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;

#ifdef LOCAL
#include "dump.hpp"
#else
#define dump(...)
#define dumpv(...)
#endif

#define rep(i, n) for (int i = 0; i < (n); i++)
#define mins(x, y) (x = min(x, y))
#define maxs(x, y) (x = max(x, y))
typedef long long ll;
typedef pair<int, int> P;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
const int MOD = 1e9 + 7;
const int INF = 1001001001;
const ll LINF = 1001002003004005006ll;

void solve() {
  ll n;
  cin >> n;
  vector<ll> dv;
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      dv.push_back(i);
      if (i * i != n && i != 1) { // nを含めたければi!=1を外す
        dv.push_back(n / i);
      }
    }
  }
  sort(dv.begin(), dv.end());
  dump(dv);
  ll ans = LINF;
  rep(i, dv.size()) {
    ll a = dv[i];
    ll b = n / dv[i];
    ans = min(ans, (a - 1) + (b - 1));
  }
  cout << ans << endl;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(15);
  // freopen("temp.1", "r", stdin);
  solve();
  return 0;
}