Problem Description

Define the digit product of a positive integer as the result of multiplying each digit of the number. For example:

The digit product of $2612$ is: $2 \times 6 \times 1 \times 2 = 24$.

Define the self-product of a positive integer as the result of multiplying the number by its digit product. For example:

The self-product of $2612$ is: $2612 \times 24 = 62688$.

Given two integers $A$ and $B$, please find the number of positive integers whose self-product lies within the interval $[A, B]$.

Input Format

Input consists of two integers $A$ and $B$ on a single line.

Output Format

Output a single integer, which is the count of positive integers whose self-product is within the interval $[A, B]$.

Sample Input and Output

Sample Input #1

20 30

Sample Output #1

2

Sample Input #2

145 192

Sample Output #2

4

Sample Input #3

2224222 2224222

Sample Output #3

1

Notes

Sample 1 Explanation

There are four positive integers that meet the criteria: $19, 24, 32, 41$. Their self-products are $171, 192, 192, 164$ respectively.

Data Size and Constraints

• For $25\%$ of the data, $A \le B \le 10^8$;
• For another $15\%$ of the data, $A \le B \le 10^{12}$;
• For $100\%$ of the data, $1 \le A \le B < 10^{18}$.

Note

This problem is translated from COCI2007-2008 COI2008 T4 UMNOZAK.

见题面 Input 部分

见题面 Output 部分