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 a, b, c, d, ans, mn = 1e9;
long long n, m, mx;
long long cnt;
char z;
string s, s1;
vector<string> v;
int main() {
  cin >> n;
  long long arr[n];
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
    if (i % 2 == 0)
      cnt += (arr[i] + 1) / 2, ans += arr[i] / 2;
    else
      ans += (arr[i] + 1) / 2, cnt += arr[i] / 2;
  }
  cout << min(cnt, ans);
}
