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: Runtime Error)

package main

import (
	"fmt"
	"sort"
)

func main() {
	var N int

	fmt.Scan(&N)

	var pf []int	
	var prime = 2
	PRIME_CHECK:
	for prime > 0 {
		if ( N % prime == 0){
			N = N / prime
			pf = append(pf,prime)
		}else{
			prime = prime + 1
		}
		if N==1 {
			break PRIME_CHECK
		}
	}	
	// fmt.Println(pf)
	// fmt.Println(len(pf))

	var a int
	var b int
	var loop = 1
	GET_TWO_NUM:
	for loop > 0 { 
		if (len(pf)==2){
			break GET_TWO_NUM
		}
		a, pf, _ = delete(pf,len(pf)/2-1)
		b, pf, _ = delete(pf,len(pf)/2-1)
		// fmt.Println(pf)
		// fmt.Println(a*b)
		pf = append(pf,a*b)
		// fmt.Println(pf)
		sort.Sort(sort.IntSlice(pf))
		// fmt.Println(pf)
	}
	var finalA int
	var finalB int

	finalA = pf[0]
	finalB = pf[1]
	// fmt.Println(finalA)
	// fmt.Println(finalB)
	fmt.Println(finalA+finalB-2)
	

}

func delete(slice []int, i int) (int, []int, error) {
    ret := slice[i]
    if len(slice) < i || len(slice) < i {
        return 0, nil, fmt.Errorf("Error")
    }
    ans := make([]int, len(slice))
    copy(ans, slice)

    ans = append(slice[:i], slice[(i+1):]...)

    return ret, ans, nil
}