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 provides ...
package main

import (
	"fmt"
	"math"
)

func main() {
	var N int
	var m int

	fmt.Scan(&N)

	m = N - 1
	for i := 0; float64(i) <= math.Sqrt(float64(N)); i++ {
		if float64(N)/float64(1+i) - math.Trunc(float64(N)/float64(1+i)) == 0 {
			if i + (N/(1+i)-1) < m {
				m = i + (N/(1+i)-1)
			}
		}
	}
	fmt.Println(m)
}