Problem:


Score : 700 points

Problem Statement

Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Constraints

2 \leq K \leq 10^5

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Sample Input 1

6

Sample Output 1

3

12=6×2 yields the smallest sum.

Sample Input 2

41

Sample Output 2

5

11111=41×271 yields the smallest sum.

Sample Input 3

79992

Sample Output 3

36



Sample input:
6


Sample output:
3

Submission status: Accepted

Solution code:
print([1, 3, 1, 1, 3, 2, 1, 9, 1, 2, 3, 2, 2, 3, 1, 2, 9, 2, 1, 3, 2, 2, 3, 1, 2, 9, 2, 2, 3, 3, 1, 6, 2, 2, 9, 3, 2, 3, 1, 5, 3, 3, 2, 9, 2, 2, 3, 2, 1, 3, 2, 3, 9, 2, 2, 3, 2, 2, 3, 2, 3, 9, 1, 2, 6, 3, 2, 3, 2, 3, 9, 2, 3, 3, 2, 2, 3, 4, 1, 9, 5, 3, 3, 2, 3, 3, 2, 2, 9, 2, 2, 3, 2, 2, 3, 2, 2, 18, 1, 2, 3, 2, 2, 3, 3, 3, 9, 2, 2, 3, 2, 2, 3, 2, 2, 9, 2, 3, 3, 2, 2, 6, 3, 1, 9, 2, 1, 3, 2, 2, 6, 2, 3, 9, 2, 2, 3, 2, 2, 3, 3, 2, 9, 2, 2, 3, 3, 2, 3, 3, 2, 9, 2, 3, 3, 2, 4, 3, 1, 2, 9, 3, 5, 6, 3, 2, 3, 2, 2, 9, 3, 3, 3, 2, 2, 3, 2, 2, 9, 2, 2, 3, 2, 3, 3, 4, 2, 9, 2, 3, 3, 2, 2, 3, 2, 2, 18, 3, 1, 3, 2, 3, 3, 5, 2, 9, 2, 2, 3, 2, 3, 3, 3, 3, 9, 3, 2, 6, 2, 3, 3, 2, 2, 9, 2, 3, 3, 2, 2, 6, 2, 2, 9, 2, 2, 6, 3, 7, 3, 2, 2, 9, 2, 2, 6, 2, 3, 3, 1, 2, 9, 2, 2, 3, 1, 2, 3, 3, 2, 9, 2, 2, 6, 3, 2, 3, 3, 2, 9, 5, 2, 3, 2, 2, 3, 3, 2, 9, 2, 2, 3, 3, 3, 3, 2, 5, 9, 2, 2, 3, 2, 2, 3, 2, 3, 18, 2, 2, 3, 3, 3, 6, 2, 2, 9, 3, 2, 3, 3, 3, 3, 2, 2, 9, 4, 3, 3, 4, 1, 3, 2, 3, 9, 2, 3, 3, 5, 2, 6, 2, 3, 9, 2, 3, 3, 2, 2, 3, 2, 4, 9, 2, 3, 3, 3, 3, 3, 2, 2, 9, 2, 2, 3, 3, 2, 3, 2, 3, 9, 2, 2, 6, 2, 2, 3, 2, 2, 9, 3, 3, 3, 2, 4, 3, 2, 3, 9, 2, 2, 3, 3, 2, 3, 2, 2, 9, 2, 2, 3, 3, 2, 3, 2, 4, 18, 3, 3, 6, 1, 2, 3, 3, 2, 9, 3, 6, 3, 2, 5, 6, 2, 2, 9, 3, 2, 3, 2, 2, 3, 2, 2, 9, 3, 2, 3, 3, 3, 