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;
unsigned long long max(unsigned long long a, unsigned long long b) {
  return (a > b) ? a : b;
}
unsigned long long min(unsigned long long a, unsigned long long b) {
  return (a < b) ? a : b;
}
int main() {
  unsigned long long n, m = 0, i, j;
  cin >> n;
  vector<unsigned long long> a(n);
  unsigned long long ev = 0, od = 0;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    m += a[i] / 2;
    a[i] %= 2;
    if (a[i] == 1) {
      if (i % 2 == 1)
        od++;
      else
        ev++;
    }
  }
  cout << m + min(ev, od) << endl;
}
