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>
#define rep(i,n) for(int i = 0; i < (n); i++)
using namespace std;
using ll = long long;
using P = pair<int, int>;

vector<ll> enum_div(ll n) {
  vector<ll> ret;
  for(ll i = 1; i*i <= n; i++) {
    if(n%i == 0) {
      ret.push_back(i);
      if(i != 1 && i*i != n) {
        ret.push_back(n/i);
      }
    }
  }
  sort(ret.begin(), ret.end());
  return ret;
}

bool isprime(ll x) {
  ll i;
  if(x < 2) return 0;
  else if(x == 2) return 1;
  if(x%2 == 0) return 0;
  for(i = 3; i*i <= x; i += 2) if(x%i == 0) return 0;
  return 1;
}

int main() {
  ll n;
  cin >> n;
  if(isprime(n)) cout << n-1 << endl;
  else {
    vector<ll> vec = enum_div(n);
    vec.push_back(n);
    ll ans = INT_MAX;
    rep(i, vec.size()) {
      ll m = vec.at(i) + n/vec.at(i) - 2;
      ans = min(ans, m);
    }
    ans = min(ans, n-1);
    cout << ans << endl;
  }
  return 0;
}