#include <bits/stdc++.h>
using namespace std;
const int N = 1e6 + 69;
const int mod = 1e9 + 7;
long long n, m, mx, ind, ans, len, x, y, a, b, c, t, k, T, w;
int fix[N], fix1[N], fix2[N];
long long A[N][3], P[N];
map<int, int> mp[N];
vector<int> V[N], edge[N], ANS;
set<pair<int, int> > s;
vector<pair<int, int> > PP;
int main() {
  ios::sync_with_stdio(0);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> x;
    b += x / 2;
    w += x / 2;
    if (x % 2 == 1) {
      if (i % 2 == 1)
        b++;
      else
        w++;
    }
  }
  cout << min(b, w) << endl;
}

### Prompt

Create a solution in Cpp for 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;
const int N = 1e6 + 69;
const int mod = 1e9 + 7;
long long n, m, mx, ind, ans, len, x, y, a, b, c, t, k, T, w;
int fix[N], fix1[N], fix2[N];
long long A[N][3], P[N];
map<int, int> mp[N];
vector<int> V[N], edge[N], ANS;
set<pair<int, int> > s;
vector<pair<int, int> > PP;
int main() {
  ios::sync_with_stdio(0);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> x;
    b += x / 2;
    w += x / 2;
    if (x % 2 == 1) {
      if (i % 2 == 1)
        b++;
      else
        w++;
    }
  }
  cout << min(b, w) << endl;
}

```