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.*;
import java.io.*;

public class Solution{
	long rem = 1000000007L;
	int[] ds;
	
	public Solution(){
		Scanner sc = new Scanner(System.in);
		int tests = 1;
        
        for(int t=1; t<=tests; t++){
			int n = sc.nextInt();
			
			int[] arr = new int[n];
			for(int i=0; i<n; i++){
				arr[i] = sc.nextInt();
			}
			
			long black = 0;
			long white = 0;
			
			for(int i=n-1; i>=0; i--){
				int half = arr[i]/2;
				int oHalf = arr[i]-half;
				if(i%2 == 0){
					white += half;
					black += oHalf;
				}
				else{
					white += oHalf;
					black += half;
				}
			}
			
			System.out.println(Math.min(white, black));
        }
	}
	
	public static void main(String[] args){
		new Solution();
	}
}