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"
	"math"
	"sort"
)

func main() {
	var n, r int
	fmt.Scan(&n)
	var a []int
	for i := 1; i*i <= n; i++ {
		if n%i == 0 {
			a = append(a, i)
			if i != n/i {
				a = append(a, n/i)
			}
		}
	}
	sort.Sort(sort.IntSlice(a))

	min := math.MaxInt64
	for i := 0; i < len(a)-1; i++ {
		for j := i + 1; j < len(a); j++ {
			if a[i]*a[j] == n {
				if min > a[j]-a[i] {
					r = (a[i] - 1) + (a[j] - 1)
					min = a[j] - a[i]
				}
			}
		}
	}
	fmt.Println(r)
}