,c_i,d_i \leq N$ * All given graphs are trees. ## Input Input is given from Standard Input in the following format: $T$ $case_1$ $:$ $case_{T}$ Each case is given in the following format: $N$ $a_1$ $b_1$ $:$ $a_{N-1}$ $b_{N-1}$ $c_1$ $d_1$ $:$ $c_{N-1}$ $d_{N-1}$ [samples]

Samples

Input #1

Output #1

1
-1

*   The graph in each case is shown below.
*   In case $1$, $A$ can be made to coincide with $B$ by choosing Vertex $1$, removing the edge connecting $1$ and $2$, and adding an edge connecting $1$ and $3$. Note that Vertex $2$ is not a leaf vertex and thus cannot be chosen.

![image](https://img.atcoder.jp/agc027/3f020b4a4e883680357cc55adb571fbc.png)

Input #2

Output #2

6
0
7

*   $A$ may coincide with $B$ from the beginning.

API Response (JSON)

{
  "problem": {
    "name": "Grafting",
    "description": {
      "content": "Snuke has found two trees $A$ and $B$, each with $N$ vertices numbered $1$ to $N$. The $i$\\-th edge of $A$ connects Vertex $a_i$ and $b_i$, and the $j$\\-th edge of $B$ connects Vertex $c_j$ and $d_j$.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 5000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc027_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke has found two trees $A$ and $B$, each with $N$ vertices numbered $1$ to $N$. The $i$\\-th edge of $A$ connects Vertex $a_i$ and $b_i$, and the $j$\\-th edge of $B$ connects Vertex $c_j$ and $d_j$....",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments