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;
const int N = 333333;
long long a[N], b[N];
long long ans, even, odd;
int n, tot;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++)
    scanf("%lld", &a[i]), ans = ans + a[i] / 2, a[i] = a[i] % 2;
  for (int i = 1; i < n; i++) {
    if (a[i] == 1 && a[i + 1] == 1) {
      a[i] = a[i + 1] = 0;
      ans++;
    }
  }
  for (int i = 1; i <= n; i++)
    if (a[i] == 1) {
      if (i % 2 == 0)
        even++;
      else
        odd++;
    }
  printf("%lld\n", ans + min(even, odd));
  return 0;
}
