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;
class BDominoForYoung {
 public:
  void solve(std::istream &in, std::ostream &out) {
    int n;
    in >> n;
    long long answer = 0;
    int total = 0;
    for (int i = 0; i < n; ++i) {
      int u;
      in >> u;
      answer += u / 2;
      if (u & 1) {
        if (i & 1) {
          total++;
          if (total <= 0) answer++;
        } else {
          total--;
          if (total >= 0) answer++;
        }
      }
    }
    out << answer << endl;
  }
};
int main() {
  BDominoForYoung solver;
  std::istream &in(std::cin);
  std::ostream &out(std::cout);
  solver.solve(in, out);
  return 0;
}
