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.Scanner;

public class que4 {

	public static void main(String[] args) {
    Scanner scn=new Scanner(System.in);
    long w=0;
    long b=0;
    int n=scn.nextInt();
    int []arr=new int[n];
    for(int i=0;i<n;i++){
    	arr[i]=scn.nextInt();
    	
    }
    
    for(int i=0;i<n;i++){
    	if(arr[i]%2==0){
    		w+=arr[i]/2;
    		b+=arr[i]/2;
    	}
    	else {
    		if(i%2==0){
    			w+=(arr[i]+1)/2;
    			b+=arr[i]/2;
    		}else{
    			b+=(arr[i]+1)/2;
    			w+=arr[i]/2;
    		}
    	}
    }
    System.out.println(Math.min(w, b));
	}

}
