Problem:
Score : 300 points

Problem Statement

2N players are running a competitive table tennis training on N tables numbered from 1 to N.

The training consists of rounds.
In each round, the players form N pairs, one pair per table.
In each pair, competitors play a match against each other.
As a result, one of them wins and the other one loses.

The winner of the match on table X plays on table X-1 in the next round,
except for the winner of the match on table 1 who stays at table 1.

Similarly, the loser of the match on table X plays on table X+1 in the next round,
except for the loser of the match on table N who stays at table N.

Two friends are playing their first round matches on distinct tables A and B.
Let's assume that the friends are strong enough to win or lose any match at will.
What is the smallest number of rounds after which the friends can get to play a match against each other?

Constraints

2 \leq N \leq 10^{18}

1 \leq A < B \leq N

All input values are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

Print the smallest number of rounds after which the friends can get to play a match against each other.

Sample Input 1

5 2 4

Sample Output 1

1

If the first friend loses their match and the second friend wins their match, they will both move to table 3 and play each other in the next round.

Sample Input 2

5 2 3

Sample Output 2

2

If both friends win two matches in a row, they will both move to table 1.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define int long long
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define rrep(i,n) for(int (i)=((n)-1);(i)>=0;(i)--)
#define itn int
#define miele(v) min_element(v.begin(), v.end())
#define maele(v) max_element(v.begin(), v.end())
#define SUM(v) accumulate(v.begin(), v.end(), 0LL)
#define lb(a, key) lower_bound(a.begin(),a.end(),key)
#define ub(a, key) upper_bound(a.begin(),a.end(),key)
#define COUNT(a, key) count(a.begin(), a.end(), key) 
#define BITCOUNT(x) __builtin_popcount(x)
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define F first
#define S second
using P = pair <int,int>;
using WeightedGraph = vector<vector <P>>;
using UnWeightedGraph = vector<vector<int>>;
using Real = long double;
using Point = complex<Real>; //Point and Vector2d is the same!
using Vector2d = complex<Real>;
const long long INF = 1LL << 60;
const int MOD = 1000000007;
const double EPS = 1e-15;
const double PI=3.14159265358979323846;
template <typename T> 
int getIndexOfLowerBound(vector <T> &v, T x){
    return lower_bound(v.begin(),v.end(),x)-v.begin();
}
template <typename T> 
int getIndexOfUpperBound(vector <T> &v, T x){
    return upper_bound(v.begin(),v.end(),x)-v.begin();
}
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
#define DUMPOUT cerr
#define repi(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
istream &operator>>(istream &is, Point &p) {
    Real a, b; is >> a >> b; p = Point(a, b); return is;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T,U> &p_var) {
    is >> p_var.first >> p_var.second;
    return is;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &vec) {
    for (T &x : vec) is >> x;
    return is;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &pair_var) {
    DUMPOUT<<'{';
    os << pair_var.first;
    DUMPOUT<<',';
    os << " "<< pair_var.second;
    DUMPOUT<<'}';
    return os;
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> &vec) {
    DUMPOUT<<'[';
    for (int i = 0; i < vec.size(); i++) 
    os << vec[i] << (i + 1 == vec.size() ? "" : " ");
    DUMPOUT<<']';
    return os;
}
template <typename T>
ostream &operator<<(ostream &os, vector<vector<T>> &df) {
  for (auto& vec : df) os<<vec;
  return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &map_var) {
    DUMPOUT << "{";
    repi(itr, map_var) {
        os << *itr;
        itr++;
        if (itr != map_var.end()) DUMPOUT << ", ";
        itr--;
    }
    DUMPOUT << "}";
    return os;
}
template <typename T>
ostream &operator<<(ostream &os, set<T> &set_var) {
    DUMPOUT << "{";
    repi(itr, set_var) {
        os << *itr;
        itr++;
        if (itr != set_var.end()) DUMPOUT << ", ";
        itr--;
    }
    DUMPOUT << "}";
    return os;
}
void print() {cout << endl;}
template <class Head, class... Tail>
void print(Head&& head, Tail&&... tail) {
  cout << head;
  if (sizeof...(tail) != 0) cout << " ";
  print(forward<Tail>(tail)...);
}
void dump_func() {DUMPOUT << '#'<<endl;}
template <typename Head, typename... Tail>
void dump_func(Head &&head, Tail &&... tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) > 0) DUMPOUT << ", ";
    dump_func(std::move(tail)...);
}
#ifdef DEBUG_
#define DEB
#define dump(...)                                                              \
    DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                            \
            << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]"        \
            << endl                                                            \
            << "    ",                                                         \
        dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

signed main(void) { cin.tie(0); ios::sync_with_stdio(false);
    int n, a, b; cin>>n>>a>>b;
    int ans = INF;
    if(abs(a-b)%2 == 0) chmin(ans, abs(a-b)/2);
    else {
        int aa = a, bb = b;
        int ltmp = 0;
        ltmp += a-1;
        aa = 1, bb = b-(a-1);
        if(bb >= 1){
            chmin(ans, ltmp + abs(bb-aa)/2 + 1);
        }
        aa = a, bb = b;
        int rtmp = 0;
        rtmp = n-bb;
        aa += rtmp;
        if(aa < n){
            chmin(ans, rtmp + abs(bb-aa)/2 + 1);
        }
    }
    chmin(ans, max(a-1 , b-1));
    chmin(ans, max(n-a , n-b));
    print(ans);
}