Score: $300$ points

问题描述

一个非负整数 $n$ 被称为好整数，当它满足以下条件时：

• 在 $n$ 的十进制表示中，所有数字都是偶数（$0$, $2$, $4$, $6$, 和 $8$）。

例如，$0$、$68$ 和 $2024$ 都是好整数。

给定一个整数 $N$，请找出第 $N$ 小的好整数。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

A non-negative integer $n$ is called a good integer when it satisfies the following condition:

• All digits in the decimal notation of $n$ are even numbers ($0$, $2$, $4$, $6$, and $8$).

For example, $0$, $68$, and $2024$ are good integers.

You are given an integer $N$. Find the $N$-th smallest good integer.

Constraints

• $1 \leq N \leq 10^{12}$
• $N$ is an integer.

Input

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

$N$

Output

Print the $N$-th smallest good integer.

Sample Input 1

8

Sample Output 1

24

The good integers in ascending order are $0, 2, 4, 6, 8, 20, 22, 24, 26, 28, \dots$.
The eighth smallest is $24$, which should be printed.

Sample Input 2

133

Sample Output 2

2024

Sample Input 3

31415926535

Sample Output 3

2006628868244228

update @ 2024/3/10 01:25:04