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.Scanner;

public class DominoForYoung {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		long[] arr = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = in.nextLong();
		}
		long[] bipartite = new long[2];
		for (int i = 0; i < n; i++) {
			bipartite[0] += arr[i] / 2;
			bipartite[1] += arr[i] / 2;
			if (arr[i] % 2 == 1) {
				if (i % 2 == 1) {
					bipartite[0]++;
				}
				else {
					bipartite[1]++;
				}
			}
			
		}
		
		System.out.println(Math.min(bipartite[0], bipartite[1]));

	}

}