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 ajava;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        long[] a = new long[n+1];
        ArrayList<Long> b = new ArrayList<Long>(); ArrayList<Long> c = new ArrayList<Long>();
        int cnt = 0; long ans = 0;
        for(int i = 0; i < n; i++) {
            a[i] = in.nextLong();
            if(a[i]%2 == 0) ans += a[i]/2;
            else {
                if(i%2 == 1) b.add(a[i]);
                else c.add(a[i]);
            }
        }
        while(cnt != b.size() && cnt != c.size()) {
            ans += (b.get(cnt) + c.get(cnt))/2;
            cnt++;
        }
        if(cnt != b.size()) {
            while(cnt != b.size()) {
                ans += b.get(cnt) /2;
                cnt++;
            }
        }
        else {
            while(cnt != c.size()) {
                ans += c.get(cnt)/2;
                cnt++;
            }
        }
        System.out.println(ans);
        in.close();
    }
}

 	 					  					 	 	    	 	 	