Tonight is brain dinner night and all zombies will gather together to scarf down some delicious brains. The artful Heidi plans to crash the party, incognito, disguised as one of them. Her objective is to get away with at least one brain, so she can analyze the zombies' mindset back home and gain a strategic advantage.

They will be N guests tonight: N - 1 real zombies and a fake one, our Heidi. The living-dead love hierarchies as much as they love brains: each one has a unique rank in the range 1 to N - 1, and Heidi, who still appears slightly different from the others, is attributed the highest rank, N. Tonight there will be a chest with brains on display and every attendee sees how many there are. These will then be split among the attendees according to the following procedure:

The zombie of the highest rank makes a suggestion on who gets how many brains (every brain is an indivisible entity). A vote follows. If at least half of the attendees accept the offer, the brains are shared in the suggested way and the feast begins. But if majority is not reached, then the highest-ranked zombie is killed, and the next zombie in hierarchy has to make a suggestion. If he is killed too, then the third highest-ranked makes one, etc. (It's enough to have exactly half of the votes – in case of a tie, the vote of the highest-ranked alive zombie counts twice, and he will of course vote in favor of his own suggestion in order to stay alive.)

You should know that zombies are very greedy and sly, and they know this too – basically all zombie brains are alike. Consequently, a zombie will never accept an offer which is suboptimal for him. That is, if an offer is not strictly better than a potential later offer, he will vote against it. And make no mistake: while zombies may normally seem rather dull, tonight their intellects are perfect. Each zombie's priorities for tonight are, in descending order: 

  1. survive the event (they experienced death already once and know it is no fun), 
  2. get as many brains as possible. 



Heidi goes first and must make an offer which at least half of the attendees will accept, and which allocates at least one brain for Heidi herself.

What is the smallest number of brains that have to be in the chest for this to be possible?

Input

The only line of input contains one integer: N, the number of attendees (1 ≤ N ≤ 109).

Output

Output one integer: the smallest number of brains in the chest which allows Heidi to take one brain home.

Examples

Input

1


Output

1


Input

4


Output

2

Note
import java.io.File;import java.io.FileInputStream;import java.io.FileNotFoundException;
import java.io.IOException;import java.io.InputStream;import java.io.PrintStream;
import java.io.PrintWriter;import java.security.AccessControlException;public class _p000690A1 {
static public void main(final String[] args) throws IOException{p000690A1._main(args);}

static private class p000690A1 extends Solver{public p000690A1(){singleTest=true;
}@Override public void solve()throws IOException{int n=sc.nextInt();sc.nextLine();
int p=n/2+n%2;pw.println(p);}static public void _main(String[]args)throws IOException
{new p000690A1().run();}}static private class MyScanner{private StringBuilder cache
=new StringBuilder();int cache_pos=0;private int first_linebreak=-1;private int 
second_linebreak=-1;private StringBuilder sb=new StringBuilder();private InputStream 
is=null;public MyScanner(final InputStream is){this.is=is;}private String charToString(final 
int c){return String.format("'%s'",c=='\n'?"\\n":(c=='\r'?"\\r":String.valueOf((char)c)));
}public int get(){int res=-1;if(cache_pos<cache.length()){res=cache.charAt(cache_pos);
cache_pos++;if(cache_pos==cache.length()){cache.delete(0,cache_pos);cache_pos=0;
}}else{try{res=is.read();}catch(IOException ex){throw new RuntimeException(ex);}
}return res;}private void unget(final int c){if(cache_pos==0){cache.insert(0,(char)c);
}else{cache_pos--;}}public String nextLine(){sb.delete(0,sb.length());int c;boolean 
done=false;boolean end=false;while((c=get())!=-1){if(check_linebreak(c)){done=true;
if(c==first_linebreak){if(!end){end=true;}else{cache.append((char)c);break;}}else 
if(second_linebreak!=-1 && c==second_linebreak){break;}}if(end && c!=first_linebreak 
&& c!=second_linebreak){cache.append((char)c);break;}if(!done){sb.append((char)c);
}}return sb.toString();}private boolean check_linebreak(int c){if(c=='\n'|| c=='\r')
{if(first_linebreak==-1){first_linebreak=c;}else if(c!=first_linebreak && second_linebreak
==-1){second_linebreak=c;}return true;}return false;}public int nextInt(){return 
Integer.parseInt(next());}public long nextLong(){return Long.parseLong(next());}
public boolean hasNext(){boolean res=false;int c;while((c=get())!=-1){if(!check_linebreak(c)
&& c!=' '&& c!='\t'){res=true;unget(c);break;}}return res;}public String next(){
sb.delete(0,sb.length());boolean started=false;int c;while((c=get())!=-1){if(check_linebreak(c)
|| c==' '|| c=='\t'){if(started){unget(c);break;}}else{started=true;sb.append((char)c);
}}return sb.toString();}public int nextChar(){return get();}public boolean eof()
{int c=get();boolean res=false;if(c!=-1){unget(c);}else{res=true;}return res;}public 
double nextDouble(){return Double.parseDouble(next());}}static private abstract class 
Solver{protected String nameIn=null;protected String nameOut=null;protected boolean 
singleTest=false;protected boolean preprocessDebug=false;protected boolean doNotPreprocess
=false;protected PrintStream debugPrintStream=null;protected MyScanner sc=null;protected 
PrintWriter pw=null;private int current_test=0;private int count_tests=0;protected 
int currentTest(){return current_test;}protected int countTests(){return count_tests;
}private void process()throws IOException{if(!singleTest){count_tests=sc.nextInt();
sc.nextLine();for(current_test=1;current_test<=count_tests;current_test++){solve();
pw.flush();}}else{count_tests=1;current_test=1;solve();pw.flush();}}abstract protected 
void solve()throws IOException;protected void run()throws IOException{boolean done
=false;try{if(nameIn!=null && new File(nameIn).exists()){try(FileInputStream fis
=new FileInputStream(nameIn);PrintWriter pw0=select_output();){done=true;sc=new 
MyScanner(fis);pw=pw0;process();}}}catch(IOException ex){}catch(AccessControlException 
ex){}if(!done){try(PrintWriter pw0=select_output();){sc=new MyScanner(System.in);
pw=pw0;process();}}}private PrintWriter select_output()throws FileNotFoundException
{if(nameOut!=null){return new PrintWriter(nameOut);}return new PrintWriter(System.out);
}}}
