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 Go (1.6) (judge verdict: Accepted)

package main

import (
        "bufio"
        "fmt"
        "math/big"
        "os"
        "strconv"
        "strings"
)

var sc = bufio.NewScanner(os.Stdin)

func init() {
        // TODO: メモリの使用量がやばいので Token ごとに読む
        // Reference: https://atcoder.jp/contests/abc148/submissions/9067537
        bufsize := 100 * 1024 * 1024
        sc.Buffer(make([]byte, bufio.MaxScanTokenSize), bufsize)
}
func readInt() int              { return readIntArray()[0] }
func readInt2() (int, int)      { a := readIntArray(); return a[0], a[1] }
func readInt3() (int, int, int) { a := readIntArray(); return a[0], a[1], a[2] }
func readIntArray() []int {
        a := make([]int, 0, 1000)
        sc.Scan()
        for _, v := range strings.Split(sc.Text(), " ") {
                vv, _ := strconv.Atoi(v)
                a = append(a, vv)
        }
        return a
}
func readString() string                    { return readStringArray()[0] }
func readString2() (string, string)         { a := readStringArray(); return a[0], a[1] }
func readString3() (string, string, string) { a := readStringArray(); return a[0], a[1], a[2] }
func readStringArray() []string             { sc.Scan(); return strings.Split(sc.Text(), " ") }

func main() {
        sn, sa, sb := readString3()
        n, _ := new(big.Int).SetString(sn, 10)
        a, _ := new(big.Int).SetString(sa, 10)
        b, _ := new(big.Int).SetString(sb, 10)

        m := new(big.Int)
        m.Mod(m.Sub(b, a), big.NewInt(int64(2)))
        cent, _ := new(big.Int).SetString(sn, 10)
        if m.Cmp(new(big.Int)) == 0 {
                // even
                cent.Div(cent.Sub(b, a), big.NewInt(int64(2)))
        }

        up := new(big.Int)
        up.Sub(b, big.NewInt(int64(1)))
        down := new(big.Int)
        down.Sub(n, a)

        var simple *big.Int
        if up.Cmp(down) == 1 {
                // up > down
                if down.Cmp(cent) == 1 {
                        // down > cent
                        simple = cent
                } else {
                        simple = down
                }
        } else {
                // up <= down
                if up.Cmp(cent) == 1 {
                        // up > cent
                        simple = cent
                } else {
                        simple = up
                }
        }

        var result *big.Int
        upcent, _ := new(big.Int).SetString(sn, 10)
        downcent, _ := new(big.Int).SetString(sn, 10)
        if m.Cmp(new(big.Int)) == 1 {
                // odd
                // ex. [100 4 31]
                // (b-a-1)/2 + a = (b+a-1)/2
                upcent.Div(upcent.Sub(upcent.Add(b, a), big.NewInt(int64(1))), big.NewInt(int64(2)))
                //upcent.Sub(upcent.Add(b, a), big.NewInt(int64(1)))

                // ex. [100 71 98]
                // (n-(a+(n+1)-b))/2 + (n+1-b) = (2n-a-b+1)/2
                downcent.Div(downcent.Add(downcent.Sub(downcent.Sub(downcent.Mul(n, big.NewInt(int64(2))), a), b), big.NewInt(int64(1))), big.NewInt(int64(2)))
                if upcent.Cmp(downcent) == 1 {
                        // upcent > downcent
                        if downcent.Cmp(simple) == 1 {
                                // downcent > simple
                                result = simple
                        } else {
                                result = downcent
                        }
                } else {
                        // upcent <= downcent
                        if upcent.Cmp(simple) == 1 {
                                // up > cent
                                result = simple
                        } else {
                                result = upcent
                        }
                }
        } else {
                result = simple
        }

        fmt.Println(result)
        //fmt.Printf("up: %v, cent: %v, down: %v, upcent: %v, downcent: %v\n", up, cent, down, upcent, downcent)
}