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)


N = int(input())

factor = []

tmp = int(N**0.5) + 1
for num in range(2,tmp):
    while N % num == 0:
        N //= num
        factor.append(num)

if N == 1:
    factor.append(N)

    A=1
    B=1
    for i in range(len(factor)):
        if i % 2 == 0:
            A *= factor[i]
        else:
            B *= factor[i]

    print(A+B-2)

else:
    A=1
    B=1
    for i in range(len(factor)):
        if i % 2 == 0:
            A *= factor[i]
        else:
            B *= factor[i]
    
    if A * B < N:
        print(A*B + N -2)
    elif A > B:
        print(A + B* N -2)
    else:
        print(A*N + B -2)