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>
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int n;
  cin >> n;
  long long int i;
  long long int count = 0;
  long long int sum = 0;
  long long int c1 = 0;
  long long int a[n + 5];
  for (i = 0; i < n; i++) {
    cin >> a[i];
    sum += a[i];
    if (count == 0) {
      c1 += (a[i] + 1) / 2;
    } else {
      c1 += (a[i] / 2);
    }
    count++;
    count = count % 2;
  }
  long long int ans = (c1 < sum - c1 ? c1 : sum - c1);
  cout << ans << endl;
}
