Chef Zidane likes the number 9. He has a number N, and he wants to turn it into a multiple of 9. He cannot add or remove digits, and he can only change one digit at a time. The only allowed operation is to increment or decrement a digit by one, and doing this takes exactly one second. Note that he cannot increase a digit 9 or decrease a digit 0, and the resulting number must not contain any leading zeroes unless N has a single digit.

Chef Zidane wants to know the minimum amount of time (in seconds) needed to accomplish this. Please help him, before his kitchen gets overwhelmed with mist!

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
Each test case consists of one line containing a single positive integer N.

-----Output-----
For each test case, output a single line containing the answer.

-----Constraints-----
- 1 ≤ T ≤ 105
- 1 ≤ N ≤ 10105
- N will not contain leading zeroes.
- Each test file is at most 3Mb in size.

-----Example-----
Input:4
1989
86236
90210
99999999999999999999999999999999999999988

Output:0
2
3
2

-----Explanation-----
Example case 1. 1989 is already divisible by 9, so no operations are needed to be performed.
Example case 2. 86236 can be turned into a multiple of 9 by incrementing the first and third digit (from the left), to get 96336. This takes 2 seconds.
Example case 3. 90210 can be turned into a multiple of 9 by decrementing the third digit twice and the fourth digit once, to get 90000. This takes 3 seconds.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '\'\'\'\n\nThis File is created by Saurabh Sisodia\nemail address... "ssisodia507@gmail.com"\n\n................................................................................\xa0\xa0\xa0\xa0............\n\n\'\'\'\nfor _ in range(int(input())):\n n=input()\n sum=0\n len=0\n for v in n:\n  len+=1\n  sum+=int(v)\n rem=sum%9\n if len>1 and sum<9:\n  ans=9-rem\n else:\n  ans=min(rem,9-rem)\n print(ans)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 12963