6, 3, 3, 9, 2, 3, 3, 2, 2, 6, 3, 2, 9, 3, 3, 3, 2, 2, 3, 2, 2, 9, 6, 2, 3, 3, 2, 3, 2, 2, 9, 2, 2, 6, 2, 2, 3, 2, 3, 9, 3, 2, 3, 2, 4, 6, 2, 3, 9, 7, 3, 3, 3, 2, 3, 2, 2, 9, 2, 2, 3, 2, 2, 6, 3, 2, 18, 3, 3, 3, 2, 1, 3, 2, 2, 9, 2, 2, 3, 2, 2, 3, 4, 1, 9, 2, 2, 3, 2, 3, 3, 2, 2, 9, 3, 2, 3, 2, 3, 6, 2, 3, 9, 2, 5, 3, 3, 3, 3, 2, 2, 9, 2, 5, 3, 2, 2, 3, 3, 2, 9, 2, 3, 3, 4, 3, 3, 2, 2, 9, 3, 2, 6, 2, 3, 3, 2, 3, 9, 3, 2, 3, 2, 2, 3, 5, 2, 9, 2, 2, 3, 2, 3, 3, 4, 2, 9, 2, 3, 3, 3, 2, 3, 3, 2, 18, 3, 2, 3, 2, 3, 3, 2, 3, 9, 3, 2, 6, 2, 2, 3, 2, 2, 9, 3, 3, 6, 2, 2, 3, 2, 3, 9, 3, 3, 3, 1, 2, 6, 2, 3, 9, 3, 4, 3, 3, 2, 3, 2, 4, 9, 1, 2, 3, 3, 2, 3, 3, 2, 9, 2, 2, 3, 3, 2, 3, 2, 5, 9, 2, 2, 6, 2, 2, 3, 3, 2, 9, 3, 2, 3, 3, 4, 3, 2, 2, 9, 2, 2, 3, 3, 2, 3, 4, 3, 9, 2, 2, 3, 3, 3, 3, 2, 3, 18, 3, 2, 3, 5, 2, 3, 2, 2, 9, 3, 2, 3, 2, 4, 3, 2, 3, 9, 2, 3, 3, 2, 2, 9, 3, 3, 9, 2, 2, 3, 2, 2, 6, 2, 2, 9, 2, 3, 3, 4, 2, 3, 2, 4, 9, 2, 3, 6, 3, 2, 3, 2, 2, 9, 4, 3, 3, 3, 2, 3, 3, 3, 9, 3, 2, 6, 2, 2, 3, 3, 3, 9, 2, 2, 3, 2, 2, 3, 2, 3, 9, 3, 2, 3, 2, 5, 3, 4, 3, 9, 2, 2, 3, 3, 2, 3, 4, 3, 18, 3, 3, 3, 3, 3, 6, 3, 1, 9, 2, 4, 3, 2, 3, 3, 2, 2, 9, 2, 3, 12, 6, 3, 3, 3, 2, 9, 5, 2, 6, 2, 2, 6, 2, 3, 9, 2, 3, 3, 2, 3, 3, 2, 2, 9, 2, 3, 3, 2, 2, 6, 2, 2, 9, 2, 3, 3, 2, 3, 3, 3, 3, 9, 3, 2, 6, 2, 3, 6, 3, 2, 9, 3, 2, 3, 3, 4, 3, 3, 2, 9, 2, 2, 6, 2, 3, 3, 2, 2, 9, 3, 3, 3, 3, 2, 3, 2, 2, 18, 2, 2, 3, 2, 2, 3, 2, 3, 9, 3, 6, 3, 2, 2, 3, 3, 3, 18, 2, 3, 3, 4, 2, 3, 2, 2, 9, 3, 2, 3, 2, 3, 6, 3, 2, 9, 2, 2, 3, 2, 2, 3, 3, 4, 9, 2, 3, 3, 2, 2, 3, 5, 2, 9, 4, 3, 6, 4, 2, 3, 3, 2, 9, 3, 7, 6, 3, 4, 3, 3, 3, 9, 2, 2, 3, 2, 2, 3, 2, 2, 9, 2, 2, 3, 2, 2, 3, 4, 2, 9, 2, 2, 6, 2, 3, 3, 2, 3, 18, 3, 3, 3, 3, 3, 3, 2, 2, 27, 1, 2, 3, 3, 2, 3, 2, 3, 9, 2, 2, 