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 Scala (2.11.7) (judge verdict: Wrong Answer)


object Main extends App {

  import scala.annotation.tailrec

  /** 素数列 */
  val primes: Stream[Long] = 2 #:: sieve(3)

  /** n 以上の素数列を返す */
  private def sieve(n: Long): Stream[Long] =
    if (primes.takeWhile(p => p * p <= n).exists(n % _ == 0)) sieve(n + 2)
    else n #:: sieve(n + 2)

  /** n を素因数分解して (素数, 指数) のシーケンスとして返す */
  def factorize(n: Long): Seq[(Long, Int)] = factorize(n, primes)

  private def factorize(n: Long, ps: Stream[Long]): List[(Long, Int)] = {
    if (n <= 1) return Nil
    val head #:: tail = ps
    if (head * head > n) return List((n, 1))
    val (exponent, quot) = calculateExponent(n, head, 0)
    if (exponent == 0) factorize(quot, tail)
    else (head, exponent) :: factorize(quot, tail)
  }

  /**
   * n を割り切ることができる prime の最大の指数と、
   * 割り切った時の商を (指数, 商) として返す
   */
  @tailrec
  private def calculateExponent(n: Long, prime: Long, exponent: Int): (Int, Long) =
    if (n % prime != 0) (exponent, n)
    else calculateExponent(n / prime, prime, exponent + 1)

  val n = scala.io.StdIn.readLine.toLong
  var ans = n - 1

  val exp = factorize(n).flatMap { nn => List.fill(nn._2)(nn._1) }
  (1 until exp.size).foreach { ii =>
    val tmp = exp.splitAt(ii)
    val anstmp = (tmp._1.product - 1) + (tmp._2.product - 1)
    if (anstmp < ans) {
      ans = anstmp
    }
  }

  println(ans)
}