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 int long long
template <class T>
bool chmax(T &a, const T &b)
{
    if (a < b)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b)
{
    if (b < a)
    {
        a = b;
        return 1;
    }
    return 0;
}
int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
constexpr array<int, 4> dx = {1, 0, -1, 0};
constexpr array<int, 4> dy = {0, 1, 0, -1};
constexpr int MOD = 100000000 + 7;

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

    int n;
    cin >> n;

    int min_x = 1, min_y = n;
    int sq_n = sqrt(n);
    for (int i = 2; i < sq_n + 10; i++)
    {
        if (n % i == 0)
        {
            int x = i, y = n / i;
            if (x + y < min_x + min_y)
            {
                min_x = x, min_y = y;
            }
        }
    }
    cout << min_x + min_y - 2 << endl;
}