AT_abc465_e.Digit Circus

Find, modulo $998244353$, the number of integers $x$ with $1 \leq x \leq N$ that satisfy exactly one of the following three conditions.

• $x$ is a multiple of $3$.
• The decimal representation of $x$ contains 3.
• Exactly three different digits are used in the decimal representation of $x$.

Here, the decimal representation of an integer should not have unnecessary leading 0s.

在模 $998244353$ 意义下，求满足以下恰好一个条件的整数 $x$ 的个数，其中 $1 \leq x \leq N$：

• $x$ 是 $3$ 的倍数；
• $x$ 的十进制表示中包含数字 3；
• $x$ 的十进制表示中恰好使用了三个不同的数字。

注意：整数的十进制表示不应包含多余的前导 0。

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

$N$

输入从标准输入中按以下格式给出：

$N$

Output the answer.

输出答案。

Sample 1 Explanation:
Among the integers from $1$ to $45$, there are $19$ integers satisfying exactly one of the conditions in the problem statement, as follows.

• There are $10$ integers satisfying only the first condition: $6, 9, 12, 15, 18, 21, 24, 27, 42, 45$.
• There are $9$ integers satisfying only the second condition: $13, 23, 31, 32, 34, 35, 37, 38, 43$.
• There are no integers satisfying only the third condition.

Sample 2 Explanation:
Below are examples of applicable integers.

• Integers satisfying only the first condition include $555$ and $1011$.
• Integers satisfying only the second condition include $343$ and $553$.
• Integers satisfying only the third condition include $1012$ and $704$.

Sample 3 Explanation:
There are no applicable integers.

Constraints

• $N$ is an integer.
• $1 \leq N < 10^{500}$

样例 1 解释：
在 $1$ 到 $45$ 的整数中，恰好满足题目所述三个条件中唯一一个条件的整数共有 $19$ 个，具体如下：

• 仅满足第一个条件的整数有 $10$ 个：$6, 9, 12, 15, 18, 21, 24, 27, 42, 45$。
• 仅满足第二个条件的整数有 $9$ 个：$13, 23, 31, 32, 34, 35, 37, 38, 43$。
• 没有任何整数仅满足第三个条件。

样例 2 解释：
以下是符合条件的整数示例：

• 仅满足第一个条件的整数包括 $555$ 和 $1011$。
• 仅满足第二个条件的整数包括 $343$ 和 $553$。
• 仅满足第三个条件的整数包括 $1012$ 和 $704$。

样例 3 解释：
不存在符合条件的整数。

约束条件

• $N$ 是一个整数。
• $1 \leq N < 10^{500}$