3, 2, 3, 3, 3, 2, 9, 2, 2, 3, 2, 4, 6, 1, 5, 9, 4, 2, 3, 2, 3, 3, 2, 2, 9, 3, 3, 3, 3, 2, 3, 2, 3, 9, 2, 3, 3, 2, 2, 3, 2, 2, 9, 3, 2, 6, 3, 2, 3, 3, 2, 9, 2, 2, 3, 5, 4, 3, 2, 3, 9, 3, 3, 3, 3, 2, 3, 2, 3, 9, 2, 2, 3, 5, 3, 3, 2, 2, 18, 2, 2, 3, 3, 3, 6, 2, 2, 9, 2, 2, 3, 3, 2, 3, 3, 4, 9, 3, 2, 3, 4, 2, 3, 2, 2, 9, 2, 3, 3, 2, 2, 6, 3, 2, 9, 3, 2, 3, 2, 2, 3, 3, 2, 9, 3, 3, 3, 2, 3, 3, 3, 2, 9, 2, 2, 3, 3, 5, 3, 2, 3, 9, 2, 2, 6, 2, 3, 3, 3, 2, 9, 3, 3, 3, 2, 4, 3, 2, 2, 9, 2, 2, 3, 3, 2, 3, 4, 3, 9, 2, 2, 3, 2, 3, 6, 2, 3, 18, 5, 3, 3, 2, 2, 3, 7, 2, 9, 3, 4, 3, 2, 2, 3, 3, 2, 9, 3, 3, 3, 2, 3, 6, 2, 2, 9, 2, 2, 3, 3, 2, 6, 2, 2, 9, 2, 3, 3, 3, 2, 6, 3, 2, 9, 2, 2, 3, 2, 2, 3, 3, 4, 9, 4, 3, 3, 3, 3, 3, 2, 1, 9, 2, 2, 6, 2, 2, 3, 3, 2, 9, 3, 3, 3, 4, 2, 3, 3, 3, 9, 2, 5, 3, 3, 2, 3, 4, 2, 9, 3, 1, 3, 2, 3, 3, 2, 3, 18, 2, 2, 3, 2, 3, 3, 2, 3, 9, 2, 2, 3, 2, 2, 3, 2, 3, 9, 2, 3, 3, 4, 2, 3, 5, 4, 9, 2, 2, 3, 2, 3, 6, 4, 2, 9, 2, 3, 3, 2, 3, 3, 2, 2, 9, 3, 3, 3, 2, 3, 3, 2, 3, 9, 4, 4, 3, 2, 2, 3, 2, 3, 9, 3, 2, 6, 2, 5, 3, 2, 3, 9, 2, 2, 3, 3, 4, 3, 3, 2, 9, 3, 2, 3, 2, 2, 3, 2, 3, 9, 3, 2, 3, 2, 2, 3, 3, 3, 18, 4, 3, 3, 2, 3, 3, 3, 5, 9, 2, 2, 3, 3, 2, 3, 2, 3, 9, 2, 3, 3, 2, 2, 3, 3, 2, 9, 4, 3, 3, 3, 2, 6, 3, 3, 9, 2, 2, 3, 3, 3, 3, 2, 2, 9, 2, 2, 9, 5, 3, 3, 3, 3, 9, 2, 2, 3, 2, 2, 3, 2, 2, 9, 2, 2, 6, 2, 2, 3, 2, 3, 9, 2, 2, 3, 3, 2, 3, 2, 4, 9, 2, 3, 3, 3, 2, 3, 4, 2, 9, 2, 2, 3, 3, 2, 6, 3, 3, 18, 2, 2, 3, 2, 2, 3, 2, 3, 9, 2, 4, 3, 3, 2, 3, 4, 3, 9, 2, 3, 3, 4, 3, 3, 3, 3, 9, 3, 3, 6, 2, 6, 6, 3, 2, 9, 2, 3, 3, 2, 3, 3, 3, 2, 9, 2, 2, 6, 2, 3, 3, 3, 2, 9, 2, 3, 3, 2, 2, 3, 3, 3, 9, 2, 3, 6, 2, 2, 3, 3, 2, 9, 5, 3, 3, 2, 4, 3, 3, 2, 9, 2, 2, 3, 2, 2, 3, 2, 3, 9, 2, 3, 3, 2, 4, 3, 3, 2, 18, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 