# Task
 You are given n rectangular boxes, the ith box has the length lengthi, the width widthi and the height heighti. 
 
 Your task is to check if it is possible to pack all boxes into one so that inside each box there is no more than one another box (which, in turn, can contain at most one another box, and so on). 
 
 More formally, your task is to check whether there is such sequence of n different numbers pi (1 ≤ pi ≤ n) that for each 1 ≤ i < n the box number pi can be put into the box number pi+1.

 A box can be put into another box if all sides of the first one are less than the respective ones of the second one. You can rotate each box as you wish, i.e. you can `swap` its length, width and height if necessary.

# Example

 For `length = [1, 3, 2], width = [1, 3, 2] and height = [1, 3, 2]`, the output should be `true`;
 
 For `length = [1, 1], width = [1, 1] and height = [1, 1],` the output should be `false`;
 
 For `length = [3, 1, 2], width = [3, 1, 2] and height = [3, 2, 1]`, the output should be `false`.
 
# Input/Output


 - `[input]` integer array `length`

    Array of positive integers.

    Constraints:

    `1 ≤ length.length ≤ 100,`

    `1 ≤ length[i] ≤ 2000.`


 - `[input]` integer array `width`

    Array of positive integers.

    Constraints:

    `width.length = length.length,`

    `1 ≤ width[i] ≤ 2000.`


 - `[input]` integer array `height`

    Array of positive integers.

    Constraints:

    `height.length = length.length,`

    `1 ≤ height[i] ≤ 2000.`


 - `[output]` a boolean value

    `true` if it is possible to put all boxes into one, `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 itertools import tee, chain,starmap\nfrom operator import lt\n\n# found at https://docs.python.org/3.6/library/itertools.html\ndef pairwise(iterable):\n    "s -> (s0,s1), (s1,s2), (s2, s3), ..."\n    a, b = tee(iterable)\n    next(b, None)\n    return zip(a, b)\n\ndef boxes_packing(length, width, height):\n    boxes = map(sorted, sorted(zip(length, width, height), key=lambda b: b[0] * b[1] * b[2]))\n    return all(starmap(lt, chain.from_iterable(zip(*a) for a in pairwise(boxes))))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'boxes_packing'
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: 7720