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: Wrong Answer)

#include<bits/stdc++.h>
#include<iomanip>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
typedef long long ll;
typedef long  l;
typedef pair<int,int> pl;
const ll INF=100000000000000001;

vector<ll> soinsu(ll n){
  vector<ll> a;
  for(ll i=2;i*i<=n;i++){
    if(n%i)continue;
    while(n%i==0){
      n/=i;
      a.push_back(i);
    }
  }
  if(n!=1)a.push_back(n);
  return a;
}

int main(){
  ll n,b;cin>>n;
  auto f=soinsu(n);
  b=1;

  ll ans=INF;
  for(ll i=0;i<f.size();i++){
    // cout<<f[i]<<endl;
     // cout<<"b "<<b<<" n "<<n<<endl;
    ll a=(b-1)+(n-1);
    ans=min(ans,a);
    b*=f[i]; n/=f[i];
  }

  cout<<ans<<endl;

  return 0;
}