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.*;

public class Main {
    public static final boolean DO_LOG = false; // TODO: move to run params
    private static Logger log = new Logger();

    static class Task {

        PrintWriter out;
        MyScanner in;
        int n;
        public void solve(MyScanner in, PrintWriter out) {
            this.in = in;
            this.out = out;


             n = in.nextInt();
             long b = 0, w= 0;
             for (int i = 0; i < n; i++) {
                 long a  = in.nextInt();
                 long s1 = a / 2;
                 if (a % 2 == 1) {
                     if (i % 2 == 0) {
                         s1++;
                     }
                 }
                 long s2 = a - s1;

                 w += s1;
                 b += s2;
             }

             log.info(w + " " + b);

             out.println(Math.min(b, w));
        }


    }

    public static void main(String[] args) {

        MyScanner in = new MyScanner();
        PrintWriter out = new PrintWriter(System.out);
        Task solver = new Task();

        solver.solve(in, out);

        out.close();
    }

    public static class Logger {

        public void info(String s) {
            if (DO_LOG) {
                System.out.println(s);
            }
        }
    }

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}

/*me after this round
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
░░░░░░░░░░░░░░░░▄▄███▄▄▄░▄▄██▄░░░░░░░
░░░░░░░░░██▀███████████████▀▀▄█░░░░░░
░░░░░░░░█▀▄▀▀▄██████████████▄░░█░░░░░
░░░░░░░█▀▀░▄██████████████▄█▀░░▀▄░░░░
░░░░░▄▀░░░▀▀▄████████████████▄░░░█░░░
░░░░░▀░░░░▄███▀░░███▄████░████░░░░▀▄░
░░░▄▀░░░░▄████░░▀▀░▀░░░░░░██░▀▄░░░░▀▄
░▄▀░░░░░▄▀▀██▀░░░░░▄░░▀▄░░██░░░▀▄░░░░
█░░░░░█▀░░░██▄░░░░░▀▀█▀░░░█░░░░░░█░░░
█░░░▄▀░░░░░░██░░░░░▀██▀░░█▀▄░░░░░░▀▀▀
▀▀▀▀░▄▄▄▄▄▄▀▀░█░░░░░░░░░▄█░░█▀▀▀▀▀█░░
░░░░█░░░▀▀░░░░░░▀▄░░░▄▄██░░░█░░░░░▀▄░
░░░░█░░░░░░░░░░░░█▄▀▀▀▀▀█░░░█░░░░░░█░
░░░░▀░░░░░░░░░░░░░▀░░░░▀░░░░▀░░░░░░░░
░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░
 */