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.io.*;
import java.text.*;
import static java.lang.System.*;
import static java.lang.Math.*;

public class main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		long res = 0, x = 0, y = 0;
		long a = 0;
		for(int i = 0; i < n; ++i){
			a = sc.nextLong();
			
			if(i % 2 == 0){
				x += (a / 2);
				y += (a + 1) / 2;
			}
			else{
				y += (a / 2);
				x += (a + 1) / 2;
			}
		}
		res += min(x, y); 
        out.println(res + "\n");
	}
}