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;
long long n;
long long a[300009];
long long dp[300009];
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0), cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  long long ans1 = 0, ans2 = 0;
  for (int i = 1; i <= n; i++) {
    ans1 += a[i] / 2ll;
    ans2 += a[i] / 2ll;
    if (!(a[i] % 2ll)) continue;
    ans1 += (i % 2ll);
    ans2 += 1 - (i % 2ll);
  }
  cout << min(ans1, ans2) << endl;
}
