#include <bits/stdc++.h>
using namespace std;
const int maxn = 300005;
long long n, a[maxn], d, sum;
int Pow(int a, int t) {
  if (t == 0) return 1;
  if (t == 1) return a;
  int P = Pow(a, t / 2);
  return P * P * Pow(a, t % 2);
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    d += (a[i] % 2) * Pow(-1, i);
    sum += a[i];
  }
  cout << (sum - abs(d)) / 2 << endl;
  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 = 300005;
long long n, a[maxn], d, sum;
int Pow(int a, int t) {
  if (t == 0) return 1;
  if (t == 1) return a;
  int P = Pow(a, t / 2);
  return P * P * Pow(a, t % 2);
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    d += (a[i] % 2) * Pow(-1, i);
    sum += a[i];
  }
  cout << (sum - abs(d)) / 2 << endl;
  return 0;
}

```