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 int mod1 = 998244353;
long long int mod = 1e9 + 7;
bool comp(pair<long long int, long long int> x,
          pair<long long int, long long int> y) {
  if (x.first > y.first) return true;
  return false;
}
long long int INF = 1e18;
long long int a[300005];
void solve() {
  long long int n;
  cin >> n;
  for (long long int i = 0; i < n; ++i) cin >> a[i];
  long long int b[2];
  b[0] = b[1] = 0;
  long long int ans = 0;
  for (int i = 0; i < n; ++i) {
    ans += a[i] / 2;
    if (a[i] % 2) ++b[i % 2];
  }
  cout << ans + min(b[0], b[1]);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int t = 1;
  while (t--) {
    solve();
    cout << "\n";
  }
  return 0;
}
