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.*;

public class D1269 {
    public static void main(String[] args)throws IOException {
        BufferedReader inp = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

        int size = Integer.parseInt(inp.readLine());
        String[] s1 = inp.readLine().split(" ");
        long[] given = new long[size];
        for(int i=0;i<size;i++){
            int a = Integer.parseInt(s1[i]);
            given[i] = a;
        }

        long black= 0;
        long white = 0;
        boolean alter = false;
        int[] rest = new int[size];
        for(int i=0;i<size;i++){
            long a = given[i]/2;
            if(alter){
                black+=a;
                white+=given[i]-a;
                alter = false;
            }
            else{
                alter = true;
                black+=given[i]-a;
                white+=a;

            }
        }


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



    }
}
