# Task
 Sorting is one of the most basic computational devices used in Computer Science. 
 
 Given a sequence (length ≤ 1000) of 3 different key values (7, 8, 9), your task is to find the minimum number of exchange operations necessary to make the sequence sorted. 

 One operation is the switching of 2 key values in the sequence.

# Example

 For `sequence = [7, 7, 8, 8, 9, 9]`, the result should be `0`.
 
 It's already a sorted sequence.

 For `sequence = [9, 7, 8, 8, 9, 7]`, the result should be `1`.
 
 We can switching `sequence[0]` and `sequence[5]`.
 
 For `sequence = [8, 8, 7, 9, 9, 9, 8, 9, 7]`, the result should be `4`.
 
 We can:
```
 [8, 8, 7, 9, 9, 9, 8, 9, 7] 
 switching sequence[0] and sequence[3]
 --> [9, 8, 7, 8, 9, 9, 8, 9, 7]
 switching sequence[0] and sequence[8]
 --> [7, 8, 7, 8, 9, 9, 8, 9, 9]
 switching sequence[1] and sequence[2]
 --> [7, 7, 8, 8, 9, 9, 8, 9, 9]
 switching sequence[5] and sequence[7]
 --> [7, 7, 8, 8, 8, 9, 9, 9, 9] 
```
So `4` is the minimum number of operations for the sequence to become sorted.

# Input/Output


 - `[input]` integer array `sequence`

  The Sequence.


 - `[output]` an integer

  the minimum number of operations.

```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 = 'def lsorter2(l):\n    intsec = [(a,b) for (a,b) in zip(l, sorted(l)) if a!=b]\n    return list(zip(*intsec))\n\ndef naturalSwap(l):\n    x1 = lsorter2(l)\n    ori = list(x1[0])\n    sort = list(x1[1])\n\n    si = [i for i, x in enumerate(sort) if x == ori[0]]\n    fi = [i for i, x in enumerate(ori) if x == sort[0]]\n\n    ci = [x for x in si if x in fi]\n\n    new_ori = [x for i,x in enumerate(ori) if i not in ci]\n\n    swap_num1 = len(ci)\n\n    si2 = [i for i, x in enumerate(ori) if x == ori[0]]\n    fi2 = [i for i, x in enumerate(sort) if x == sort[0]]\n\n    ci2 = [x for x in si2 if x in fi2]\n\n    new_ori2 = [x for i,x in enumerate(ori) if i not in ci2]\n\n    swap_num2 = len(ci2)\n\n    swap_real= min(swap_num1,swap_num2)\n\n    to_force_swap1 = ci[:swap_real]\n    to_force_swap2 = ci2[:swap_real]\n\n    to_force_swap3 = to_force_swap1 + to_force_swap2\n\n    new_list = [x for i, x in enumerate(ori) if i not in to_force_swap3]\n    return (new_list, swap_real)\n\ndef forcedSwap(l):\n    x1 = lsorter2(l)\n    ori = list(x1[0])\n    sort = list(x1[1])\n\n    idx = ori.index(sort[0])\n    ori[0], ori[idx] = ori[idx], ori[0]\n    return ori\n\n\n\ndef exchange_sort(l):\n    swaps = 0\n    dlist = l[:]\n    cnt = 1\n    if dlist == sorted(dlist):\n        return 0\n    \n    else:\n        while cnt > 0 and len(dlist) > 0:\n            cnt = 0\n            x1 = naturalSwap(dlist)\n            cnt = x1[1]\n            swaps += x1[1]\n            dlist = x1[0]\n        while len(dlist) > 2:\n            x2 = forcedSwap(dlist)\n            swaps+=1\n            dlist = x2\n        return swaps\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'exchange_sort'
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: 5700