Description

Given $x, y$, output the number of leap years in the interval $[x, y]$, and on the next line output all leap year numbers, separated by spaces.

Input Format

Input two positive integers $x, y$, separated by a space.

Output Format

On the first line, output a positive integer representing the number of leap years in the interval $[x, y]$.

On the second line, output several positive integers: all leap year numbers in monotonically increasing order by year.

1989 2001

3
1992 1996 2000

Hint

Constraints: the testdata guarantees that $1582 \le x < y \le 3000$.

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