Contest Duration: ~ (local time) (100 minutes) Back to Home
C - Walk on Multiplication Table /

Time Limit: 2 sec / Memory Limit: 1024 MB

制約

• 2 \leq N \leq 10^{12}
• N は整数である。

入力

N


入力例 1

10


出力例 1

5


5 回の移動で (2,5) に到達することができます。5 回未満の移動では 10 が書かれたマスに到達することは出来ません。

入力例 2

50


出力例 2

13


13 回の移動で (5,10) に到達できます。

入力例 3

10000000019


出力例 3

10000000018


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.