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 Ruby (2.3.3) (judge verdict: Accepted)

input = gets

N = input.split(" ")[0].to_i

rt_n = Math.sqrt(N).to_i
ans = []

# 対象性により、a >= bとできるので、a*aの二次元配列を探索すれば良い
# 上記の平方根をとって、a <= sqrt(N)の範囲で、N = a * bとなるbを求める
1.upto(rt_n) do |a|
  if N%a == 0
    b = N / a
    
    # 移動回数(ido)は、a + b -2で求まる
    ido = a + b -2
    ans.push(ido)
  else
    next
  end
end

# 移動回数が最小の値を返す
p ans.min