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;
const int N = 3e5 + 7;
long long a[3];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  clock_t ttt = clock();
  int n;
  cin >> n;
  int cur = 0;
  for (int i = 1; i <= n; ++i) {
    int b;
    cin >> b;
    int k = b / 2;
    if (b & 1) ++k;
    a[cur] += k;
    a[cur ^ 1] += b - k;
    cur ^= 1;
  }
  cout << min(a[0], a[1]) << '\n';
  cerr << "Time taken " << (double)(clock() - ttt) / CLOCKS_PER_SEC
       << " seconds\n";
  return 0;
}
