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 long long read() {
  char ch = getchar();
  long long p = 1, data = 0;
  while (ch < '0' || ch > '9') {
    if (ch == '-') p = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    data = data * 10 + (ch ^ 48);
    ch = getchar();
  }
  return p * data;
}
inline long long qpow(long long a, long long b) {
  long long r = 1;
  while (b) {
    if (b & 1) r = a * r;
    a = a * a;
    b >>= 1;
  }
  return r;
}
inline long long gcd(long long a, long long b) {
  if (!a || !b) return (!a) ? b : a;
  while (b ^= a ^= b ^= a %= b)
    ;
  return a;
}
inline long long lcm(long long a, long long b) { return a * b / gcd(a, b); }
void exgcd(long long a, long long b, long long &x, long long &y) {
  if (!b)
    x = 1, y = 0;
  else {
    exgcd(b, a % b, y, x);
    y -= x * (a / b);
  }
}
const int mod = 1e9 + 7;
int main() {
  int n = read();
  long long a[2] = {0, 0};
  for (int i = 1; i <= n; i++) {
    long long x = read();
    a[i & 1] += x / 2 + x % 2;
    a[1 - i & 1] += x / 2;
  }
  printf("%lld\n", min(a[0], a[1]));
  return 0;
}
