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.util.*;
import java.io.*;

public class D {
    public static void main(String[] args) throws IOException{
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        int n = Integer.parseInt(f.readLine());
        long[] arr = new long[n];
        StringTokenizer st = new StringTokenizer(f.readLine());
        for(int i = 0; i < n; i++) arr[i] = Long.parseLong(st.nextToken());
        long black = 0;
        long white = 0;
        for(int i = 0; i < n; i++){
            if(i%2 == 0){
                black+=(arr[i]/2);
                white+=((arr[i]) - (arr[i]/2));
            }else{
                white+=(arr[i]/2);
                black+=((arr[i]) - (arr[i]/2));
            }
        }
        out.println(Math.min(white, black));



        out.close();
    }
}
