A lot of goods have an  International Article Number (formerly known as "European Article Number") abbreviated "EAN". EAN is a 13-digits barcode consisting of 12-digits data followed by a single-digit checksum (EAN-8 is not considered in this kata).


The single-digit checksum is calculated as followed (based upon the 12-digit data):

The digit at the first, third, fifth, etc. position (i.e. at the odd position) has to be multiplied with "1". 
The digit at the second, fourth, sixth, etc. position (i.e. at the even position) has to be multiplied with "3".
Sum these results. 

If this sum is dividable by 10, the checksum is 0. Otherwise the checksum has the following formula:

  checksum = 10 - (sum mod 10)

For example, calculate the checksum for "400330101839" (= 12-digits data):

4·1 + 0·3 + 0·1 + 3·3 + 3·1 + 0·3 + 1·1 + 0·3 + 1·1 + 8·3 + 3·1 + 9·3
= 4 + 0 + 0 + 9 + 3 + 0 + 1 + 0 + 1 + 24 + 3 + 27 
= 72
10 - (72 mod 10) = 8 ⇒ Checksum: 8

Thus, the EAN-Code is 4003301018398 (= 12-digits data followed by single-digit checksum).
 
Your Task
Validate a given EAN-Code. Return true if the given EAN-Code is valid, otherwise false.

Assumption
You can assume the given code is syntactically valid, i.e. it only consists of numbers and it exactly has a length of 13 characters.

Examples

```python
validate_ean("4003301018398") # => True
validate_ean("4003301018392") # => False
```

Good Luck and have fun.

```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 = "def validate_ean(code):\n    '''Return True if code is a valid EAN-13 code (else False)'''\n    \n    # separate single-digit checksum from code\n    check_digit = int(code[-1])\n    # convert 12-digit string to list of int\n    code = list(map(int, code[:-1]))\n    # multiply digits at even positions with 3\n    totals = sum([digit * 3 if pos % 2 == 0 else digit for pos, digit in enumerate(code, 1)])\n    \n    if totals % 10 == 0:\n        checksum = 0\n    else:\n        checksum = 10 - (totals % 10)\n    return check_digit == checksum"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'validate_ean'
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: 5898