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.lang.*;
import java.util.*;
import java.io.*;

public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);

        final int n = scan.nextInt();
        int input[] = new int[n];
        for (int i = 0; i < n; i++) {
            input[i] = scan.nextInt();
        }

        long answer = 0;
        for (int i = 0; i < n; i++) {
            answer += input[i] / 2;
            input[i] %= 2;
        }

        int odd = 0, even = 0;
        for (int i = 0; i < n; i++) {
            if (input[i] == 1) {
                if (i % 2 == 0) {
                    even++;
                } else {
                    odd++;
                }
            }
        }
        answer += Math.min(odd, even);
        System.out.println(answer);
    }
}
