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: Time Limit Exceeded)

a = gets.chomp.to_i

MAX = 10**12
def solve(a)
    ms = 1..MAX

    # find the first n to start
    n = -1
    ms.each {|m|
        if a < m*m
            n = m
            break
        end
    }

    # iterate from (n,1)~(n,n)
    while (n <= MAX)
        (1..n).each {|i|
            if a == i*n
                return (n-1) + (i-1)
            end
        }
        n += 1
    end
end

puts solve(a)