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;
const long long maxn = 300086;
long long n, a[maxn];
inline long long min(long long x, long long y) { return x > y ? y : x; }
inline long long max(long long x, long long y) { return x > y ? x : y; }
inline long long read() {
  char ch = getchar();
  while (ch < 48) ch = getchar();
  long long r = 0;
  while (ch > 47) r = r * 10 + (ch ^ 48), ch = getchar();
  return r;
}
long long ans;
long long black, white;
signed main() {
  n = read();
  for (long long i = 1; i <= n; ++i) a[i] = read();
  for (long long i = 1; i <= n; ++i)
    if (i & 1)
      black += (a[i] >> 1), white += ((a[i] + 1) >> 1);
    else
      black += ((a[i] + 1) >> 1), white += ((a[i]) >> 1);
  cout << min(white, black);
}
