Given an integer array arr, remove a subarray (can be empty) from arr such that the remaining elements in arr are non-decreasing.
A subarray is a contiguous subsequence of the array.
Return the length of the shortest subarray to remove.
 
Example 1:
Input: arr = [1,2,3,10,4,2,3,5]
Output: 3
Explanation: The shortest subarray we can remove is [10,4,2] of length 3. The remaining elements after that will be [1,2,3,3,5] which are sorted.
Another correct solution is to remove the subarray [3,10,4].
Example 2:
Input: arr = [5,4,3,2,1]
Output: 4
Explanation: Since the array is strictly decreasing, we can only keep a single element. Therefore we need to remove a subarray of length 4, either [5,4,3,2] or [4,3,2,1].

Example 3:
Input: arr = [1,2,3]
Output: 0
Explanation: The array is already non-decreasing. We do not need to remove any elements.

Example 4:
Input: arr = [1]
Output: 0

 
Constraints:

1 <= arr.length <= 10^5
0 <= arr[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 findLengthOfShortestSubarray(self, arr: List[int]) -> int:\n        # Find the longest monotonically non-decreasing prefix array in [0, i]\n        n = len(arr)\n        l = 1\n        while l < n and arr[l-1] <= arr[l]:\n            l += 1\n        l -= 1  \n        if l >= n - 2:\n            return n - 1 - l\n                \n        # Find the longest monotonically non-decreasing suffix array in [j, n - 1]\n        r = n - 2\n        while r >= 0 and arr[r] <= arr[r+1]:\n            r -= 1\n        r += 1\n        if r <= 1:\n            return r\n    \n        # Start off with min of either left or right side removed as the min_to_move\n        min_to_remove = min(n - 1, n - 1 - (l + 1) + 1, r)\n        # Try to merge [0..i] from the left into [r..n-1]. We start with assuming\n        # entire right side [r..n-1] could be included and try to see if [0], [0, 1] and so on\n        # from the left side could be merged in. Until we hit some i on the left side that is \n        # too large for the current arr[r], retreat r back further to the right to try\n        # against a bigger value. Keep trying until we run out of either room for i to expand\n        # toward the right or for no more r left to retreat to the right.\n        i = 0\n        while i < l + 1:\n            if arr[i] <= arr[r]:\n                min_to_remove = min(min_to_remove, r - i - 1)\n                # we could definitely include arr[i] into the result\n                i += 1\n            elif r < n - 1:\n                # We cannot include arr[r] into the result but we could\n                # include arr[i] into the result\n                r += 1\n                i += 1\n            else:\n                break\n        \n        return min_to_remove\n\n        \n    def findLengthOfShortestSubarray_bruteforce_bsearch(self, arr: List[int]) -> int:\n        # Returns the smallest index `idx` such that arr[idx] >= val\n        def bsearch(val, low, high):\n            while low < high:\n                mid = (low + high) // 2\n                if arr[mid] >= val:\n                    high = mid\n                else:\n                    low = mid + 1\n            if val > arr[high]:\n                return high + 1\n            return high\n        \n        # Find the longest monotonically non-decreasing prefix array in [0, i]\n        n = len(arr)\n        curr_max = float('-inf')\n        i = 0\n        while i < n:\n            if arr[i] < curr_max:\n                break\n            curr_max = arr[i]\n            i += 1\n        i -= 1  \n        if i >= n - 2:\n            return n - 1 - i\n                \n        # Find the longest monotonically non-decreasing suffix array in [j, n - 1]\n        curr_min = float('inf')\n        j = n - 1\n        while j >= 0:\n            if arr[j] > curr_min:\n                break\n            curr_min = arr[j]\n            j -= 1\n        j += 1\n        if j <= 1:\n            return j\n        \n        # For each value arr[k], in [0, i], find the `right_idx` into the suffix array in [j, n - 1]\n        # such that arr[k] >= arr[right_idx]. We want to find the one that results in the longest\n        # sequence [0..k] + [right_idx..n-1]\n        min_to_remove = float('inf')\n        for k in range(i, -1, -1):\n            right_idx = bsearch(arr[k], j, n - 1)\n            l = k + 1 + n - right_idx\n            to_remove = n - l\n            min_to_remove = min(min_to_remove, to_remove)\n            \n        # For each value arr[k], in [j, n-1], find the `left_idx` into the prefix array in [0, i]\n        # such that arr[k] >= arr[left_idx - 1]. We want to find the one that results in the longest\n        # sequence [0..left_idx-1] + [k..n-1]\n        for k in range(j, n):\n            left_idx = bsearch(arr[k], 0, i)\n            l = left_idx + n - k\n            to_remove = n - l\n            min_to_remove = min(min_to_remove, to_remove)\n        \n        return min_to_remove\n        \n        \n\n        \n        \n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'findLengthOfShortestSubarray'
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: 5918