To 3

AtCoder

IDabc182_c

Time2000ms

Memory256MB

Difficulty—

Given is a positive integer $N$, where none of the digits is $0$. Let $k$ be the number of digits in $N$. We want to make a multiple of $3$ by erasing at least $0$ and at most $k-1$ digits from $N$ and concatenating the remaining digits without changing the order. Determine whether it is possible to make a multiple of $3$ in this way. If it is possible, find the minimum number of digits that must be erased to make such a number. ## Constraints * $1 \le N \lt 10^{18}$ * None of the digits in $N$ is $0$. ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

1

By erasing the $5$, we get the number $3$, which is a multiple of $3$. Here we erased the minimum possible number of digits - $1$.

Input #2

Output #2

0

Note that we can choose to erase no digit.

Input #3

Output #3

1

For example, by erasing the $8$, we get the number $622734$, which is a multiple of $3$.

Input #4

Output #4

\-1

Note that we must erase at least $0$ and at most $k-1$ digits, where $k$ is the number of digits in $N$, so we cannot erase all the digits.  
In this case, it is impossible to make a multiple of $3$ in the way described in the problem statement, so we should print `-1`.

API Response (JSON)

{
  "problem": {
    "name": "To 3",
    "description": {
      "content": "Given is a positive integer $N$, where none of the digits is $0$.   Let $k$ be the number of digits in $N$. We want to make a multiple of $3$ by erasing at least $0$ and at most $k-1$ digits from $N$ ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc182_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a positive integer $N$, where none of the digits is $0$.  \nLet $k$ be the number of digits in $N$. We want to make a multiple of $3$ by erasing at least $0$ and at most $k-1$ digits from $N$ ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments