Your task is to form an integer array nums from an initial array of zeros arr that is the same size as nums.
Return the minimum number of function calls to make nums from arr.
The answer is guaranteed to fit in a 32-bit signed integer.
 
Example 1:
Input: nums = [1,5]
Output: 5
Explanation: Increment by 1 (second element): [0, 0] to get [0, 1] (1 operation).
Double all the elements: [0, 1] -> [0, 2] -> [0, 4] (2 operations).
Increment by 1 (both elements)  [0, 4] -> [1, 4] -> [1, 5] (2 operations).
Total of operations: 1 + 2 + 2 = 5.

Example 2:
Input: nums = [2,2]
Output: 3
Explanation: Increment by 1 (both elements) [0, 0] -> [0, 1] -> [1, 1] (2 operations).
Double all the elements: [1, 1] -> [2, 2] (1 operation).
Total of operations: 2 + 1 = 3.

Example 3:
Input: nums = [4,2,5]
Output: 6
Explanation: (initial)[0,0,0] -> [1,0,0] -> [1,0,1] -> [2,0,2] -> [2,1,2] -> [4,2,4] -> [4,2,5](nums).

Example 4:
Input: nums = [3,2,2,4]
Output: 7

Example 5:
Input: nums = [2,4,8,16]
Output: 8

 
Constraints:

1 <= nums.length <= 10^5
0 <= nums[i] <= 10^9

```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 minOperations(self, nums: List[int]) -> int:\n        # After having implemented minOperations_dumb_solution(), we realize that \n        # the number of op 1 we'll need to do is just the number of times we need\n        # to divide the max even number we ever encounter to get it down to zero. \n        # Because, a division would reduce everyone by 2 and when the smaller even\n        # numbers we see gets down to zero, it will no longer be affected. We only care\n        # about dividing the biggest even number down to zero.\n        cost = 0\n        max_nb_op_1 = 0\n        for i in range(len(nums)):\n            nb_op_0 = nb_op_1 = 0\n            x = nums[i]\n            while x > 0:\n                if x % 2 != 0:\n                    nb_op_0 += x % 2\n                    x -= x % 2\n                if x > 0:\n                    nb_op_1 += 1\n                    x = x // 2\n            cost += nb_op_0\n            max_nb_op_1 = max(max_nb_op_1, nb_op_1)\n        cost += max_nb_op_1\n        return cost\n    \n    def minOperations_dumb_solution(self, nums: List[int]) -> int:\n        # Key insight is if nums[i] is odd, there's no way we could have arrived at nums[i]\n        # via op 1, i.e. by multiplying by 2 some previous value. So the only way we could\n        # have gotten here is by using op 0, nums[i] % 2 times. That is we need to skim off\n        # the remainder part that makes it non-even before we can consider using op 1.\n        cost = 0\n        while True:\n            all_zeros = True\n            all_evens = True\n            for i in range(len(nums)):\n                if nums[i] == 0:\n                    continue\n                \n                all_zeros = False\n                if nums[i] % 2 != 0:\n                    cost += nums[i] % 2\n                    nums[i] = nums[i] - (nums[i] % 2)\n                    all_evens = False\n            \n            if all_zeros:\n                break\n            while all_evens:\n                for i in range(len(nums)):\n                    nums[i] = nums[i] // 2\n                    if nums[i] % 2 != 0:\n                        all_evens = False\n                cost += 1\n                \n        return cost\n                    \n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'minOperations'
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: 5518