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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

// namespaceの値をコンテスト名にして運用
namespace ABC144C
{
    class Input
    {
        /// <summary>
        /// 1行の入力を取得する
        /// </summary>
        /// <returns>文字列</returns>
        public string String()
        {
            return Console.ReadLine();
        }

        /// <summary>
        /// 複数行の入力を取得
        /// </summary>
        /// <returns>文字列の配列</returns>
        public string[] ArrayString(int rowNumber)
        {
            string[] s = new string[rowNumber];
            for (int i = 0; i < rowNumber; i++)
            {
                s[i] = String();
            }

            return s;
        }

        /// <summary>
        /// 1行の入力を取得
        /// </summary>
        /// <returns>int型の値</returns>
        public int Int()
        {
            return int.Parse(String());
        }

        /// <summary>
        /// 1行の入力を取得
        /// </summary>
        /// <returns>int型の配列</returns>
        public int[] ArrayInt()
        {
            return Split().Select(int.Parse).ToArray();
        }

        /// <summary>
        /// 複数行の入力を取得
        /// </summary>
        /// <param name="rowNumber">行数</param>
        /// <returns>int型の配列</returns>
        public int[] ArrayInt(int rowNumber)
        {
            int[] ints = new int[rowNumber];
            for (int i = 0; i < rowNumber; i++)
            {
                ints[i] = Int();
            }

            return ints;
        }

        /// <summary>
        /// 1行の入力を取得
        /// </summary>
        /// <returns>long型の値</returns>
        public long Long()
        {
            return long.Parse(String());
        }

        /// <summary>
        /// 1行の入力を取得
        /// </summary>
        /// <returns>long型の配列</returns>
        public long[] ArrayLong()
        {
            return Split().Select(long.Parse).ToArray();
        }

        public long[] ArrayLong(int rowNumber)
        {
            long[] longs = new long[rowNumber];
            for (int i = 0; i < rowNumber; i++)
            {
                longs[i] = Long();
            }

            return longs;
        }

        /// <summary>
        /// 1行の入力を取得
        /// </summary>
        /// <returns>double型の値</returns>
        public double Double()
        {
            return double.Parse(String());
        }

        /// <summary>
        /// 1行の入力を取得
        /// </summary>
        /// <returns>double型の配列</returns>
        public double[] ArrayDouble()
        {
            return Split().Select(double.Parse).ToArray();
        }

        private IEnumerable<string> Split()
        {
            return String().Split(' ');
        }
    }

    class Program
    {
        static void Main(string[] args)
        {
            Solver solver = new Solver();
            solver.Solve();
        }
    }

    class Solver
    {
        public Solver()
        {
            Input input = new Input();
            N = input.Long();
        }

        private long N;

        public void Solve()
        {
            long root = (long)Math.Sqrt(N);
            while (root > 1)
            {
                if (N % root == 0)
                {
                    Console.WriteLine(root + N / root - 2);
                    return;
                }

                root--;
            }
            Console.WriteLine(N - 1);
        }
    }
}