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 Python (3.4.3) (judge verdict: Wrong Answer)

#
# abc144 c
#
import unittest
from io import StringIO
import sys
import math


def input():
    return sys.stdin.readline().rstrip()


def resolve():
    N = int(input())

    S = math.ceil(math.sqrt(N))
    ans = N - 1

    for i in range(1, S):
        if N % i == 0:
            j = N // i
            ans = min(ans, i+j-2)
    print(ans)


class TestClass(unittest.TestCase):
    def assertIO(self, input, output):
        stdout, stdin = sys.stdout, sys.stdin
        sys.stdout, sys.stdin = StringIO(), StringIO(input)
        resolve()
        sys.stdout.seek(0)
        out = sys.stdout.read()[: -1]
        sys.stdout, sys.stdin = stdout, stdin
        self.assertEqual(out, output)

    def test_入力例_1(self):
        input = """10"""
        output = """5"""
        self.assertIO(input, output)

    def test_入力例_2(self):
        input = """50"""
        output = """13"""
        self.assertIO(input, output)

    def test_入力例_3(self):
        input = """10000000019"""
        output = """10000000018"""
        self.assertIO(input, output)


if __name__ == "__main__":
    # unittest.main()
    resolve()