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>
#pragma GCC optimize("-O3")
using namespace std;
long long MOD = 1e9 + 7;
void solve() {
  int n;
  cin >> n;
  vector<long long> arr(n + 1);
  for (int i = 1; i <= n; i++) cin >> arr[i];
  long long a = 0;
  long long sum = 0;
  for (int i = 1; i <= n; i++) {
    sum += arr[i];
    if (arr[i] & 1) {
      if (i % 2 == 1)
        a++;
      else
        a--;
    }
  }
  cout << (sum - abs(a)) / 2;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t = 1;
  while (t--) {
    solve();
  }
  return 0;
}
