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>
//package cf;
import java.io.*;
import java.util.*;
import java.lang.*;
import java.math.*;
public class USACO {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter (System.out);
        //BufferedReader reader = new BufferedReader(new InputStreamReader(new FileInputStream("input.txt")));
        long n = Integer.parseInt(reader.readLine());
        StringTokenizer st = new StringTokenizer(reader.readLine()," ");
        long a=0;
        long b=0;
        for (int i=0;i<n;i++) {
        	long j = Integer.parseInt(st.nextToken());
        	if (i%2==0) {
        		a=a+j/2;
        		b=b+(j+1)/2;
        	} else {
        		b=b+j/2;
        		a=a+(j+1)/2;
        	}
        }
        out.println(Math.min(a,b));
        reader.close();
        out.close();
    }
}