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 9.2.1) (judge verdict: Accepted)

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

vector<ll> prime;//素因数分解で出てきた素数を全て挿入するvector

//O(√n)
//整列済み
/*
void prime_factorize(ll n){
    if(n<=1) return;
    ll l=sqrt(n);
    for(ll i=2; i<=l; i++){
        if(n%i==0){
        prime_factorize(i);
        prime_factorize(ll(n/i));
        return;
        }
    }
    prime.push_back(n);
    return;
}
*/
int main() {
    ll N;
    cin >> N;
    vector<ll> cnt;
    for (ll i=1; i*i<=N; i++) {
        if (N%i==0) {
            cnt.push_back(i+N/i-2);
        }
    }
    sort(cnt.begin(),cnt.end());
    cout << cnt[0] << endl;
    /*
    prime_factorize(N);
    ll n = prime.size();
    vector<ll> vec(n);
    vec[0] = prime[0];
    for (ll i=1; i<n; i++) {
        if (prime[i-1]==prime[i]) {
            vec[i]=vec[i-1]*prime[i];
        }
        else {
            vec[i]=prime[i];
        }
    }
    vector<ll> cnt(n);
    for (ll i=0; i<n; i++) {
        cnt[i] = vec[i] + N/vec[i] - 2;
    }
    sort(cnt.begin(),cnt.end());
    cout << cnt[0] << endl;
    */
}