AT_arc227_c.Follow the Letters

You are given a string $S$ of length $N$ consisting of lowercase English letters. Let $S_i$ denote the $i$-th character of $S$.

There are $N$ islands arranged in a circle, numbered island $1$, island $2$, $\ldots$, island $N$ in clockwise order. In particular, the island clockwise-adjacent to island $N$ is island $1$. The character $S_i$ is written on island $i$. Initially, there is one person on each island.

You can perform the following operation zero or more times.

• Choose one character $c$ that appears in $S$. Every person departs from the island they are currently on and moves one island at a time in the clockwise direction. Each person stops as soon as they first arrive, after departing, at an island on which the character $c$ is written. Even if the island a person is currently on has the character $c$ written on it, that person still departs.

Let $K$ be the minimum possible number of islands that have one or more people on them after all operations are finished.

Find $K$, and a sequence of operations that makes the number of islands with one or more people equal to $K$ after the operations.

Under the constraints of this problem, it can be proved that there always exists a sequence of operations of length at most $10^6$ that makes the number of islands with one or more people equal to $K$.

给你一个长度为 $N$ 的字符串 $S$，其中仅包含小写英文字母。记 $S_i$ 为字符串 $S$ 的第 $i$ 个字符。

有 $N$ 座岛屿按顺时针方向围成一圈，编号为岛屿 $1$、岛屿 $2$、$\ldots$、岛屿 $N$。特别地，岛屿 $N$ 顺时针方向的相邻岛屿是岛屿 $1$。岛屿 $i$ 上写着字符 $S_i$。初始时，每座岛屿上恰好有一个人。

你可以执行以下操作零次或多次：

• 选择一个在 $S$ 中出现的字符 $c$。此时，所有当前位于某座岛屿上的人均离开该岛，并逐岛沿顺时针方向移动；每个人在离开起始岛屿后，首次到达一座写有字符 $c$ 的岛屿时即停止。即使某人当前所在的岛屿上已写有字符 $c$，该人仍必须离开该岛。

设 $K$ 为所有操作结束后，至少有一人的岛屿数量的最小可能值。

请找出该最小值 $K$，并构造一个操作序列，使得执行该序列后，至少有一人的岛屿数量恰好为 $K$。

在本题约束下，可以证明：总存在一个长度不超过 $10^6$ 的操作序列，使得最终至少有一人的岛屿数量等于 $K$。

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

$N$
$S$

输入从标准输入中按以下格式给出：

$N$
$S$

Let $L$ be an integer representing the number of operations, and let $X$ be a string representing the sequence of operations. Output in the following format:

$K$
$L$
$X$

If $L=0$, output the third line as an empty line.

$L$ must satisfy $0 \le L \le 10^6$.

$X$ must be a string of length $L$ consisting of characters that appear in $S$, and the $i$-th character of $X$ represents the character chosen in the $i$-th operation.

After performing the operations according to the sequence $X$, the number of islands with one or more people must be $K$.

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

设 $L$ 为表示操作次数的整数，$X$ 为表示操作序列的字符串。请按如下格式输出：

$K$
$L$
$X$

若 $L=0$，则第三行输出为空行。

$L$ 必须满足 $0 \le L \le 10^6$。

$X$ 必须是长度为 $L$ 的字符串，其每个字符均来自集合 $S$；其中 $X$ 的第 $i$ 个字符表示第 $i$ 次操作所选的字符。

按照操作序列 $X$ 执行所有操作后，含有一人或以上人员的岛屿数量必须恰好为 $K$。

若存在多个满足条件的输出，可任选其一输出。

Sample 1 Explanation:
If we perform the operation choosing the character b, everyone gathers on the island on which the character b is written. The number of islands with people becomes $1$, and this is the minimum.

Sample 2 Explanation:
By choosing a first and then b, everyone gathers on the same island. The number of islands with people becomes $1$, and this is the minimum.

Sample 3 Explanation:
No matter which operation is performed, each person moves to the next island in the clockwise direction. Therefore, the number of islands with people is always $4$, so $K=4$. In this sample output, no operation is performed.

Constraints

• $1 \le N \le 1000$
• $S$ is a string of length $N$ consisting of lowercase English letters.
• $N$ is an integer.

样例 1 解释：
如果我们执行选择字符 b 的操作，则所有人将聚集在写有字符 b 的岛屿上。此时有人居住的岛屿数量为 $1$，这是最小值。

样例 2 解释：
先选择 a，再选择 b，所有人将聚集在同一座岛屿上。此时有人居住的岛屿数量为 $1$，这是最小值。

样例 3 解释：
无论执行哪一种操作，每个人均会顺时针移动到下一座岛屿。因此，有人居住的岛屿数量恒为 $4$，故 $K=4$。本样例的输出中未执行任何操作。

约束条件

• $1 \le N \le 1000$
• $S$ 是一个长度为 $N$ 的字符串，仅由小写英文字母组成。
• $N$ 是一个整数。