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C - Walk on Multiplication Table

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 $N$.

10

5

$(2,5)$ can be reached in five moves. We cannot reach a square that contains $10$ in less than five moves.

50

13

$(5, 10)$ can be reached in $13$ moves.

10000000019

10000000018

Both input and output may be enormous.