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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

typedef pair<long long,long long> P;

int main(){
    long long N; cin >> N;
    //vector<unsigned long long> memo(1000000000000,-1);
    //array<array<long long,1000000>,1000000> memo;
    queue<P> q;

    q.push(P (1,1));
    while(q.size()){
        P p = q.front(); q.pop();

        //計算したことあるかの確認
        //if(memo.at(p.first).at(p.second) != -1) continue;
        //cout << p.first << p.second << endl;

        if(p.first * p.second == N){
            long long ans = (p.first - 1) +  (p.second - 1);
            cout << ans << endl;
            break;
        }else if(p.first <= p.second){
            q.push(P (p.first + 1,1));
        }else{
            q.push(P (p.first,p.second + 1));
        };
    }
    return 0;
}