#include <bits/stdc++.h>
using namespace std;
int main(void) {
  long long black, white;
  int n;
  scanf("%d", &n);
  black = white = 0;
  for (int i = 1; i <= n; i++) {
    long long m;
    scanf("%I64d", &m);
    black += m / 2;
    white += m / 2;
    if (m & 1) {
      if (i & 1)
        black++;
      else
        white++;
    }
  }
  long long ans = min(black, white);
  printf("%I64d\n", ans);
}

### Prompt

Please create a solution in CPP to the following problem:

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>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int main(void) {
  long long black, white;
  int n;
  scanf("%d", &n);
  black = white = 0;
  for (int i = 1; i <= n; i++) {
    long long m;
    scanf("%I64d", &m);
    black += m / 2;
    white += m / 2;
    if (m & 1) {
      if (i & 1)
        black++;
      else
        white++;
    }
  }
  long long ans = min(black, white);
  printf("%I64d\n", ans);
}

```