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.util.*;
import java.io.*;

public class Dominos {

    public static void main(String[] args) throws IOException {
        FastReader sc = new FastReader();
        PrintWriter pw = new PrintWriter(System.out);

        int n = sc.nextInt();
        int[] list = new int[n];
        for(int i = 0; i<n; i++){
            list[i] = sc.nextInt();
        }
        long w = 0;
        long b = 0;
        boolean curr = true;
        for(int i = list.length - 1; i >= 0; i--){
            if(curr){
                w += (long)(Math.ceil(list[i]/2.0));
                b += (long)(list[i]/2.0);
            }
            else{
                w += (long)(list[i]/2.0);
                b += (long)(Math.ceil(list[i]/2.0));
            }
            //pw.println(b + " " + w + " " + curr);
            curr = !curr;
        }
        pw.println(Math.min(b,w));
        pw.close();
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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;
        }
    }
}