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.lang.*;
public class Main
{
	public static void main(String[] args) {
	    
	    Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        long a[]=new long[n];
        long b=0,w=0;
        for(int i=0;i<n;i++){
          a[i]=input.nextLong();
          if(i%2==0){
              b+=Math.ceil(a[i]/2.0);
              w+=(a[i]/2);
          }
          else{
              b+=(a[i]/2);
              w+=Math.ceil(a[i]/2.0);
          } 
        }
		System.out.println(Math.min(b,w));
	}
}