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(2)
using namespace std;
const int INF = 1e9 + 7;
const int N = 2e5 + 7;
const int M = 5e6 + 7;
signed main() {
  ios::sync_with_stdio(false);
  long long cnt[2] = {0, 0};
  int n;
  cin >> n;
  for (int i = 1, x; i <= n; i++) {
    cin >> x;
    cnt[i % 2] += (x / 2) * 1ll + x % 2;
    cnt[i % 2 ^ 1] += (x / 2) * 1ll;
  }
  cout << min(cnt[0], cnt[1]) << "\n";
  return 0;
}
