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.*;
import java.util.*;

public class D{

	public static BufferedReader br;
	public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
	static int n;
	static long[] a;
	public static void main(String[] args) throws IOException {
		readInput();
		long sol =0;
		long total = 0;
		for (int i = 0; i < n; i++) {
			if ((i & 1) == 0) {
				sol += a[i]&1;
			}
			else sol -= a[i]&1;
			total += a[i];
		}
		out.println((total - Math.abs(sol))>>1);
		out.close();
	}

	public static void readInput() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		n = Integer.parseInt(br.readLine());
		a = new long[n]; StringTokenizer st = new StringTokenizer(br.readLine());
		for (int i = 0; i < n; i++) {
			a[i] = Long.parseLong(st.nextToken());
		}
	}
}
