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>) {
    val n = readLine()!!.toLong()

    fun f(x: Long): List<Long> {
        val list = mutableListOf<Long>()
        var t = x
        var i = 2L

        while (t > 1 && i * i <= x) {
            if (t % i == 0L) {
                list.add(i)
                t /= i
                continue
            }
            i++
        }
        list.add(t)

        return list
    }

    var a = 1L
    var b = 1L
    val xs = f(n)

    for (x in xs.sortedDescending()) {
        if (a <= b) {
            a *= x
        } else {
            b *= x
        }
    }

    println(a + b - 2)
}