Palindromic Dates

In daily life, a unique date can be determined by its year, month, and day. In this problem, a date is represented by an 8-digit number in the format YYYYMMDD, where the first 4 digits represent the year, the next 2 digits represent the month, and the last 2 digits represent the day. Note that each real date has a unique 8-digit representation, and two different dates will have different representations.

A date is defined as palindromic if and only if its 8-digit representation is a palindrome. In other words, if we denote the representation as a sequence of digits \(d_1 d_2 d_3 d_4 d_5 d_6 d_7 d_8\), the date is palindromic if:

[ \forall, i,(1 \le i \le 8),\quad d_i = d_{9-i} ]

For example:

• The date November 19, 2016 is represented as 20161119 and is not a palindrome.
• The date January 2, 2010 is represented as 20100102 and is a palindrome.
• The date October 2, 2010 is represented as 20101002 and is not a palindrome.

It is known that the number of days in each month is as follows:

• Months 1, 3, 5, 7, 8, 10, 12 have 31 days.
• Months 4, 6, 9, 11 have 30 days.
• February has 28 days in a common year and 29 days in a leap year.

A year is a leap year if and only if it satisfies one of the following conditions:

[ \text{(1) } (\text{year} \bmod 4 = 0) \text{ and } (\text{year} \bmod 100 \neq 0) \quad \text{or} \quad \text{(2) } (\text{year} \bmod 400 = 0). ]

Your task is: Given two dates (in the 8-digit format) that represent the start and end dates (inclusive), determine how many real dates within this range are palindromic.

Note: A palindromic 8-digit number in the format YYYYMMDD must satisfy that for the year string Y1Y2Y3Y4, the month is formed as Y4Y3 and the day is formed as Y2Y1.

inputFormat

The input consists of a single line containing two 8-digit numbers separated by a space. The first number is the start date and the second number is the end date. Both dates are in the format YYYYMMDD.

You can assume that the start date is not later than the end date and that both dates represent valid calendar dates.

outputFormat

Output a single integer representing the number of palindromic dates between the given start and end dates (inclusive).

sample

20100101 20101231

1