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 = 1e6 + 5;
const int MOD = 998244353;
int main() {
  int n;
  while (cin >> n) {
    int p;
    long long x = 0, y = 0;
    for (int i = 1; i <= n; i++) {
      cin >> p;
      x += p / 2;
      y += p / 2;
      if (p % 2) {
        if (i % 2)
          x++;
        else
          y++;
      }
    }
    printf("%I64d\n", min(x, y));
  }
}
