Youngsik Function

For a natural number N with at least two digits, define the Youngsik function F(N) as follows.

F(N) is the number made by writing, from left to right, the differences between each pair of adjacent digits of N. Each difference is the larger digit minus the smaller digit. For example, F(5913) = 482, F(1198) = 081 = 81, and F(666) = 00 = 0.

Starting from a natural number N, repeatedly form the sequence N, F(N), F(F(N)), ... until a one-digit number first appears. That last one-digit number is called the fingerprint of N. For example, when N = 5913, the sequence is 5913, 482, 46, 2, so the fingerprint of 5913 is 2.

A number is lucky if its fingerprint is 7. Count how many lucky numbers are between A and B, inclusive.

The first line contains two natural numbers A and B separated by a space.

1 <= A <= B <= 1,000,000,000.

Print the number of lucky numbers between A and B, inclusive.

From 1 through 100, the lucky numbers are 7, 18, 29, 70, 81, and 92, for a total of 6.