#include <bits/stdc++.h>
const double eps = (1e-9);
using namespace std;
int dcmp(long double a, long double b) {
  return fabsl(a - b) <= eps ? 0 : (a > b) ? 1 : -1;
}
int getBit(long long num, int idx) { return ((num >> idx) & 1ll) == 1; }
int setBit1(long long num, long long idx) { return num | (1ll << idx); }
long long setBit0(long long num, int idx) { return num & ~(1ll << idx); }
long long flipBit(long long num, int idx) { return num ^ (1ll << idx); }
void run() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
int countNumBit1(int mask) {
  int ret = 0;
  while (mask) {
    mask &= (mask - 1);
    ++ret;
  }
  return ret;
}
const int N = 300000 + 9;
long long arr[N];
int main() {
  run();
  int n;
  cin >> n;
  long long wh = 0, bl = 0;
  for (int i = 1; i <= n; i++) cin >> arr[i];
  int mx = arr[1];
  for (int i = 1; i <= n; i++) {
    int no;
    no = arr[i];
    if (i % 2 == (mx - no + 1) % 2) {
      wh += (no + 1) / 2;
      bl += no / 2;
    } else {
      wh += no / 2;
      bl += (no + 1) / 2;
    }
  }
  cout << min(wh, bl) << endl;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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>
const double eps = (1e-9);
using namespace std;
int dcmp(long double a, long double b) {
  return fabsl(a - b) <= eps ? 0 : (a > b) ? 1 : -1;
}
int getBit(long long num, int idx) { return ((num >> idx) & 1ll) == 1; }
int setBit1(long long num, long long idx) { return num | (1ll << idx); }
long long setBit0(long long num, int idx) { return num & ~(1ll << idx); }
long long flipBit(long long num, int idx) { return num ^ (1ll << idx); }
void run() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
int countNumBit1(int mask) {
  int ret = 0;
  while (mask) {
    mask &= (mask - 1);
    ++ret;
  }
  return ret;
}
const int N = 300000 + 9;
long long arr[N];
int main() {
  run();
  int n;
  cin >> n;
  long long wh = 0, bl = 0;
  for (int i = 1; i <= n; i++) cin >> arr[i];
  int mx = arr[1];
  for (int i = 1; i <= n; i++) {
    int no;
    no = arr[i];
    if (i % 2 == (mx - no + 1) % 2) {
      wh += (no + 1) / 2;
      bl += no / 2;
    } else {
      wh += no / 2;
      bl += (no + 1) / 2;
    }
  }
  cout << min(wh, bl) << endl;
}

```