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: Wrong Answer)

#include<stdio.h>
long long sq(long long n){
    long long i,m=10;
    for(i=0;i<12;i++){
        if(n<=m)break;
        else m*=10;
    }
    return i+1;
}
long long power(long long x,long long y){
    for(long long i=0;i<y;i++){
        x*=x;
    }
    return x;
}
long long divide(long long n){
    if(n%2==0)return n/2;
    else return n/2+1;
}
int main(void){
    long long n,res1,res2;
    scanf("%lld",&n);
    res1=1;
    res2=n;
    for(long long i=1;i<=power(10,divide(sq(n)));i++){
        if(n<i*i)break;
        if((n%i==0)&&((res1+res2)>(i+n/i))){
            res1=i;
            res2=n/i;
        }
    }
    printf("%lld\n",res1+res2-2);
    return 0;
}