#include <bits/stdc++.h>
using namespace std;
const int maxn = 3e5 + 5;
int n, a[maxn];
int q[maxn], h, t;
int main() {
  ios::sync_with_stdio(0);
  cin >> n;
  h = 0;
  long long ans = 0;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
    if (a[i] % 2 == 0) {
      ans += a[i] / 2;
      continue;
    }
    if (!h) {
      q[++h] = i;
    } else {
      if ((i - q[h]) % 2 == 0) {
        q[++h] = i;
        continue;
      }
      ans += (a[i] + a[q[h]]) / 2;
      --h;
    }
  }
  while (h) {
    ans += a[q[h]] / 2, --h;
  }
  cout << ans;
  return 0;
}

### Prompt

Please create a solution in cpp 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;
const int maxn = 3e5 + 5;
int n, a[maxn];
int q[maxn], h, t;
int main() {
  ios::sync_with_stdio(0);
  cin >> n;
  h = 0;
  long long ans = 0;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
    if (a[i] % 2 == 0) {
      ans += a[i] / 2;
      continue;
    }
    if (!h) {
      q[++h] = i;
    } else {
      if ((i - q[h]) % 2 == 0) {
        q[++h] = i;
        continue;
      }
      ans += (a[i] + a[q[h]]) / 2;
      --h;
    }
  }
  while (h) {
    ans += a[q[h]] / 2, --h;
  }
  cout << ans;
  return 0;
}

```