#include <bits/stdc++.h>
using namespace std;
int main() {
  long long i, j, n, m, k;
  cin >> n;
  long long a[n];
  long long ma = 0;
  vector<long long> d;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] > ma) ma = a[i];
  }
  long long u = 0;
  long long o = -2;
  for (i = 0; i < n; i++) {
    u = u + a[i] / 2;
    if (a[i] % 2 != 0) {
      if (d.size() > 0 && abs(i - d[d.size() - 1]) % 2 == 1) {
        u++;
        d.pop_back();
      } else {
        d.push_back(i);
      }
    }
  }
  cout << u;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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 main() {
  long long i, j, n, m, k;
  cin >> n;
  long long a[n];
  long long ma = 0;
  vector<long long> d;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] > ma) ma = a[i];
  }
  long long u = 0;
  long long o = -2;
  for (i = 0; i < n; i++) {
    u = u + a[i] / 2;
    if (a[i] % 2 != 0) {
      if (d.size() > 0 && abs(i - d[d.size() - 1]) % 2 == 1) {
        u++;
        d.pop_back();
      } else {
        d.push_back(i);
      }
    }
  }
  cout << u;
}

```