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 P609B {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        int[] rows = new int[n];
        String[] line = br.readLine().split(" ");
        long white = 0;
        long black = 0;
        for(int i=0; i<n; i++) {
            rows[i] = Integer.parseInt(line[i]);
            int bigger = rows[i] / 2 + (rows[i] % 2 == 0 ? 0 : 1);
            int smaller = rows[i] / 2;
            if(i%2 == 0) {
                white += bigger;
                black += smaller;
            } else {
                white += smaller;
                black += bigger;
            }
        }

        System.out.println(Math.min(white, black));


    }
}
