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.io.*;

public class YoungDomino {
	public static void main(String[] args) throws IOException
	{
		//holy shite i actually experienced overflow
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int num = Integer.parseInt(br.readLine());
		String[] temp = br.readLine().split(" ");
		long black = 0;
		long white = 0;
		int column;
		for (int i = 0; i < num; i++)
		{
			column = Integer.parseInt(temp[i]);
			black += column/2;
			white += column/2;
			if (column%2 == 1)
			{
				if (i%2 == 0)
					black++;
				else
					white++;
			}
		}
		System.out.println(Math.min(black, white));
		
	}
}
