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 A {
	public static void main (String[] args) { new A(); }

	A() {
		Scanner s = new Scanner(System.in);
		System.err.println("");

		int n = s.nextInt();
		int[] a = new int[n];
		for(int i = 0; i < n; i++) a[i] = s.nextInt();
		long[] cnt = new long[2];
		for(int i = 0; i < n; i++) {
			int p1 = i&1, p2 = p1^1;
			cnt[p1] += a[i]/2 + (a[i]&1);
			cnt[p2] += a[i]/2;
		}
		System.out.println(Math.min(cnt[0], cnt[1]));
		
	}
}