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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define int long long
using P = pair<int, int>;
constexpr array<int, 4> dx = {1, 0, -1, 0};
constexpr array<int, 4> dy = {0, 1, 0, -1};
constexpr int INF = 1000000000000000007LL;
constexpr int MOD = 1000000000 + 7;
// constexpr int MOD = 998244353;
template <class T>
bool chmax(T &a, const T &b)
{
    if (a < b)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b)
{
    if (b < a)
    {
        a = b;
        return 1;
    }
    return 0;
}
constexpr int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
constexpr int fact(int n) { return n > 1 ? n * fact(n - 1) % MOD : 1; }
int modinv(int a)
{
    int b = MOD, u = 1, v = 0;
    while (b)
    {
        int t = a / b;
        a -= t * b;
        swap(a, b);
        u -= t * v;
        swap(u, v);
    }
    u %= MOD;
    if (u < 0)
        u += MOD;
    return u;
}
constexpr int modpow(int a, int n)
{
    int rtn = 1;
    while (n > 0)
    {
        if (n & 1)
            rtn = rtn * a % MOD;
        a = a * a % MOD;
        n >>= 1;
    }
    return rtn;
}

signed main()
{
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << setprecision(10);

    int a, b, n;
    cin >> n >> a >> b;

    // 簡略化のため a <= b となるように交換する
    if (a > b)
        swap(a, b);

    int ans = INF;
    // 差が偶数 → そのまま近づくように勝つ 負ける
    if (abs(a - b) % 2 == 0)
    {
        ans = abs(a - b) / 2;
    }
    else
    // 差が奇数 → どちらかが1卓で勝つorN卓で負けるして差を偶数にする
    // ex. 100 2 7 は4ゲーム
    {

        {
            int aa = a, bb = b;
            int step1 = a - 1 + 1; // A が1卓で勝つまでのゲーム数
            aa = 1;
            bb = b - step1; // その後同じ卓で合うまでのゲーム数
            int step2 = abs(aa - bb) / 2;

            ans = min(step1 + step2, ans);
        }
        {
            int aa = a, bb = b;
            int step1 = n - b + 1; // B がN卓で負けるまでのゲーム数
            aa = a + step1;
            bb = n; // その後同じ卓で合うまでのゲーム数
            int step2 = abs(aa - bb) / 2;

            ans = min(step1 + step2, ans);
        }
    }
    cout << ans << endl;
}