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"

func main() {
	var n int
	fmt.Scan(&n)

	nums := primeFactors(n)
	if len(nums) >= 3 {
		var fst int
		var scd int
		for i, v := range nums {
			if i == 0 {
				fst = v
				continue
			} else if i == 1 {
				fst *= v
				continue
			}
			scd += v
		}
		if fst != 1 {
			fst--
		}
		if scd != 1 {
			scd--
		}
		fmt.Println(fst + scd)
	} else if len(nums) == 2 {
		fst := nums[0]
		scd := nums[1]
		if fst != 1 {
			fst--
		}
		if scd != 1 {
			scd--
		}
		fmt.Println(fst + scd)
	} else {
		fmt.Println(nums[0] - 1)
	}
}

func primeFactors(n int) (pfs []int) {
	// Get the number of 2s that divide n
	for n%2 == 0 {
		pfs = append(pfs, 2)
		n = n / 2
	}

	// n must be odd at this point. so we can skip one element
	// (note i = i + 2)
	for i := 3; i*i <= n; i = i + 2 {
		// while i divides n, append i and divide n
		for n%i == 0 {
			pfs = append(pfs, i)
			n = n / i
		}
	}

	// This condition is to handle the case when n is a prime number
	// greater than 2
	if n > 2 {
		pfs = append(pfs, n)
	}

	return
}