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 maxn = 300 * 1000 + 10;
int a[maxn], n;
long long sum, w, b;
long long ABS(long long x) {
  if (x < 0) return -x;
  return x;
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    sum += a[i];
    if (i & 1) {
      w += (a[i] + 1) / 2;
      b += a[i] / 2;
    } else {
      b += (a[i] + 1) / 2;
      w += a[i] / 2;
    }
  }
  cout << (sum - ABS(w - b)) / 2;
  return 0;
}
