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.util.Arrays;

public class Main {
	static int inf = 1000000000;
	public static void main(String ards[])
	{
		Scanner cin = new Scanner(System.in);
		
		int n = cin.nextInt();
		int num = 0;
		long b = 0;
		long w = 0;
		for(int i = 0;i<n;i++){
	        long a = cin.nextLong();
	        if(num == 0){
	            b += (a/2 + a%2);
	            w += a/2;
	            num = 1;
	        }
	        else{
	            num = 0;
	            b += a/2;
	            w += (a/2+a%2);
	        }
	    } 
		long ans = Math.min(b, w);
        System.out.println(ans);
	}
}
 		 				   		    	  	 	  	 		