## Check Digits

Some numbers are more important to get right during data entry than others: a common example is product codes.

To reduce the possibility of mistakes, product codes can be crafted in such a way that simple errors are detected. This is done by calculating a single-digit value based on the product number, and then appending that digit to the product number to arrive at the product code.

When the product code is checked, the check digit value is stripped off and recalculated. If the supplied value does not match the recalculated value, the product code is rejected.

A simple scheme for generating self-check digits, described here, is called Modulus 11 Self-Check.

## Calculation method

Each digit in the product number is assigned a multiplication factor. The factors are assigned ***from right to left***, starting at `2` and counting up. For numbers longer than six digits, the factors restart at `2` after `7` is reached. The product of each digit and its factor is calculated, and the products summed. For example:

```python
digit     :  1    6    7    7    0    3    6    2    5
factor    :  4    3    2    7    6    5    4    3    2
           ---  ---  ---  ---  ---  ---  ---  ---  ---
             4 + 18 + 14 + 49 +  0 + 15 + 24 +  6 + 10 = 140
```

Then the sum of the products is divided by the prime number `11`. The remainder is inspected, and:

* if the remainder is `0`, the check digit is also `0`
* if the remainder is `1`, the check digit is replaced by an uppercase `X`
* for all others, the remainder is subtracted from `11`

The result is the **check digit**.

## Your task

Your task is to implement this algorithm and return the input number with the correct check digit appended.

## Examples

```python
input: "036532"

product sum = 2*2 + 3*3 + 5*4 + 6*5 + 3*6 + 0*7 = 81
remainder   = 81 mod 11 = 4
check digit = 11 - 4 = 7

output: "0365327"
```

```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

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "add_check_digit=lambda s:s+'0X987654321'[sum((i%6+2)*int(d)for i,d in enumerate(s[::-1]))%11]"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'add_check_digit'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5663