4, 6, 3, 3, 6, 1, 2, 9, 3, 2, 3, 4, 2, 3, 3, 2, 9, 3, 3, 3, 3, 2, 6, 2, 2, 9, 2, 2, 3, 3, 2, 12, 3, 6, 9, 3, 3, 3, 3, 3, 3, 2, 3, 9, 4, 5, 3, 2, 3, 6, 2, 2, 9, 2, 3, 6, 2, 2, 3, 3, 2, 9, 2, 2, 6, 3, 4, 3, 2, 2, 9, 3, 3, 3, 2, 2, 3, 2, 7, 9, 3, 2, 3, 3, 4, 3, 5, 2, 18, 2, 2, 6, 2, 2, 3, 2, 3, 9, 3, 2, 3, 3, 2, 3, 2, 2, 9, 3, 2, 3, 4, 3, 3, 3, 2, 9, 3, 3, 3, 2, 2, 6, 4, 2, 9, 3, 2, 6, 3, 3, 3, 2, 2, 9, 2, 3, 3, 2, 2, 3, 3, 3, 9, 4, 3, 3, 2, 3, 3, 2, 2, 9, 3, 2, 6, 2, 3, 6, 2, 2, 9, 3, 2, 3, 3, 2, 3, 2, 5, 9, 2, 3, 3, 3, 2, 3, 2, 3, 9, 2, 3, 3, 2, 2, 3, 2, 4, 18, 2, 2, 3, 2, 3, 3, 2, 2, 9, 2, 4, 3, 3, 2, 3, 3, 3, 9, 2, 3, 3, 6, 2, 3, 2, 2, 9, 2, 2, 3, 3, 3, 6, 3, 4, 18, 3, 2, 3, 3, 2, 3, 2, 4, 9, 2, 3, 3, 3, 2, 3, 2, 2, 9, 2, 3, 3, 2, 2, 3, 3, 2, 9, 3, 2, 6, 3, 3, 3, 2, 3, 9, 3, 2, 3, 2, 2, 3, 2, 2, 9, 2, 2, 3, 3, 3, 3, 4, 3, 9, 2, 2, 3, 3, 2, 3, 3, 2, 18, 2, 3, 3, 3, 5, 3, 2, 2, 9, 3, 4, 3, 3, 2, 6, 5, 4, 9, 2, 2, 3, 4, 3, 3, 2, 3, 9, 3, 3, 3, 7, 2, 6, 2, 3, 9, 4, 4, 3, 2, 3, 6, 3, 2, 9, 5, 2, 3, 2, 2, 3, 3, 2, 9, 2, 3, 3, 3, 2, 3, 2, 3, 9, 2, 2, 6, 2, 2, 3, 3, 2, 9, 2, 3, 3, 2, 4, 3, 2, 3, 9, 3, 2, 3, 2, 4, 6, 2, 2, 9, 3, 2, 3, 4, 2, 3, 3, 2, 18, 3, 3, 3, 3, 3, 3, 3, 3, 9, 3, 4, 3, 2, 2, 6, 2, 2, 27, 3, 1, 3, 2, 3, 3, 2, 3, 9, 2, 5, 3, 2, 2, 6, 3, 3, 9, 2, 2, 3, 2, 3, 3, 3, 2, 9, 3, 3, 3, 2, 3, 3, 2, 3, 9, 6, 2, 3, 2, 3, 3, 2, 2, 9, 4, 2, 6, 4, 1, 3, 5, 2, 9, 2, 4, 6, 2, 4, 3, 3, 2, 9, 3, 2, 3, 2, 2, 3, 2, 2, 9, 3, 3, 3, 3, 3, 3, 3, 3, 18, 2, 2, 3, 3, 2, 3, 3, 2, 9, 2, 2, 6, 3, 2, 3, 2, 2, 9, 2, 2, 3, 4, 2, 3, 2, 2, 9, 3, 3, 3, 2, 3, 6, 2, 3, 9, 2, 4, 3, 3, 3, 6, 2, 4, 9, 2, 2, 3, 2, 2, 3, 2, 5, 9, 4, 3, 3, 2, 2, 3, 3, 2, 9, 2, 3, 6, 3, 3, 3, 3, 3, 9, 2, 2, 3, 3, 2, 3, 3, 3, 9, 2, 2, 3, 2, 2, 3, 2, 5, 9, 