# Task

John and Alice have an appointment today. 

In the morning, John starts from (`0,0`) and goes to the place (`a,b`) where he is dating. Unfortunately, John had no sense of direction at all, so he moved 1 step in a random direction(up, down, left or right) each time. For example, if John at (x,y), next step he may move to `(x+1,y), (x-1,y),(x,y+1) or (x,y-1)`. 

Obviously, when he arrived at the destination, it was already too late and Alice had already left. It's a sadly story :(

The second day, Alice asked John why he didn't go to the dating place. John said he took `s` steps to his date yesterday.

Alice wants to know whether John is lying. Please help Alice to judge.

Given two coordinates `a, b` and the step `s`, return `true` if John tells the truth, `false` otherwise.

# Input/Output


`[input]` integer `a`

The x-coordinates of the dating site.

`-10^7 <= a <= 10^7`

`[input]` integer `b`

The y-coordinates of the dating site.

`-10^7 <= b <= 10^7`

`[input]` integer `s`

A positive integer.  The steps John using.

`0 < s <= 10^9`

`[output]` a boolean value

return `true` if John tells the truth, `false` otherwise.

# Example

For `a = 3, b = 3, s = 6`, the output should be `true`.

A possible path is: 

`(0,0) -> (0,1) -> (0,2) -> (0,3) -> (1,3) -> (2,3) -> (3,3)`

For `a = 3, b = 3, s = 8`, the output should be `true`.

A possible path is: 

`(0,0) -> (0,1) -> (1,1) -> (1,2) -> (2,2) -> (2,1) -> (3,1) -> (3,2) -> (3,3)`

For `a = 4, b = 5, s = 10`, the output should be `false`.

John can't reach coordinates (a, b) using 10 steps, he's lying ;-)

```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 is_john_lying(a, b, s):\n    return s >= abs(a) + abs(b) and s % 2 == (a + b) % 2'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'is_john_lying'
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: 5426