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 "fmt"

func prmFac(x int) map[int]bool {
	pfm := make(map[int]bool)
	pfm[1] = true
	for i := 2; i*i <= x; i++ {
		for x%i == 0 {
			x /= i
			pfm[i] = true
		}
	}
	if x > 1 {
		pfm[x] = true
	}
	return pfm
}

func main() {
	var n int
	fmt.Scan(&n)

	pf := prmFac(n)
	max := 1
	for k := range pf {
		if k > max {
			max = k
		}
	}
	a, b := max, n/max
	fmt.Println((a - 1) + (b - 1))
}