Magical Ornament

AtCoder

IDabc190_e

Time2000ms

Memory256MB

Difficulty—

There are $N$ kinds of magical gems, numbered $1, 2, \ldots, N$, distributed in the AtCoder Kingdom. Takahashi is trying to make an ornament by arranging gems in a row. For some pairs of gems, we can put the two gems next to each other; for other pairs, we cannot. We have $M$ pairs for which the two gems can be adjacent: (Gem $A_1$, Gem $B_1$), (Gem $A_2$, Gem $B_2$), $\ldots$, (Gem $A_M$, Gem $B_M$). For the other pairs, the two gems cannot be adjacent. (Order does not matter in these pairs.) Determine whether it is possible to form a sequence of gems that has one or more gems of each of the kinds $C_1, C_2, \dots, C_K$. If the answer is yes, find the minimum number of stones needed to form such a sequence. ## Constraints * All values in input are integers. * $1 ≤ N ≤ 10^5$ * $0 ≤ M ≤ 10^5$ * $1 ≤ A_i < B_i ≤ N$ * If $i ≠ j$, $(A_i, B_i) ≠ (A_j, B_j)$. * $1 ≤ K ≤ 17$ * $1 ≤ C_1 < C_2 < \dots < C_K ≤ N$ ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $A_2$ $B_2$ $\hspace{7mm}\vdots$ $A_M$ $B_M$ $K$ $C_1$ $C_2$ $\cdots$ $C_K$ [samples]

Samples

Input #1

Output #1

5

For example, by arranging the gems in the order $[1, 4, 2, 4, 3]$, we can form a sequence of length $5$ with Gems $1, 2, 3$.

Input #2

Output #2

\-1

Input #3

Output #3

11

For example, by arranging the gems in the order $[1, 6, 7, 5, 8, 3, 9, 3, 8, 10, 2]$, we can form a sequence of length $11$ with Gems $1, 2, 7, 9$.

API Response (JSON)

{
  "problem": {
    "name": "Magical Ornament",
    "description": {
      "content": "There are $N$ kinds of magical gems, numbered $1, 2, \\ldots, N$, distributed in the AtCoder Kingdom.   Takahashi is trying to make an ornament by arranging gems in a row.   For some pairs of gems, we ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc190_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ kinds of magical gems, numbered $1, 2, \\ldots, N$, distributed in the AtCoder Kingdom.  \nTakahashi is trying to make an ornament by arranging gems in a row.  \nFor some pairs of gems, we ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments