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.math.BigInteger;
import java.util.*;
import java.io.*;


public class Main {

    public static void main(String[] args) throws FileNotFoundException {
        Scanner in = new Scanner(System.in);;
        PrintWriter out = new PrintWriter(System.out);
        int T = in.nextInt();
        long a = 0;
        long b = 0;
        while (T-- > 0){
            int p = in.nextInt();
            a+=(p/2);
            b+=(p/2);
            if((T&1) == 0)a+=(p&1);
            else b+=(p&1);
        }
        a = Math.min(a,b);
        out.println(a);
        out.close();
    }
}