3, 2, 3, 5, 2, 3, 2, 3, 18, 2, 2, 3, 2, 3, 3, 2, 3, 9, 3, 4, 6, 3, 2, 3, 2, 3, 9, 2, 2, 6, 2, 3, 3, 3, 3, 9, 2, 2, 3, 2, 3, 6, 4, 3, 9, 3, 3, 3, 2, 3, 3, 2, 4, 9, 2, 2, 3, 3, 2, 3, 2, 3, 9, 4, 2, 3, 3, 2, 3, 3, 2, 9, 2, 3, 6, 2, 3, 3, 2, 3, 9, 2, 3, 3, 2, 6, 3, 3, 2, 9, 2, 4, 3, 4, 3, 3, 2, 3, 9, 2, 3, 3, 3, 2, 3, 2, 2, 18, 3, 3, 3, 2, 3, 3, 2, 2, 9, 2, 2, 3, 2, 4, 3, 2, 3, 9, 5, 2, 3, 2, 2, 3, 3, 2, 9, 2, 2, 3, 2, 2, 6, 3, 2, 9, 3, 2, 3, 2, 3, 3, 2, 2, 9, 4, 3, 3, 3, 2, 3, 4, 2, 9, 4, 3, 3, 3, 2, 6, 2, 2, 9, 2, 2, 6, 2, 3, 3, 3, 3, 9, 2, 3, 3, 3, 4, 3, 3, 2, 9, 3, 2, 3, 2, 3, 3, 4, 2, 9, 3, 2, 6, 2, 2, 3, 3, 2, 18, 2, 5, 3, 3, 2, 3, 2, 2, 9, 2, 4, 3, 2, 7, 3, 2, 2, 9, 3, 3, 3, 4, 3, 3, 2, 2, 9, 2, 3, 3, 3, 3, 12, 2, 2, 9, 2, 3, 3, 3, 2, 3, 5, 2, 9, 3, 2, 6, 2, 2, 3, 2, 3, 9, 4, 2, 3, 2, 2, 3, 2, 3, 18, 2, 3, 6, 3, 2, 3, 2, 2, 9, 4, 2, 3, 3, 2, 3, 2, 3, 9, 2, 2, 6, 3, 3, 3, 2, 3, 9, 3, 2, 3, 2, 3, 3, 2, 2, 18, 2, 3, 3, 3, 3, 3, 4, 3, 9, 3, 4, 3, 3, 2, 3, 3, 3, 9, 3, 2, 3, 4, 2, 3, 1, 5, 9, 2, 2, 3, 2, 3, 6, 3, 2, 9, 2, 3, 3, 2, 3, 3, 2, 4, 9, 2, 3, 3, 3, 2, 3, 2, 4, 9, 2, 2, 3, 3, 3, 3, 3, 3, 9, 2, 2, 6, 5, 2, 3, 2, 3, 9, 2, 2, 3, 3, 4, 3, 2, 4, 9, 3, 3, 3, 1, 2, 3, 4, 2, 9, 3, 3, 3, 2, 2, 3, 3, 3, 18, 2, 2, 6, 2, 2, 3, 2, 2, 9, 3, 2, 3, 3, 2, 3, 3, 3, 9, 2, 2, 3, 2, 3, 3, 3, 2, 9, 2, 4, 3, 2, 2, 6, 3, 2, 9, 2, 2, 3, 3, 3, 3, 2, 4, 9, 2, 2, 3, 3, 5, 3, 4, 3, 9, 8, 2, 3, 2, 2, 3, 3, 2, 9, 3, 3, 6, 2, 4, 3, 2, 2, 9, 2, 2, 3, 3, 2, 3, 2, 2, 9, 3, 2, 3, 2, 2, 3, 2, 2, 9, 5, 3, 3, 3, 3, 3, 3, 2, 18, 3, 3, 3, 3, 2, 3, 3, 2, 9, 3, 4, 3, 4, 2, 3, 2, 2, 9, 2, 2, 3, 2, 2, 3, 3, 2, 9, 6, 3, 3, 2, 2, 6, 3, 2, 9, 5, 3, 3, 2, 2, 3, 3, 2, 9, 3, 2, 3, 2, 3, 3, 2, 3, 18, 4, 2, 3, 2, 3, 3, 2, 3, 9, 3, 3, 6, 2, 2, 3, 2, 2, 9, 2, 5, 3, 2, 2, 3, 3, 