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>
#define REP(i, n) for (int i = 0; i < n; i++)
#define REPR(i, n) for (int i = n; i >= 0; i--)
#define FOR(i, m, n) for (int i = m; i < n; i++)
#define FORR(i, m, n) for (int i = m; i >= n; i--)
#define ALL(x) (x).begin(), (x).end()
const long long INF = 1e15;
using namespace std;
typedef long long ll;

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

bool is_prime(ll x) {
  for (ll i = 2; i * i <= x; i++) {
    if (x % i == 0) return false;
  }
  return true;
}

int main() {
  ll n;
  cin >> n;
  if (is_prime(n)) {
    cout << n - 1 << endl;
    return 0;
  }
  auto div = divisor(n);
  ll ans = INF;
  for (auto x : div) {
    ll y = n / x;
    ans = min(ans, x - 1 + y - 1);
  }
  cout << ans << endl;

  return 0;
}