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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

/**
 *
 * @author kaixi_000
 */
public class Cf1268B {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int N=Integer.parseInt(br.readLine());
        long black=0; long white=0;
        StringTokenizer st=new StringTokenizer(br.readLine());
        boolean odd=false;
        while(st.hasMoreTokens()) {
            int x=Integer.parseInt(st.nextToken());
            if(odd){
                black+=(x+1)/2;
                white+=(x)/2;
            }else{
                black+=(x)/2;
                white+=(x+1)/2;
            }
            odd=!odd;
        }
        System.out.println(Math.min(white,black));
    }
    
}