2, 9, 3, 3, 3, 2, 3, 3, 2, 2, 9, 2, 4, 3, 2, 3, 3, 3, 3, 18, 2, 4, 3, 3, 2, 3, 3, 2, 9, 3, 2, 3, 2, 3, 3, 5, 2, 9, 5, 2, 6, 2, 3, 3, 3, 3, 9, 2, 2, 3, 3, 2, 6, 3, 3, 9, 3, 2, 3, 3, 3, 3, 3, 2, 9, 2, 2, 3, 3, 3, 3, 2, 2, 9, 4, 4, 6, 3, 3, 3, 2, 3, 9, 2, 3, 6, 3, 3, 3, 3, 3, 9, 2, 2, 6, 2, 6, 3, 2, 3, 9, 3, 2, 3, 2, 2, 3, 2, 2, 9, 3, 2, 3, 2, 3, 9, 3, 5, 18, 3, 3, 3, 2, 3, 6, 3, 3, 9, 3, 2, 3, 2, 2, 3, 2, 2, 9, 2, 2, 3, 2, 2, 3, 2, 2, 9, 2, 2, 3, 2, 2, 6, 3, 2, 9, 2, 2, 3, 5, 2, 3, 3, 4, 9, 2, 2, 3, 2, 2, 3, 6, 3, 9, 2, 2, 3, 2, 2, 3, 4, 2, 9, 3, 2, 6, 3, 2, 3, 3, 3, 9, 2, 3, 3, 3, 4, 3, 2, 3, 9, 2, 2, 3, 2, 2, 3, 4, 3, 9, 2, 3, 6, 2, 3, 3, 3, 3, 18, 2, 2, 3, 2, 3, 3, 3, 2, 9, 2, 10, 3, 2, 2, 3, 3, 3, 9, 3, 2, 3, 4, 5, 3, 3, 3, 27, 2, 3, 3, 2, 4, 6, 3, 2, 9, 3, 2, 3, 3, 2, 3, 2, 4, 9, 3, 3, 3, 2, 3, 3, 3, 2, 9, 2, 3, 3, 3, 3, 6, 3, 2, 9, 6, 2, 6, 3, 3, 3, 2, 2, 9, 3, 2, 3, 3, 4, 3, 2, 2, 9, 3, 4, 3, 2, 3, 3, 2, 2, 9, 2, 2, 3, 2, 3, 6, 3, 2, 18, 3, 3, 3, 3, 3, 6, 2, 3, 9, 3, 2, 6, 3, 3, 3, 2, 2, 9, 2, 2, 3, 4, 3, 3, 3, 2, 9, 3, 2, 3, 3, 3, 6, 3, 2, 9, 2, 7, 3, 2, 3, 3, 2, 4, 9, 3, 5, 3, 3, 3, 3, 2, 2, 9, 4, 1, 3, 3, 3, 3, 2, 4, 9, 2, 2, 6, 2, 2, 3, 4, 2, 9, 2, 3, 3, 3, 2, 3, 3, 3, 9, 4, 2, 3, 3, 3, 3, 6, 2, 9, 4, 2, 3, 3, 3, 3, 2, 2, 18, 2, 3, 3, 3, 2, 3, 2, 3, 9, 3, 4, 3, 2, 3, 3, 3, 2, 9, 3, 3, 3, 4, 5, 6, 3, 3, 9, 3, 2, 6, 3, 1, 6, 2, 3, 9, 2, 3, 3, 2, 2, 3, 2, 4, 9, 2, 3, 3, 2, 3, 3, 2, 2, 9, 2, 3, 3, 3, 3, 3, 2, 3, 9, 2, 3, 6, 2, 2, 3, 2, 5, 9, 2, 2, 3, 2, 2, 3, 3, 3, 9, 2, 2, 12, 2, 3, 3, 6, 2, 9, 2, 3, 3, 3, 2, 3, 2, 3, 18, 3, 3, 3, 3, 2, 3, 3, 2, 9, 4, 4, 3, 5, 3, 3, 3, 2, 9, 3, 3, 6, 2, 2, 3, 2, 3, 9, 2, 2, 3, 3, 2, 6, 2, 2, 9, 2, 2, 3, 3, 3, 3, 2, 4, 9, 2, 2, 3, 2, 3, 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