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"
	"math"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func main() {
	input := scanInt64Num()
	fmt.Println(check(input))
}

// example
func check(num int64) (steps int64) {
	// worst case
	if num%2 == 0 {
		steps = num / 2
	} else {
		steps = num - 1
	}

	limit := int64(math.Sqrt(float64(num)))
	var i, tmp int64

	for i = 3; i <= limit; i++ {
		if num%i == 0 {
			tmp = i + num/i - 2
			if tmp < steps {
				steps = tmp
			}
		}
	}
	return
}

func scanInt64Num() (num int64) {
	sc.Scan()

	num, e := strconv.ParseInt(sc.Text(), 10, 64)
	if e != nil {
		panic(e)
	}
	return num
}