Score : $300$ points

问题描述

存在一个具有 $N$ 个转轴的老虎机。
第 $i$ 个转轴上的符号排列由长度为 $10$ 的字符串 $S_i$ 表示，其中恰好包含每个字符 0、1、$\ldots$、9 各一次。

每个转轴都有一个对应的按钮。对于每个非负整数 $t$，高桥可以在转轴开始旋转后$t$秒时选择按下任意一个按钮（或不操作）。
如果在转轴开始旋转后$t$秒时按下第 $i$ 个转轴的按钮，则第 $i$ 个转轴会停止并显示 $S_i$ 中的第 $((t\bmod{10})+1)$ 个字符。
这里，$t\bmod{10}$ 表示当 $t$ 除以 $10$ 时的余数。

高桥希望让所有转轴停下并显示相同的字符。
找出转轴开始旋转后实现这一目标所需的最短秒数。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

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:

$N$

$S_1$

$S_2$

$\vdots$

$S_N$

Output

Print the minimum number of seconds needed to achieve Takahashi's objective after the start of the spin.

Sample Input 1

3
1937458062
8124690357
2385760149

Sample 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 $6$.

Sample Input 2

5
0123456789
0123456789
0123456789
0123456789
0123456789

Sample Output 2

40

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

update @ 2024/3/10 10:45:26