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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

Var n,ans:Qword;
    i:Longint;
Function prime(n:Qword):Boolean;
    Var i:Longint;
        OK:Boolean;
    Begin
        OK:=n>=2;
        For i:=2 to trunc(sqrt(n)) do
            If n mod i = 0 then begin
                OK:=False; Break;
            End;
        Exit(OK);
    End;
Begin
    Readln(n);
    If prime(n) then writeln(n-1)
    Else begin
        For i:=trunc(sqrt(n)) downto 2 do
            If n mod i = 0 then begin
                ans:=(i-1)+(n div i -1); Break;
            End;
        Writeln(ans);
    End;
End.