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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.*;

public class D {

    void solve() throws Exception {
        long n = nl();
        long w = 0;
        long b = 0;
        for (long i = 0; i < n; i++) {
            long t = nl();
            if (i % 2 == 0) {
                w += t / 2 + t % 2;
                b += t / 2;
            } else {
                w += t / 2;
                b += t / 2 + t % 2;
            }
        }
        out.println(Math.min(w, b));
    }

    void run() throws Exception {
        initIO();
        solve();
        out.flush();
    }

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

    /**
     * IO.
     */

    PrintWriter out;
    BufferedReader br;
    StringTokenizer tokenizer;

    void initIO() {
        out = new PrintWriter(System.out);
        br = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = null;
    }

    int ni() throws Exception {
        return Integer.parseInt(ns());
    }

    long nl() throws Exception {
        return Long.parseLong(ns());
    }

    double nd() throws Exception {
        return Double.parseDouble(ns());
    }

    int[] nia(int n) throws Exception {
        int[] x = new int[n];
        for (int i = 0; i < x.length; i++) {
            x[i] = ni();
        }
        return x;
    }

    long[] nla(int n) throws Exception {
        long[] x = new long[n];
        for (int i = 0; i < x.length; i++) {
            x[i] = nl();
        }
        return x;
    }

    double[] nda(int n) throws Exception {
        double[] x = new double[n];
        for (int i = 0; i < x.length; i++) {
            x[i] = nd();
        }
        return x;
    }

    String ns() throws Exception {
        while (tokenizer == null || !tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(br.readLine());
        return tokenizer.nextToken();
    }

    String nline() throws Exception {
        tokenizer = null;
        return br.readLine();
    }
}
