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.math.BigInteger;
import java.util.*;
public class Hello {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long n = sc.nextInt();
		long white = 0;
		long black = 0;
		long sum = 0;
		for(int i=0;i<n;i++) {
			int a = sc.nextInt();
			sum+=a;
			if(i%2==0)
				white += (a+1)/2;
			else {
				white += a/2;
			}
		}
		//System.out.println(white);
		//System.out.println(sum);
		System.out.println(Math.min(sum-white, white));
	}
}
