Problem:
Score : 100 points

Problem Statement

You are parking at a parking lot. You can choose from the following two fee plans:

Plan 1: The fee will be A×T yen (the currency of Japan) when you park for T hours.

Plan 2: The fee will be B yen, regardless of the duration.

Find the minimum fee when you park for N hours.

Constraints

1≤N≤20

1≤A≤100

1≤B≤2000

All input values are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

When the minimum fee is x yen, print the value of x.

Sample Input 1

7 17 120

Sample Output 1

119

If you choose Plan 1, the fee will be 7×17=119 yen.

If you choose Plan 2, the fee will be 120 yen.

Thus, the minimum fee is 119 yen.

Sample Input 2

5 20 100

Sample Output 2

100

The fee might be the same in the two plans.

Sample Input 3

6 18 100

Sample Output 3

100

Solution in Pascal (FPC 2.6.2) (judge verdict: Accepted)

program Project1;
             
{$APPTYPE CONSOLE}
         
uses
  SysUtils,math;
var
  g,r,a,h,w,i,j,count,x,y,sw,m,n,b,c,soeji,sum,max,k,t,z:Integer;
  //l:array of Integer;
  l,l1,l2:int64;
  s,s123,s1,s2,s3:string;
  tf:Boolean;
  //nyu:TStringList;
  xc,yc,space:char;
begin
  try
    { TODO -oUser -cConsole Main : ここにコードを記述してください }
    Read(n);
    Read(a);
    Readln(b);

    Writeln(((n*a)+b-abs((n*a)-b))div 2);
    Readln;
  except
    on E: Exception do
      Writeln(E.ClassName, ': ', E.Message);
  end;
end.