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 {
    val N = readLong
    val max = Math.sqrt(N)
    def calc(c:Long, i:Long, j:Long):Array[Long] =  {
        if(c + 1 > max) {
            Array(i,j)
        } else {
            var ji = j
          	var ii = i
            if(N%c==0) {
                ji = N / c
                ii = c
            }
            calc(c+1, ii , ji)
        }
    }
    var ans = calc(1, 1 ,N)
    println(ans(0) + ans(1) - 2)        

}