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: Wrong Answer)

fun main(args: Array<String>) {
    var n = readLine()!!.toLong()

    var l = mutableListOf<Int>()
    var i = 2
    var c = Math.sqrt(n.toDouble())
    var t1 = 1L
    var t2 = 1L
    while (n != 1L){
        if (n %  i == 0L){
            l.add(i)
            n /= 2
        }else{
            i++
            if(i > c){
                t2 = n
                break
            }
        }
    }
    for (i in l){
        if (t1 > t2) t2 *= i
        else t1 *= i
    }
    println(t1 + t2 - 2)
}