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)

def factorizeFlat(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            while temp%i==0:
                arr.append(i)
                temp //= i

    if temp!=1:
        arr.append(temp)

    if arr==[]:
        arr.append(n)

    return arr

n = int(input())
p = factorizeFlat(n)
a = p.pop(0)
b = p.pop() if len(p) > 0 else 1
while(len(p) > 0):
    #print("a:{} b:{} l:{} r:{} p:{}".format(a, b, p[0], p[-1], p))
    if (a * p[0]) < (b * p[-1]):
        a = a * p.pop(0)
    else:
        b = b * p.pop()
#print("a:{} b:{}".format(a, b))
print(a - 1 + b - 1)