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 C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<stdio.h>
#include<stdlib.h>
int main(){
    long long n,i,j;
    
    scanf("%lld",&n);
    long long tmp = n-1; //初期化
    long long ans_x = 1;
    long long ans_y = n;
    
    for(i = 1; i <= n/2 ; i++){
        if(n % i == 0){
            int syou = n/i;
            int sa = llabs(syou-i);
            if(sa < tmp){
                ans_x = i;
                ans_y = syou;
                tmp = sa;
//                printf("%lld %lld is best sa is %lld\n",ans_x,ans_y,tmp);
            }
        }
    }
    printf("%lld\n",ans_x + ans_y - 2);
    return 0;
}