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 PyPy3 (2.4.0) (judge verdict: Accepted)

N = int(input())

def yakusuu(N):
    ret1 = []
    ret2 = []
    for i in range(1,int(N**0.5)+1):
        if N%i==0:
            ret1.append(i)
            ret2.append(N//i)
    return ret1,ret2

X,Y = yakusuu(N)

ans = 10**13
for i,x in enumerate(X):
    y = Y[i]
    ans = min(ans,abs(x-1)+abs(y-1))
print(ans)