# Task
 Imagine a standard chess board with only two white and two black knights placed in their standard starting positions: the white knights on b1 and g1; the black knights on b8 and g8.

 There are two players: one plays for `white`, the other for `black`. During each move, the player picks one of his knights and moves it to an unoccupied square according to standard chess rules. Thus, a knight on d5 can move to any of the following squares: b6, c7, e7, f6, f4, e3, c3, and b4, as long as it is not occupied by either a friendly or an enemy knight.

 The players take turns in making moves, starting with the white player. Given the configuration `positions` of the knights after an unspecified number of moves, determine whose turn it is.

# Example

 For `positions = "b1;g1;b8;g8"`, the output should be `true`.

 The configuration corresponds to the initial state of the game. Thus, it's white's turn.

# Input/Output


 - `[input]` string `positions`

    The positions of the four knights, starting with white knights, separated by a semicolon, in the chess notation.


 - `[output]` a boolean value

    `true` if white is to move, `false` otherwise.

```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 = 'from typing import Dict, Generator, List, Tuple\n\nK_MOVES = [\n    (a, b) \n    for a in [-2, -1, 1, 2] \n    for b in [-2, -1, 1, 2] \n    if abs(a) != abs(b)\n]\n\ndef gen_k_moves(k: Tuple[int, int]) -> Generator[Tuple[int, int], None, None]:\n    """\n    Generates all valid knight moved from the given point\n    """\n    kc, kr = k\n    for dc, dr in K_MOVES:\n        c, r = kc + dc, kr + dr\n        if 1 <= r <= 8 and 1 <= c <= 8:\n            yield c, r\n\ndef solve(k: Tuple[int, int]) -> Dict[Tuple[int, int], int]:\n    """\n    Given the starting point of a knight k, return a dict of postions to minimum moves to that position\n    """\n    solutions = {}\n    \n    edges = [k]\n    visited = set()\n    steps = 0\n    while edges:\n        visited.update(edges)\n        for edge in edges:\n            solutions[edge] = steps\n        steps += 1\n        new_edges = []\n        for edge in edges:\n            for nk in gen_k_moves(edge):\n                if nk in visited:\n                    continue\n                new_edges.append(nk)\n                visited.add(nk)\n        edges = new_edges\n    return solutions\n\nw1_solutions = solve((2, 1))\nw2_solutions = solve((7, 1))\nb1_solutions = solve((2, 8))\nb2_solutions = solve((7, 8))\n\ndef whose_turn(positions):\n    positions = [\n        (ord(s[0]) - ord(\'a\') + 1, int(s[1])) \n        for s in positions.split(\';\')\n    ]\n    w1 = w1_solutions[positions[0]], w2_solutions[positions[0]]\n    w2 = w1_solutions[positions[1]], w2_solutions[positions[1]]\n    b1 = b1_solutions[positions[2]], b2_solutions[positions[2]]\n    b2 = b1_solutions[positions[3]], b2_solutions[positions[3]]\n    \n    whites = min(w1[0] + w2[1], w1[1] + w2[0])\n    blacks = min(b1[0] + b2[1], b1[1] + b2[0])\n    return (whites % 2) == (blacks % 2)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'whose_turn'
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: 6476