You are given an integer N. Consider all possible segments on the coordinate axis with endpoints at integer points with coordinates between 0 and N, inclusive; there will be <image> of them.

You want to draw these segments in several layers so that in each layer the segments don't overlap (they might touch at the endpoints though). You can not move the segments to a different location on the coordinate axis. 

Find the minimal number of layers you have to use for the given N.

Input

The only input line contains a single integer N (1 ≤ N ≤ 100).

Output

Output a single integer - the minimal number of layers required to draw the segments for the given N.

Examples

Input

2


Output

2


Input

3


Output

4


Input

4


Output

6

Note

As an example, here are the segments and their optimal arrangement into layers for N = 4.

<image>
import java.util.*;

public class Problem2 {

    public static int n;
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        Set<Otr> set = new TreeSet<>();


        n = scanner.nextInt();
        for(int i = 0; i <= n; ++i) {
            for(int j = i + 1; j <= n; ++j) {
                set.add(new Otr(i, j));
            }
        }

//        System.out.println(set.size());
//        System.out.println(set);

        Set<Layer> layers = new HashSet<>();

        Iterator<Otr> iter = set.iterator();
        while (iter.hasNext()) {
            Otr otr = iter.next();
            boolean added = false;

            Iterator<Layer> layerIterator = layers.iterator();
            while (layerIterator.hasNext()) {
                Layer layer = layerIterator.next();
                if (layer.add(otr)) {
                    added = true;
                    break;
                }
            }

            if (!added) {
                Layer newLayer = new Layer();
                newLayer.add(otr);
                layers.add(newLayer);
            }
        }

        System.out.println(layers.size());
        //System.out.println(layers);

    }

    public static class Otr implements Comparable<Otr>{
        public int left;
        public int right;

        public Otr(int l, int r) {
            left = l;
            right = r;
        }

        public int len() {
            return right - left;
        }

        @Override
        public String toString() {
            return "[" + left + "," + right + "]";
        }

        @Override
        public int compareTo(Otr o) {
            int len1 = len();
            int len2 = o.len();

            if (len1 != len2) return Integer.compare(len2, len1);

            return Integer.compare(left, o.left);
        }

        public boolean intersect(Otr other) {
            if (left >= other.right) return false;
            if (other.left >= right) return false;

            return true;
        }
    }

    public static class Layer {
        List<Otr> list = new ArrayList<>();

        public boolean add(Otr newOtr) {
            boolean added = true;

            for(Otr otr : list) {
                if (otr.intersect(newOtr)) {
                    added = false;
                    break;
                }
            }

            if (added) {
                list.add(newOtr);
            }

            return added;
        }

        @Override
        public String toString() {
            StringBuilder sb = new StringBuilder();
            sb.append("{ ");
            for(Otr otr : list) {
                sb.append(otr);
                sb.append(" , ");

            }

            sb.append("}\n");
            return sb.toString();
        }
    }
}
