# 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 = 'from collections import defaultdict, Counter\n\n# the special case allows for linear solution\ndef exchange_sort(sequence):\n    n_sevens, n_eights = sequence.count(7), sequence.count(8)\n    sevens = defaultdict(lambda: 0, Counter(sequence[:n_sevens]))\n    eights = defaultdict(lambda: 0, Counter(sequence[n_sevens:n_sevens + n_eights]))\n    nines = defaultdict(lambda: 0, Counter(sequence[n_sevens + n_eights:]))\n    direct_78 = min(sevens[8], eights[7])\n    direct_79 = min(sevens[9], nines[7])\n    direct_89 = min(eights[9], nines[8])\n    sevens[8] -= direct_78\n    nines[7] -= direct_79\n    nines[8] -= direct_89\n    eights[7] -= direct_78\n    eights[9] -= direct_89\n    sevens[7], eights[8], nines[9] = 0, 0, 0\n    return direct_78 + direct_79 + direct_89 + sum(nines.values()) * 2'
_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: 10924