A [Word Square](https://en.wikipedia.org/wiki/Word_square) is a set of words written out in a square grid, such that the same words can be read both horizontally and vertically. The number of words, equal to the number of letters in each word, is known as the *order* of the square.

For example, this is an *order* `5` square found in the ruins of Herculaneum:

![](https://i.gyazo.com/e226262e3ada421d4323369fb6cf66a6.jpg)

Given a string of various uppercase `letters`, check whether a *Word Square* can be formed from it. 

Note that you should use each letter from `letters` the exact number of times it occurs in the string. If a *Word Square* can be formed, return `true`, otherwise return `false`.

__Example__

  * For `letters = "SATORAREPOTENETOPERAROTAS"`, the output should be
  `WordSquare(letters) = true`.
    It is possible to form a *word square* in the example above.

  * For `letters = "AAAAEEEENOOOOPPRRRRSSTTTT"`, (which is sorted form of `"SATORAREPOTENETOPERAROTAS"`), the output should also be
  `WordSquare(letters) = true`.

  * For `letters = "NOTSQUARE"`, the output should be
  `WordSquare(letters) = false`.
  
__Input/Output__

* [input] string letters

  A string of uppercase English letters.
  
  Constraints: `3 ≤ letters.length ≤ 100`.


* [output] boolean

  `true`, if a Word Square can be formed;
  
  `false`, if a Word Square cannot be formed.

```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 collections import Counter\n\ndef word_square(letters):\n    N = len(letters)**0.5\n    return not N%1 and (sum(v&1 for v in Counter(letters).values()) <= N)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'word_square'
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: 9792