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;
long long MOD = 1e+9 + 7;
const long long INFLL = 0x3f3f3f3f3f3f3f3f;
const int INF = 0x3f3f3f3f;
const long long MAXN = 1e+5 + 7;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long i, j, n;
  cin >> n;
  vector<long long> inp(n);
  for (auto& a : inp) cin >> a;
  long long sumw = 0, sumb = 0;
  for (i = 0; i < n; ++i)
    sumw += (inp[i] + (inp[i] % 2 == i % 2)) / 2,
        sumb += (inp[i] + (inp[i] % 2 != i % 2)) / 2;
  cout << min(sumw, sumb) << '\n';
  return 0;
}
