AT_arc227_a.Fermat Point of Binary Strings

A string of length $2N$ that contains $N$ occurrences of each of 0 and 1 is called a good string.

For good strings $S$ and $T$, let $\operatorname{dist}(S, T)$ denote the minimum number of swaps required to make $S$ equal to $T$ by swapping two adjacent characters of $S$ zero or more times.

You are given good strings $A$, $B$, and $C$. Among all good strings $X$, find one that minimizes the value of

\[ \operatorname{dist}(A, X)+\operatorname{dist}(B, X)+\operatorname{dist}(C, X), \]

and output it together with the minimum value.

长度为 $2N$ 且恰好包含 $N$ 个字符 0 和 $N$ 个字符 1 的字符串称为好字符串。

对于两个好字符串 $S$ 和 $T$，记 $\operatorname{dist}(S, T)$ 为：通过对 $S$ 中相邻字符进行零次或多次交换，使其变为 $T$ 所需的最少交换次数。

给定三个好字符串 $A$、$B$ 和 $C$。在所有好字符串 $X$ 中，找出一个使下式取最小值的 $X$：

[
\operatorname{dist}(A, X)+\operatorname{dist}(B, X)+\operatorname{dist}(C, X),
]

并输出该 $X$ 及对应的最小值。

The input is given from Standard Input in the following format:

$N$
$A$
$B$
$C$

输入从标准输入中按以下格式给出：

$N$
$A$
$B$
$C$

Let $K$ be the minimum value to be found, and let $X$ be a good string that achieves it. Output $K$ and $X$ in the following format:

$K$
$X$

If multiple outputs satisfy the conditions, you may output any of them.

设 $K$ 为待求的最小值，$X$ 为达到该最小值的一个好字符串。请按以下格式输出 $K$ 和 $X$：

$K$
$X$

若存在多个满足条件的输出，可任选其一输出。

Sample 1 Explanation:
If we choose 1010 as the good string $X$, then $\operatorname{dist}(A, X)$, $\operatorname{dist}(B, X)$, and $\operatorname{dist}(C, X)$ are $1$, $0$, $3$, respectively, and their sum is $4$. The sum of the distances cannot be made smaller than $4$.

Sample 2 Explanation:
Since the three input strings are all equal, choosing the same string as $X$ makes the sum of the distances $0$.

Constraints

• $1 \le N \le 2 \times 10^5$
• Each of $A$, $B$, and $C$ is a good string of length $2N$.
• $N$ is an integer.

样例 1 解释：
若选择 1010 作为好字符串 $X$，则 $\operatorname{dist}(A, X)$、$\operatorname{dist}(B, X)$ 和 $\operatorname{dist}(C, X)$ 分别为 $1$、$0$、$3$，其和为 $4$。该距离之和无法小于 $4$。

样例 2 解释：
由于三个输入字符串完全相同，选择该字符串作为 $X$ 可使距离之和为 $0$。

约束条件

• $1 \le N \le 2 \times 10^5$
• $A$、$B$ 和 $C$ 均为长度为 $2N$ 的好字符串。
• $N$ 为整数。