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>
#include <bits/stdc++.h>
using namespace std;
template <class T>
void print(const T niz[], const int siz) {
  for (int i = 0; i < siz; i++) cout << niz[i] << " ";
  cout << endl;
}
int n;
long long niz[300005];
long long beli, crni;
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n;
  for (int(i) = (1); (i) <= (n); ++(i)) {
    cin >> niz[i];
    int b = (niz[i] + 1) / 2;
    int c = niz[i] - b;
    if (i % 2 == 0) {
      beli += b;
      crni += c;
    } else {
      beli += c;
      crni += b;
    }
  }
  cout << min(crni, beli);
  return 0;
}
