Uh oh, Someone at the office has dropped all these sequences on the floor and forgotten to label them with their correct bases. 

We have to fix this before the boss gets back or we're all going to be fired!

This is what your years of coding have been leading up to, now is your time to shine!

## Task

You will have to create a function which takes in a sequence of numbers in **random order** and you will have to return the correct base of those numbers.

The base is the number of unique digits. For example, a base 10 number can have 10 unique digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and a base 2 number (Binary) can have 2 unique digits: 0 and 1.

### Constraints

The sequence will always be 10 numbers long and we know that the base is going to be between 2 and 10 inclusive so no need to worry about any letters. When sorted, the sequence is made up of consecutive numbers.

### Examples

```
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10" ]     -->  10
[ "1", "2", "3", "4", "5", "6", "10", "11", "12", "13" ]  -->   7
```

**Good luck!**

```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 base_finder(seq):\n    base = 0\n    for i in range(10): #as the sequence will always be 10 numbers long\n        number = seq[i] # converting each list element to a string\n        for i in range(len(number)): \n            if int(number[i]) > base: # Comparing each character of string to base\n                base = int(number[i]) # updating the base value\n    return base+1 # return base value \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'base_finder'
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: 5482