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;
int gcd(int a, int b) {
  if (b == 0) return a;
  a %= b;
  return gcd(b, a);
}
int main() {
  long long n;
  cin >> n;
  vector<long long> v(n);
  for (int i = 0; i < n; i++) cin >> v[i];
  int f = 1;
  map<long long, long long> m;
  for (int i = 0; i < v.size(); i++) {
    if (f == 1) {
      m[1] += v[i] % 2;
    } else {
      m[-1] += v[i] % 2;
    }
    f *= -1;
  }
  long long sum = 0;
  for (int i = 0; i < n; i++) sum += v[i];
  cout << (sum - abs(m[1] - m[-1])) / 2 << endl;
  return 0;
}
