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;
inline int read() {
  int x = 0;
  bool f = 1;
  char c = getchar();
  for (; !isdigit(c); c = getchar())
    if (c == '-') f = 0;
  for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0';
  if (f) return x;
  return 0 - x;
}
const int inf = 0x3f3f3f3f;
const int maxn = 200000 + 10;
int n, x, p = 0;
long long w, b;
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> x;
    b += x / 2;
    w += x / 2;
    if (x & 1) {
      b += p;
      w += !p;
    }
    p = !p;
  }
  cout << min(b, w) << endl;
  return 0;
}
