Problem:
Score : 300 points

Problem Statement

Takahashi is standing on a multiplication table with infinitely many rows and columns.

The square (i,j) contains the integer i \times j. Initially, Takahashi is standing at (1,1).

In one move, he can move from (i,j) to either (i+1,j) or (i,j+1).

Given an integer N, find the minimum number of moves needed to reach a square that contains N.

Constraints

2 \leq N \leq 10^{12}

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the minimum number of moves needed to reach a square that contains the integer N.

Sample Input 1

10

Sample Output 1

5

(2,5) can be reached in five moves. We cannot reach a square that contains 10 in less than five moves.

Sample Input 2

50

Sample Output 2

13

(5, 10) can be reached in 13 moves.

Sample Input 3

10000000019

Sample Output 3

10000000018

Both input and output may be enormous.

Solution in Kotlin (1.0.0) (judge verdict: Accepted)

import java.io.*
import java.util.*

fun main(args: Array<String>) {
    val inputStream = System.`in`
    val outputStream = System.out
    val inp = Main.InputReader(inputStream)
    val out = PrintWriter(outputStream)
    val solver = Main.TaskC()
    solver.solve(inp, out)
    out.close()
}

class Main {
    internal class TaskC {
        fun solve(inp: InputReader, out: PrintWriter) {
            var n = inp.nextLong()
            var ans = Long.MAX_VALUE
            var d = 2L
            var isSimple = true
            while (d * d <= n) {
                if (n % d == 0L) {
                    isSimple = false
                    val curDist = (d - 1) + (n / d - 1)
                    ans = Math.min(ans, curDist)
                }
                d++
            }
            if (isSimple)
                ans = n - 1
            out.println(ans)
        }
    }

    internal class InputReader(stream: InputStream) {
        private var reader: BufferedReader = BufferedReader(InputStreamReader(stream), 32768)
        private var tokenizer: StringTokenizer? = null

        init {
            tokenizer = null
        }

        operator fun next(): String {
            while (tokenizer == null || !tokenizer!!.hasMoreTokens()) {
                try {
                    tokenizer = StringTokenizer(reader.readLine())
                } catch (e: IOException) {
                    throw RuntimeException(e)
                }
            }
            return tokenizer!!.nextToken()
        }

        fun nextInt(): Int {
            return Integer.parseInt(next())
        }

        fun nextLong(): Long {
            return next().toLong()
        }
    }
}