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.*;
public class Main
{
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		long t=2;
		long[] arr=new long[n];
		int f=-1,p=-1;
		long ans=0;
		for(int i=1;i<=n;i++)
		{
		    long x=sc.nextInt();
		    if(p==-1)
		        arr[++p]=x;
		    else
		    {
		        if(arr[p]>x)
		            {ans+=(arr[p]-x)/t;
		            arr[p]-=(t*((arr[p]-x)/t));}
		        if(arr[p]==x)
		        {
		            ans+=x;
		            p--;
		        }
		        else 
		            arr[++p]=x;
		    }
		}
		long a=0,b=0;
		for(int i=0;i<=p;i++)
		{
		    a+=arr[i]/t;
		    b+=(arr[i]-(arr[i]/t));
		}
		ans+=Math.min(a,b);
		System.out.println(ans);
		
		
	}
}
