A few years ago, Aaron left his old school and registered at another due to security reasons. Now he wishes to find Jane, one of his schoolmates and good friends.

There are `n` schools numbered from 1 to `n`. One can travel between each pair of schools by buying a ticket. The ticket between schools `i` and `j` costs `(i + j) modulo (n + 1)` and can be used multiple times. Help Aaron find the minimum total cost to visit all schools. He can start and finish at any school.

Range : 1 ≤ n ≤ 10^(6)

```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 find_jane(n):\n    return (n-1) // 2\n    \n"""\n1,2,3,...,n\ncost = (a+b) % (n+1)\n\nbest association is:\n    b = n+1-a  ->  cost=0\n    \n    1 2 3 4 5     -> 1 <-> 5\n                     2 <-> 4\n\nto link ("L") those two, the best remaining way is:\n    b = n+1-a+1  -> cost=1\n\n    1 2 3 4 5     -> 1 <-> 5: 0\n                  L: 5 <-> 2: 1\n                     2 <-> 4: 0\n                  L: 4 <-> 3: 1\n                 --------------\n                 total cost = 2\n\n\n    1 2 3 4       -> 1 <-> 4: 0\n                  L: 4 <-> 2: 1\n                     2 <-> 3: 0\n                 --------------\n                 total cost = 1\n\nAnd so on...\n"""'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'find_jane'
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: 5278