Run-length encoding is a string compression method that works by replacing consecutive identical characters (repeated 2 or more times) with the concatenation of the character and the number marking the count of the characters (length of the run). For example, to compress the string "aabccc" we replace "aa" by "a2" and replace "ccc" by "c3". Thus the compressed string becomes "a2bc3".
Notice that in this problem, we are not adding '1' after single characters.
Given a string s and an integer k. You need to delete at most k characters from s such that the run-length encoded version of s has minimum length.
Find the minimum length of the run-length encoded version of s after deleting at most k characters.
 
Example 1:
Input: s = "aaabcccd", k = 2
Output: 4
Explanation: Compressing s without deleting anything will give us "a3bc3d" of length 6. Deleting any of the characters 'a' or 'c' would at most decrease the length of the compressed string to 5, for instance delete 2 'a' then we will have s = "abcccd" which compressed is abc3d. Therefore, the optimal way is to delete 'b' and 'd', then the compressed version of s will be "a3c3" of length 4.
Example 2:
Input: s = "aabbaa", k = 2
Output: 2
Explanation: If we delete both 'b' characters, the resulting compressed string would be "a4" of length 2.

Example 3:
Input: s = "aaaaaaaaaaa", k = 0
Output: 3
Explanation: Since k is zero, we cannot delete anything. The compressed string is "a11" of length 3.

 
Constraints:

1 <= s.length <= 100
0 <= k <= s.length
s contains only 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 = "from functools import lru_cache\nclass Solution:\n    def getLengthOfOptimalCompression(self, s: str, k: int) -> int:\n \n        @lru_cache(None)\n        def singlelen(n: int) :\n            if not isinstance(n, int):\n                print(n)\n            if n <= 1:\n                return n\n            elif n < 10:\n                return 2\n            elif n < 100:\n                return 3\n            else:\n                return 4\n            \n        def encode(s):\n            last, len = '' , 0\n            res = []\n            for c in s:\n                if c == last:\n                    len += 1\n                else :\n                    if last != '':\n                        res.append((last, len))\n                    last, len = c, 1\n            if len != 0:\n                res.append((last, len))\n            return res\n        def add(curchar, curlen: int , code):\n            #print(32, type(curlen), end= ' ')\n            if len(code) == 0:\n                return 0, curchar, curlen \n            \n            prevsum  = 0\n            for n, l in code:\n                if n == curchar:\n                    curlen += l\n                else:\n                    prevsum += singlelen(curlen)\n                    curchar, curlen = n, l  \n                    #print(43, type(curlen), end= ' ')\n            return (prevsum, curchar, curlen) \n        \n        @lru_cache(None)\n        def dp(code, remain, todel, curchar, curlen: int):\n            #print(sum(tuple(zip(*code))[1]), remain, todel, curchar, curlen)\n            if remain == todel:\n                #print(49, type(curlen), end= ' ')\n                return singlelen(curlen)\n            if todel == 0:\n                (prelen, curchar, curlen) = add(curchar, curlen, code)\n                #print(53, type(curlen), end= ' ')\n                return prelen + singlelen(curlen)\n            \n            if len(code) < 1 or len(code[0]) < 1: \n                print((57, code, remain, todel, curchar, curlen))\n            if code[0][0] == curchar:\n                curlen += code[0][1]\n                remain -= code[0][1]\n                if remain < todel:\n                    curlen += todel - remain\n                    remain = todel\n                    return singlelen(curlen)\n                else:\n                    code = code[1:]\n                if len(code) == 0:\n                    return singlelen(curlen)\n                \n            cases = []\n            \n            if todel >= code[0][1]:\n                #print(63, type(curlen), end= ' ')\n                cases.append(dp(code[1:], remain - code[0][1], todel - code[0][1], curchar, curlen))\n        \n            (prelen, newchar, newlen) = add(curchar, curlen, code[:1]) \n            #print(67, type(newlen), end= ' ') \n            for trydel in range(max(0, todel - remain + code[0][1] ),  min(code[0][1], todel + 1)) :\n                cases.append(prelen  + dp(code[1:], remain - code[0][1], todel - trydel, newchar, newlen - trydel))\n\n            # remove all current stride, remove partial of current stride, keep current stride \n        \n            if len(cases) == 0:\n                #81       4                          1       1      b        3       -  0       b        5\n                #  (('b', 2), ('a', 1), ('c', 1)) ((0, 2), (2, 2))\n                #81       2                          1       1      c        4       -  0       c        6 \n                # | (('c', 2),)  ((0, 2), (2, 2))\n                print((81, sum(tuple(zip(*code))[1]), remain, todel, curchar, curlen,'-',prelen, newchar, newlen, '|', code, ((0, todel - remain + code[0][1] ),  (code[0][1], todel + 1))))\n            return min(cases)\n        \n    \n        code = tuple( encode(s))\n        print((code, len(s))) \n        print((sum(tuple(zip(*code))[1])))\n        \n        return dp( code, len(s), k, '', 0)\n    \n    def getLengthOfOptimalCompression2(self, s: str, k: int) -> int:\n        N = len(s)\n        if N == k:\n            return 0\n        @lru_cache(None)\n        def singlelen(n) :\n            if n <= 1:\n                return n\n            elif n < 10:\n                return 2\n            elif n < 100:\n                return 3\n            else:\n                return 4\n                \n        def finallen(prev):\n            return prev[0] + singlelen(prev[1]) \n        \n        def add(prev, s):\n            if len(s) == 0:\n                return prev \n            \n            prevsum, curlen, cur = prev\n            for n in s:\n                if n == cur:\n                    curlen += 1\n                else:\n                    prevsum += singlelen(curlen)\n                    curlen, cur= 1, n  \n                \n            return (prevsum, curlen, s[-1:]) \n        \n        @lru_cache(None)\n        def dp(s, k, prev):\n            if k == 0:\n                return finallen(add(prev, s))\n            if len(s) == k:\n                return finallen(prev)\n\n            cur, s = s[:1], s[1:]\n            while cur == prev[2] and len(s) > k:\n                prev = add(prev,cur) \n                cur, s = s[:1], s[1:] \n\n            return min (dp(s, k - 1, prev), dp(s, k, add(prev,cur))) \n        \n        return dp(s, k, (0, 0, ''))\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'getLengthOfOptimalCompression'
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: 18176