You are given a string s containing lowercase letters and an integer k. You need to :

First, change some characters of s to other lowercase English letters.
Then divide s into k non-empty disjoint substrings such that each substring is palindrome.

Return the minimal number of characters that you need to change to divide the string.
 
Example 1:
Input: s = "abc", k = 2
Output: 1
Explanation: You can split the string into "ab" and "c", and change 1 character in "ab" to make it palindrome.

Example 2:
Input: s = "aabbc", k = 3
Output: 0
Explanation: You can split the string into "aa", "bb" and "c", all of them are palindrome.
Example 3:
Input: s = "leetcode", k = 8
Output: 0

 
Constraints:

1 <= k <= s.length <= 100.
s only contains lowercase English letters.

```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 cost(self, i, j):\n        if i + 1 >= j:\n            return 0\n        if i + 2 == j:\n            return 0 if self.s[i] == self.s[j - 1] else 1\n        \n        try:\n            return self.cost_cache[(i, j)]\n        except KeyError:\n            ret = self.cost(i + 1, j - 1) + (0 if self.s[i] == self.s[j - 1] else 1)\n            self.cost_cache[(i, j)] = ret\n            return ret\n        \n    def num_changes(self, i, kk):\n        rem_len = len(self.s) - i\n        if rem_len < kk:\n            return self.MAX\n        if rem_len == kk:\n            return 0\n        if kk == 1:\n            return self.cost(i, len(self.s))\n        \n        try:\n            return self.num_changes_cache[(i, kk)]\n        except KeyError:\n            ret = self.MAX\n            for j in range(i + 1, len(self.s) - (kk - 1) + 1):\n                ret = min(ret, self.cost(i, j) + self.num_changes(j, kk - 1))\n            self.num_changes_cache[(i, kk)] = ret\n            return ret\n            \n    def palindromePartition(self, s: str, k: int) -> int:\n        self.s = s\n        self.MAX = len(s)\n        self.cost_cache = {}\n        self.num_changes_cache = {}\n        \n        for l in range(3, len(s)):\n            for i in range(len(s) - l + 1):\n                j = i + l\n                self.cost(i, j)\n        for i in range(len(s) - 3, -1, -1):\n            for kk in range(2, min(len(s) - i - 1, k - 1) + 1):\n                self.num_changes(i, kk)\n                \n        return self.num_changes(0, k)\n                \n        \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'palindromePartition'
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: 7782