Remember the story of Little Match Girl? By now, you know exactly what matchsticks the little match girl has, please find out a way you can make one square by using up all those matchsticks. You should not break any stick, but you can link them up, and each matchstick must be used exactly one time.

 Your input will be several matchsticks the girl has, represented with their stick length. Your output will either be true or false, to represent whether you could make one square using all the matchsticks the little match girl has.

Example 1:

Input: [1,1,2,2,2]
Output: true

Explanation: You can form a square with length 2, one side of the square came two sticks with length 1.



Example 2:

Input: [3,3,3,3,4]
Output: false

Explanation: You cannot find a way to form a square with all the matchsticks.



Note:

The length sum of the given matchsticks is in the range of 0 to 10^9.
The length of the given matchstick array will not exceed 15.

```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 = 'class Solution:\n     def makesquare(self, nums):\n         """\n         :type nums: List[int]\n         :rtype: bool\n         """\n #         if sum(nums) % 4 != 0 or len(nums) < 4 or max(nums) > sum(nums) / 4 :\n #             return False\n         \n #         nums.sort(reverse=True)      \n         \n #         if nums[0] < sum(nums) / 4 and nums[0]  + nums[-1] >  sum(nums):\n #             return False\n         \n #         def dfs(nums, pos, target):\n #             if pos == len(nums):\n #                 return True\n             \n #             for i in range(4):\n #                 if target[i] >= nums[pos]:\n #                     target[i] -= nums[pos]\n #                     if dfs(nums, pos + 1, target):\n #                         return True\n #                     target[i] += nums[pos]\n                     \n                     \n #             return False\n             \n #         return dfs(nums, 0,  [sum(nums) / 4] * 4)\n     \n     \n         total = sum(nums)\n         if total%4 != 0 or len(nums)<4: return False\n         size = total/4\n         nums.sort(reverse=True)\n         used = [False]*len(nums)\n         def dfs(i, expect):\n             if i >= len(nums): return expect%size == 0\n             if used[i]: return dfs(i+1, expect)\n             used[i] = True\n             if nums[i] == expect: return True\n             if nums[i] < expect:\n                 expect -= nums[i]\n                 available = [j for j in range(i+1, len(nums)) if not used[j]]\n                 for x in available:\n                     if dfs(x, expect): \n                         return True\n             used[i] = False\n             return False\n         for i in range(len(nums)):\n             if not dfs(i, size): return False\n         return True'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'makesquare'
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: 6644