You are given a string $s[1 \dots n]$ consisting of lowercase Latin letters. It is guaranteed that $n = 2^k$ for some integer $k \ge 0$.

The string $s[1 \dots n]$ is called $c$-good if at least one of the following three conditions is satisfied:  The length of $s$ is $1$, and it consists of the character $c$ (i.e. $s_1=c$); The length of $s$ is greater than $1$, the first half of the string consists of only the character $c$ (i.e. $s_1=s_2=\dots=s_{\frac{n}{2}}=c$) and the second half of the string (i.e. the string $s_{\frac{n}{2} + 1}s_{\frac{n}{2} + 2} \dots s_n$) is a $(c+1)$-good string;  The length of $s$ is greater than $1$, the second half of the string consists of only the character $c$ (i.e. $s_{\frac{n}{2} + 1}=s_{\frac{n}{2} + 2}=\dots=s_n=c$) and the first half of the string (i.e. the string $s_1s_2 \dots s_{\frac{n}{2}}$) is a $(c+1)$-good string. 

For example: "aabc" is 'a'-good, "ffgheeee" is 'e'-good.

In one move, you can choose one index $i$ from $1$ to $n$ and replace $s_i$ with any lowercase Latin letter (any character from 'a' to 'z').

Your task is to find the minimum number of moves required to obtain an 'a'-good string from $s$ (i.e. $c$-good string for $c=$ 'a'). It is guaranteed that the answer always exists.

You have to answer $t$ independent test cases.

Another example of an 'a'-good string is as follows. Consider the string $s = $"cdbbaaaa". It is an 'a'-good string, because:  the second half of the string ("aaaa") consists of only the character 'a';  the first half of the string ("cdbb") is 'b'-good string, because:   the second half of the string ("bb") consists of only the character 'b';  the first half of the string ("cd") is 'c'-good string, because:   the first half of the string ("c") consists of only the character 'c';  the second half of the string ("d") is 'd'-good string.   


-----Input-----

The first line of the input contains one integer $t$ ($1 \le t \le 2 \cdot 10^4$) — the number of test cases. Then $t$ test cases follow.

The first line of the test case contains one integer $n$ ($1 \le n \le 131~072$) — the length of $s$. It is guaranteed that $n = 2^k$ for some integer $k \ge 0$. The second line of the test case contains the string $s$ consisting of $n$ lowercase Latin letters.

It is guaranteed that the sum of $n$ does not exceed $2 \cdot 10^5$ ($\sum n \le 2 \cdot 10^5$).


-----Output-----

For each test case, print the answer — the minimum number of moves required to obtain an 'a'-good string from $s$ (i.e. $c$-good string with $c =$ 'a'). It is guaranteed that the answer exists.


-----Example-----
Input
6
8
bbdcaaaa
8
asdfghjk
8
ceaaaabb
8
bbaaddcc
1
z
2
ac

Output
0
7
4
5
1
1

```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 = 'import sys\n# sys.stdin = open("in", "r")\n# sys.stdout = open("out", "w")\n\ninp = sys.stdin.read().split(); ii = 0\nt = int(inp[0]); ii += 1\nfor _ in range(t):\n\tn = int(inp[ii]); ii += 1\n\ts = inp[ii]; ii += 1\n\tif n == 1:\n\t\tif \'a\' in s:\n\t\t\tprint(0)\n\t\telse:\n\t\t\tprint(1)\n\t\tcontinue\n\tstack = [[0, n, ord(\'a\'), 0]]\n\tans = n\n\twhile stack:\n\t\tl, r, c, cost = stack[-1]\n\t\tstack.pop()\n\t\tif r-l == 1:\n\t\t\tif chr(c) in s[l:r]:\n\t\t\t\tans = min(ans, cost)\n\t\t\telse:\n\t\t\t\tans = min(ans, cost+1)\n\t\t\tcontinue\n\t\t\n\t\tmid = (l+r)//2\n\t\tstack.append([l, mid, c+1, r-mid+cost-s[mid:r].count(chr(c))])\n\t\tstack.append([mid, r, c+1, mid-l+cost-s[l:mid].count(chr(c))])\n\tprint(ans)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13445