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;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define reps(i, n) for (int i = 1; i <= (n); i++)
#define all(x) (x).begin(), (x).end()
#define rv(s) reverse((s).begin(), (s).end())
#define pii pair<int, int>
#define int int64_t
#define re(s) reverse((s).begin(), (s).end())
#define setout(n, x) setw(n) << setfill(x)
#define Fixed fixed << setprecision(10);
const long long mod = 1e9 + 7;

signed main()
{
   cin.tie(0);
   ios::sync_with_stdio(false);

   int n, cnt = 0, ans = 0;
   cin >> n;
   int a = sqrt(n);
   vector<int> x;

   reps(i, a)
   {
      if (n % i == 0)
      {
         ans = (i - 1) + (n / i - 1);
         x.push_back(ans);
      }
   }

   sort(all(x));

   cout << x[0] << '\n';
}