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 {
	final static int maxn=(int)3e5+10;
	static long a[]=new long [maxn];
	static long   dp[]=new long [maxn];
 public static void main(String args[])
 {
	 //System.out.println(1);
	 Scanner input=new Scanner(System.in);
	 int n=input.nextInt();
	 for(int i=1;i<=n;i++)
		 a[i]=input.nextLong();
	long x=0,y=0;
	for(int i=1;i<=n;i++)
	{
		if(i%2==1)
		{
			x+=(a[i])/2;y+=(a[i]+1)/2;
		}
		else
		{
			x+=(a[i]+1)/2;y+=(a[i])/2;
		}
	}
	System.out.println(Math.min(x, y));
	 
 }
}

   	  							 	  			  			  				