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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

typedef unsigned long long ll;
const ll INF = 1010000000000000017LL;
const ll MOD = 1000000007LL;

#define REP(i, n) for(ll i = 0 ; i < n; i++)

//#define DEBUG(fmt, ...)
#define DEBUG(fmt, ...) fprintf(stderr, fmt "\n", ##__VA_ARGS__)

int main(){
    std::cout<<std::fixed<<std::setprecision(10);

    ll N;
    cin >> N;

    ll m = INF;
    for(ll i = 1; i*i <= N; i++ ){
        if( N%i == 0 ){
            m = min(m, (i-1)+(N/i-1));
        }
    }
    cout << m << endl;
}