A10939 | Divide by Three

A positive integer number $n$ is written on a blackboard. It consists of not more than $10^{5}$ digits. You have to transform it into a beautiful number by erasing some of the digits, and you want to erase as few digits as possible.

The number is called beautiful if it consists of at least one digit, doesn't have leading zeroes and is a multiple of $3$ . For example, 0, 99, 10110 are beautiful numbers, and 00, 03, 122 are not.

Write a program which for the given $n$ will find a beautiful number such that $n$ can be transformed into this number by erasing as few digits as possible. You can erase an arbitraty set of digits. For example, they don't have to go one after another in the number $n$ .

If it's impossible to obtain a beautiful number, print -1. If there are multiple answers, print any of them.

The first line of input contains $n$ — a positive integer number without leading zeroes ( $1<=n<10^{100000}$ ).

Print one number — any beautiful number obtained by erasing as few as possible digits. If there is no answer, print $-1$ .