#include <bits/stdc++.h>
using namespace std;
void err(istream_iterator<string> it) {}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << '\n';
  err(++it, args...);
}
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long t, q, n, m, prev, maxx, i, j, k1, k2, k3, k, x, y, flag, sum, cnt,
      ans;
  cin >> n;
  vector<long long> v(n);
  for (i = 0; i < n; i++) {
    cin >> v[i];
  }
  long long w, b;
  w = b = 0;
  for (i = 0; i < n; i++) {
    k = v[i] / 2;
    if (i % 2 == 0) {
      w += k;
      b += (v[i] - k);
    } else {
      b += k;
      w += (v[i] - k);
    }
  }
  cout << min(w, b) << '\n';
  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;
void err(istream_iterator<string> it) {}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << '\n';
  err(++it, args...);
}
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long t, q, n, m, prev, maxx, i, j, k1, k2, k3, k, x, y, flag, sum, cnt,
      ans;
  cin >> n;
  vector<long long> v(n);
  for (i = 0; i < n; i++) {
    cin >> v[i];
  }
  long long w, b;
  w = b = 0;
  for (i = 0; i < n; i++) {
    k = v[i] / 2;
    if (i % 2 == 0) {
      w += k;
      b += (v[i] - k);
    } else {
      b += k;
      w += (v[i] - k);
    }
  }
  cout << min(w, b) << '\n';
  return 0;
}

```