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>
////////////////////---------------------------SHUBHAM CHAUDHARI-------------------------------///////////////////////


import java.util.*;

public class Main {
    public static void main(String[] args) {

        Scanner in=new Scanner(System.in);
        int n=in.nextInt();
        long cntw=0;
        long cntb=0;
        for(int i=0;i<n;i++)
        {
            long m=in.nextLong();
            long a=(m+1)/2;
            long b=(m)/2;
            if((i&1)>0)
            {
                cntw+=a;cntb+=b;
            }
            else
            {
                cntb+=a;cntw+=b;
            }
        }
        System.out.println(Math.min(cntb,cntw));

    }



}