Slot Strategy

AtCoder

IDabc252_c

Time2000ms

Memory256MB

Difficulty—

There is a slot machine with $N$ reels. The placement of symbols on the $i$\-th reel is represented by a string $S_i$ of length $10$ containing each of `0`, `1`, $\ldots$, `9` exactly once. Each reel has a corresponding button. For each non-negative integer $t$, Takahashi can press one of the buttons of his choice (or do nothing) $t$ seconds after the reels start spinning. If the button for the $i$\-th reel is pressed $t$ seconds after the start of the spin, the $i$\-th reel will stop to display the $((t\bmod{10})+1)$\-th character of $S_i$. Here, $t\bmod{10}$ denotes the remainder when $t$ is divided by $10$. Takahashi wants to stop all reels to make them display the same character. Find the minimum number of seconds needed to achieve his objective after the start of the spin. ## Constraints * $2\leq N\leq 100$ * $N$ is an integer. * $S_i$ is a string of length $10$ containing each of `0`, `1`, $\ldots$, `9` exactly once. ## Input Input is given from Standard Input in the following format: $N$ $S_1$ $S_2$ $\vdots$ $S_N$ [samples]

Samples

Input #1

Output #1

6

Takahashi can make all reels display `8` in $6$ seconds after the start of the spin by stopping them as follows.

*   $0$ seconds after the start of the spin, press the button for the $2$\-nd reel, making it stop to display the $((0\bmod{10})+1=1)$\-st character of $S_2$, `8`.
*   $2$ seconds after the start of the spin, press the button for the $3$\-rd reel, making it stop to display the $((2\bmod{10})+1=3)$\-rd character of $S_3$, `8`.
*   $6$ seconds after the start of the spin, press the button for the $1$\-st reel, making it stop to display the $((6\bmod{10})+1=7)$\-th character of $S_1$, `8`.

There is no way to make all reels display the same character in five seconds or less, so the answer is $6$.

Input #2

Output #2

40

Note that he must _stop_ all reels to make them display the same character.

API Response (JSON)

{
  "problem": {
    "name": "Slot Strategy",
    "description": {
      "content": "There is a slot machine with $N$ reels.   The placement of symbols on the $i$\\-th reel is represented by a string $S_i$ of length $10$ containing each of `0`, `1`, $\\ldots$, `9` exactly once. Each ree",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc252_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a slot machine with $N$ reels.  \nThe placement of symbols on the $i$\\-th reel is represented by a string $S_i$ of length $10$ containing each of `0`, `1`, $\\ldots$, `9` exactly once.\nEach ree...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments