You have an array $a$ of length $n$. For every positive integer $x$ you are going to perform the following operation during the $x$-th second:

  Select some distinct indices $i_{1}, i_{2}, \ldots, i_{k}$ which are between $1$ and $n$ inclusive, and add $2^{x-1}$ to each corresponding position of $a$. Formally, $a_{i_{j}} := a_{i_{j}} + 2^{x-1}$ for $j = 1, 2, \ldots, k$. Note that you are allowed to not select any indices at all. 

You have to make $a$ nondecreasing as fast as possible. Find the smallest number $T$ such that you can make the array nondecreasing after at most $T$ seconds.

Array $a$ is nondecreasing if and only if $a_{1} \le a_{2} \le \ldots \le a_{n}$.

You have to answer $t$ independent test cases.


-----Input-----

The first line contains a single integer $t$ ($1 \le t \le 10^{4}$) — the number of test cases.

The first line of each test case contains single integer $n$ ($1 \le n \le 10^{5}$) — the length of array $a$. It is guaranteed that the sum of values of $n$ over all test cases in the input does not exceed $10^{5}$.

The second line of each test case contains $n$ integers $a_{1}, a_{2}, \ldots, a_{n}$ ($-10^{9} \le a_{i} \le 10^{9}$).


-----Output-----

For each test case, print the minimum number of seconds in which you can make $a$ nondecreasing.


-----Example-----
Input
3
4
1 7 6 5
5
1 2 3 4 5
2
0 -4

Output
2
0
3



-----Note-----

In the first test case, if you select indices $3, 4$ at the $1$-st second and $4$ at the $2$-nd second, then $a$ will become $[1, 7, 7, 8]$. There are some other possible ways to make $a$ nondecreasing in $2$ seconds, but you can't do it faster.

In the second test case, $a$ is already nondecreasing, so answer is $0$.

In the third test case, if you do nothing at first $2$ seconds and select index $2$ at the $3$-rd second, $a$ will become $[0, 0]$.

```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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'for _ in range(int(input())):\n    n = int(input())\n    l1 = list(map(int, input().split()))\n    answer = 0\n    max_so_far = l1[0]\n    for i in range(1, n):\n        if l1[i] >= max_so_far:\n            max_so_far = l1[i]\n        else:\n            answer = max(answer, (max_so_far - l1[i]).bit_length())\n        \n        \n    print(answer)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13125