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D - Lunlun Number /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• X を(leading zeroなしで)十進数表記した際に、隣り合うどの 2 つの桁の値についても、差の絶対値が 1 以下

### 制約

• 1 \leq K \leq 10^5
• 入力はすべて整数である。

### 入力

K


### 入力例 1

15


### 出力例 1

23


1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22, 23
ですので、答えは 23 です。

### 入力例 2

1


### 出力例 2

1


### 入力例 3

13


### 出力例 3

21


### 入力例 4

100000


### 出力例 4

3234566667


Score : 400 points

### Problem Statement

A positive integer X is said to be a lunlun number if and only if the following condition is satisfied:

• In the base ten representation of X (without leading zeros), for every pair of two adjacent digits, the absolute difference of those digits is at most 1.

For example, 1234, 1, and 334 are lunlun numbers, while none of 31415, 119, or 13579 is.

You are given a positive integer K. Find the K-th smallest lunlun number.

### Constraints

• 1 \leq K \leq 10^5
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

K


### Sample Input 1

15


### Sample Output 1

23


We will list the 15 smallest lunlun numbers in ascending order:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22, 23.
Thus, the answer is 23.

### Sample Input 2

1


### Sample Output 2

1


### Sample Input 3

13


### Sample Output 3

21


### Sample Input 4

100000


### Sample Output 4

3234566667


Note that the answer may not fit into the 32-bit signed integer type.