#include <bits/stdc++.h>
using namespace std;
inline int Get() {
  char c;
  bool o = false;
  while (!isdigit(c = getchar()))
    if (c == '-') o = true;
  int x = c - '0';
  while (isdigit(c = getchar())) x = x * 10 + c - '0';
  return o ? -x : x;
}
long long ans;
int top[2];
int main() {
  int n = Get();
  for (int i = 1; i <= n; ++i) {
    int x = Get();
    ans += (x >> 1);
    int b = i & 1;
    if (x & 1) {
      if (top[!b])
        --top[!b], ++ans;
      else
        ++top[b];
    }
  }
  printf("%lld", ans);
}

### Prompt

Please formulate a CPP solution 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;
inline int Get() {
  char c;
  bool o = false;
  while (!isdigit(c = getchar()))
    if (c == '-') o = true;
  int x = c - '0';
  while (isdigit(c = getchar())) x = x * 10 + c - '0';
  return o ? -x : x;
}
long long ans;
int top[2];
int main() {
  int n = Get();
  for (int i = 1; i <= n; ++i) {
    int x = Get();
    ans += (x >> 1);
    int b = i & 1;
    if (x & 1) {
      if (top[!b])
        --top[!b], ++ans;
      else
        ++top[b];
    }
  }
  printf("%lld", ans);
}

```