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.lang.reflect.Array;
import java.util.*;

import static java.lang.Math.*;

public class Main {
    void run() throws IOException {
        int n = nextInt();
        int[] a = new int[n];
        for (int i = 0; i < a.length; i++) {
            a[i] = nextInt();
        }
        long black = 0;
        long white = 0;
        for (int i = 0; i < a.length; i++) {
            if (i % 2 == 0) {
                black += a[i] / 2 + a[i] % 2;
                white += a[i] / 2;
            } else {
                black += a[i] / 2;
                white += a[i] / 2 + a[i] % 2;
            }
        }
        pw.print(min(black,white));
        pw.close();
    }

    class point implements Comparable<point> {
        int x, y;

        public point(int a, int b) {
            x = a;
            y = b;
        }

        @Override
        public int compareTo(point o) {
            if (o.x == this.x) return Integer.compare(o.y, this.y);
            return Integer.compare(o.x, this.x);
        }

    }

    long mod = (long) 1e9 + 7;
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    //BufferedReader br = new BufferedReader(new FileReader("qual.in"));

    StringTokenizer st = new StringTokenizer("");
    PrintWriter pw = new PrintWriter(System.out);
    //PrintWriter pw = new PrintWriter("qual.out");

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

    String next() throws IOException {
        if (!st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }

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

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

    public Main() throws FileNotFoundException {
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }
}