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: Accepted)

package main

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

var sc = bufio.NewScanner(os.Stdin)

func init() {
	const maxWord = (1 << 30)
	buf := []byte{}
	sc.Buffer(buf, maxWord)
	sc.Split(bufio.ScanWords)
}

func input() string {
	sc.Scan()
	return sc.Text()
}

func min(x, y int) int {
	if x < y {
		return x
	}
	return y
}

func main() {
	n, _ := strconv.Atoi(input())

	ans := n - 1
	for i := 1; i*i <= n; i++ {
		if n%i == 0 {
			q := n / i
			ans = min(ans, i+q-2)
		}
	}
	fmt.Println(ans)
}