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 Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
     Scanner sc=new Scanner (System.in);
     while(sc.hasNext()) {
    	 long n=sc.nextLong();
    	 long  A=0,B=0;
    	 for (int i = 0; i < n; i++) {
			long m=sc.nextLong();
			long a=(m+1)/2;
			long b=m-a;
			if((i&1)==0) {
				A+=a;B+=b;
			}else {
				A+=b;B+=a;
			}
		}
    	 System.out.println(Math.min(A,B));
     }
	}

}
