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;
const int inf = 1e9 + 7;
const long long longinf = 1LL << 60;
const long long mod = 1e9 + 7;
const long double eps = 1e-10;
template <typename T1, typename T2>
inline void chmin(T1 &a, T2 b) {
  if (a > b) a = b;
}
template <typename T1, typename T2>
inline void chmax(T1 &a, T2 b) {
  if (a < b) a = b;
}
void solve() {
  int n;
  cin >> n;
  vector<long long> A(n);
  for (int i = (int)(0); i < (int)(n); i++) cin >> A[i];
  vector<long long> cnt(2);
  for (int i = (int)(0); i < (int)(n); i++) {
    cnt[i & 1] += A[i] / 2;
    cnt[!(i & 1)] += A[i] - A[i] / 2;
  }
  cout << min(cnt[0], cnt[1]) << '\n';
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int T = 1;
  while (T--) solve();
  return 0;
}
