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;
int n;
int a[300100];
int color[300100];
void paint(int x, int y, int k) { color[x] = ((k - y + 1) % 2 + 2) % 2; }
int get(int x, int y) { return (color[x] + y - 1) % 2; }
long long cnt(int x, int k) {
  if (k == color[x])
    return (a[x] + 1) / 2;
  else
    return a[x] / 2;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  color[1] = 0;
  long long c0 = 0LL, c1 = 0LL;
  c0 += cnt(1, 0);
  c1 += cnt(1, 1);
  for (int i = 2; i <= n; i++) {
    paint(i, a[i], 1 - get(i - 1, a[i]));
    c0 += cnt(i, 0);
    c1 += cnt(i, 1);
  }
  cout << min(c0, c1) << endl;
  return 0;
}
