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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var slice []int

func main() {
	stdin := bufio.NewScanner(os.Stdin)
	stdin.Scan()
	text := stdin.Text()
	target, _ := strconv.Atoi(text)
	slice = devide(target)
	dai, shou := slice[len(slice)-1], 1
	//fmt.Println(len(slice))
	for _, v := range slice {
		shou *= v
		if dai < shou {
			tmp := shou
			shou = dai
			dai = tmp
		}
	}
	dai /= slice[len(slice)-1]
	//偶数のやつは2で割れる。
	//「target = x * y」にしたときに、最小になるx,yの組み合わせを求める

	fmt.Println(dai + shou - 2)
}

func devide(num int) []int {
	flag := true
	slice = append(slice, 1)
	for i := 2; i < num/2; i++ {
		if num%i == 0 {
			slice = append(slice, i)
			flag = false
			devide(num / i)
			break
		}
	}
	if flag {
		slice = append(slice, num)
	}
	return slice
}