#include <bits/stdc++.h>
using namespace std;
int n;
long long x, sum, sub;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = (1); i <= (n); i++) {
    cin >> x;
    sum += x;
    if (x & 1) {
      if (i & 1)
        ++sub;
      else
        --sub;
    }
  }
  cout << (sum - abs(sub)) / 2;
}

### Prompt

Generate a CPP solution to the following problem:

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>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int n;
long long x, sum, sub;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = (1); i <= (n); i++) {
    cin >> x;
    sum += x;
    if (x & 1) {
      if (i & 1)
        ++sub;
      else
        --sub;
    }
  }
  cout << (sum - abs(sub)) / 2;
}

```