Given two arrays $$$a$$$ and $$$b$$$ of length n consisting of values $$$0, 1, 2, 3$$$ and $$$4$$$ you can do the following operation at most $$$8 \cdot n$$$ times:
Choose an index $$$i$$$ and let $$$a[i] := (a[i - 1] + a[i] + a[i + 1]) \mod 5$$$.
All the operations on indices are modulo $$$n$$$.
Check if it is possible to make both arrays equal.
The first line of the input contains single number $$$n$$$ ($$$5 \leq n \leq 10^5$$$) — the length of both arrays.
The second line contains $$$n$$$ numbers $$$a_0, a_1 ... a_{n - 1}$$$ ($$$0 \leq a_i \leq 4$$$) — elements of an array.
The third line contains analogous description of array $$$b$$$.
If it is not possible to make both arrays equal output $$$-1$$$.
If it is possible to make both arrays equal the first line should contain $$$0 \leq k \leq 8 \cdot n$$$ — the number of operations.
The following $$$k$$$ lines each should contain a single number $$$0 \leq t_i \leq n - 1$$$ — the index chosen in the $$$i$$$-th operation.
5 1 0 0 1 0 1 0 0 1 1
3 4 4 4
