You are given a Young diagram. 

Given diagram is a histogram with n columns of lengths a_1, a_2, …, a_n (a_1 ≥ a_2 ≥ … ≥ a_n ≥ 1).

<image> Young diagram for a=[3,2,2,2,1].

Your goal is to find the largest number of non-overlapping dominos that you can draw inside of this histogram, a domino is a 1 × 2 or 2 × 1 rectangle.

Input

The first line of input contain one integer n (1 ≤ n ≤ 300 000): the number of columns in the given histogram.

The next line of input contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 300 000, a_i ≥ a_{i+1}): the lengths of columns.

Output

Output one integer: the largest number of non-overlapping dominos that you can draw inside of the given Young diagram.

Example

Input


5
3 2 2 2 1


Output


4

Note

Some of the possible solutions for the example:

<image> <image>
import java.io.*;
import java.util.StringTokenizer;

public class Main {

    public void solve(InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; ++i) {
            a[i] = in.nextInt();
        }
        long b = 0, w = 0;
        boolean isBlack = true;
        for (int i = 0; i < n; ++i) {
            if (a[i] % 2 == 1) {
                if (isBlack) {
                    b += a[i] / 2 + 1;
                    w += a[i] / 2;
                } else {
                    b += a[i] / 2;
                    w += a[i] / 2 + 1;
                }
            } else {
                b += a[i] / 2;
                w += a[i] / 2;
            }
            isBlack = !isBlack;
        }
        out.println(Math.min(w, b));
    }

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        new Main().solve(in, out);
        out.flush();
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}
