__Definition:__ According to Wikipedia, a [complete binary tree](https://en.wikipedia.org/wiki/Binary_tree#Types_of_binary_trees) is a binary tree _"where every level, except possibly the last, is completely filled, and all nodes in the last level are as far left as possible."_

The Wikipedia page referenced above also mentions that _"Binary trees can also be stored in breadth-first order as an implicit data structure in arrays, and if the tree is a complete binary tree, this method wastes no space."_

Your task is to write a method (or function) that takes an array (or list, depending on language) of integers and, assuming that the array is ordered according to an _in-order_ traversal of a complete binary tree, returns an array that contains the values of the tree in breadth-first order.

__Example 1:__
Let the input array be `[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]`. This array contains the values of the following complete binary tree. 


```
          _ 7_
        /      \
       4        9
     /   \     / \
   2      6   8   10
  / \     /
 1   3   5
```
In this example, the input array happens to be sorted, but that is _not_ a requirement.

__Output 1:__ The output of the function shall be an array containing the values of the nodes of the binary tree read top-to-bottom, left-to-right. In this example, the returned array should be:

```[7, 4, 9, 2, 6, 8, 10, 1, 3, 5]```


__Example 2:__
Let the input array be `[1, 2, 2, 6, 7, 5]`. This array contains the values of the following complete binary tree. 


```
        6
      /   \
    2       5
   / \     /
  1   2   7
 
```
Note that an in-order traversal of this tree produces the input array.

__Output 2:__ The output of the function shall be an array containing the values of the nodes of the binary tree read top-to-bottom, left-to-right. In this example, the returned array should be:

```[6, 2, 5, 1, 2, 7]```

```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 = 'import math\n\ndef complete_binary_tree(a):\n    if len(a) < 2: return a\n    \n    root = build(a)\n    res = []\n    getLevelOrder(root, res)\n    return res\n\nclass Node:\n\n    def __init__(self, data, left, right):\n\n        self.left = left\n        self.right = right\n        self.data = data\n        \n    def __str__(self):\n        return f"left = {self.left}, right = {self.right}, data = {self.data}"\n        \ndef build(a):\n\n    if len(a) == 0:\n        return None\n    if len(a) == 1:\n        return Node(a[0], None, None)\n    \n    level = math.log2(len(a))\n    level = math.ceil(level) + (1 if int(level) == level else 0)\n    \n    if len(a) >= 2 ** (level - 2) * 3 - 1:\n        root = 2 ** (level - 1) - 1\n    else:\n        root = len(a) - 2 ** (level - 2)\n    \n    left = build(a[:root])\n    right = build(a[root+1:])\n    return Node(a[root], left, right)\n\ndef getLevelOrder(root, res): \n    h = height(root) \n    for i in range(1, h+1): \n        getGivenLevel(root, i, res) \n\ndef getGivenLevel(root , level, res): \n    if root is None: \n        return\n    if level == 1: \n        res.append(root.data)\n    elif level > 1 : \n        getGivenLevel(root.left , level-1, res) \n        getGivenLevel(root.right , level-1, res)\n\n        \ndef height(node): \n    if node is None: \n        return 0 \n    else : \n        # Compute the height of each subtree  \n        lheight = height(node.left) \n        rheight = height(node.right) \n        \n        #Use the larger one \n        if lheight > rheight : \n            return lheight+1\n        else: \n            return rheight+1'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'complete_binary_tree'
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: 5374