AT_abc456_d.Not Adjacent 2

You are given a string $S$ consisting of a, b, c.

Find the number of non-empty subsequences of $S$ in which no two adjacent characters are the same, modulo $998244353$.

Two subsequences are considered distinct if they are taken from different positions, even if they are identical as strings.

What is a subsequence? A subsequence of $S$ is a string obtained by removing zero or more characters from $S$ and concatenating the remaining characters in their original order. For example, ab, ac are subsequences of abc, but ca, bb are not subsequences of abc.

给你一个仅由字符 a、b、c 组成的字符串 $S$。

请你计算 $S$ 的非空子序列中，满足任意两个相邻字符均不相同的子序列个数，并对 $998244353$ 取模。

即使两个子序列作为字符串完全相同，只要它们是从原字符串中不同位置选取的，就视为不同的子序列。

什么是子序列？字符串 $S$ 的一个子序列是指从 $S$ 中删除零个或多个字符后，将剩余字符按其在 $S$ 中的原始顺序拼接而成的字符串。例如，ab 和 ac 都是 abc 的子序列，但 ca 和 bb 不是 abc 的子序列。

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

$S$

输入从标准输入中以如下格式给出：

$S$

Output the answer.

输出答案。

Sample 1 Explanation:
The subsequences in which no two adjacent characters are the same are the following $11$:

• a (the $1$st character of $S$)
• b (the $2$nd character of $S$)
• b (the $3$rd character of $S$)
• c (the $4$th character of $S$)
• ab (the $1$st, $2$nd characters of $S$)
• ab (the $1$st, $3$rd characters of $S$)
• ac (the $1$st, $4$th characters of $S$)
• bc (the $2$nd, $4$th characters of $S$)
• bc (the $3$rd, $4$th characters of $S$)
• abc (the $1$st, $2$nd, $4$th characters of $S$)
• abc (the $1$st, $3$rd, $4$th characters of $S$)

Note that, as with the $2$nd and $3$rd entries, two subsequences are considered distinct if they are taken from different positions, even if they are identical as strings.

Sample 2 Explanation:
Output the count modulo $998244353$.

Constraints

• $S$ is a string of length between $1$ and $3 \times 10^5$, inclusive, consisting of a, b, c.

样例 1 解释：
满足“任意两个相邻字符均不相同”这一条件的子序列共有以下 $11$ 个：

• a（取自 $S$ 的第 $1$ 个字符）
• b（取自 $S$ 的第 $2$ 个字符）
• b（取自 $S$ 的第 $3$ 个字符）
• c（取自 $S$ 的第 $4$ 个字符）
• ab（取自 $S$ 的第 $1$、$2$ 个字符）
• ab（取自 $S$ 的第 $1$、$3$ 个字符）
• ac（取自 $S$ 的第 $1$、$4$ 个字符）
• bc（取自 $S$ 的第 $2$、$4$ 个字符）
• bc（取自 $S$ 的第 $3$、$4$ 个字符）
• abc（取自 $S$ 的第 $1$、$2$、$4$ 个字符）
• abc（取自 $S$ 的第 $1$、$3$、$4$ 个字符）

注意：如第 $2$ 和第 $3$ 项所示，即使两个子序列作为字符串完全相同，只要它们取自原字符串中不同的位置，即视为不同的子序列。

样例 2 解释：
输出结果对 $998244353$ 取模。

约束条件

• $S$ 是一个仅由字符 a、b、c 组成的字符串，其长度在 $1$ 到 $3 \times 10^5$（含）之间。