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>
inline int read() {
  char c;
  int x;
  for (c = getchar(); !isdigit(c); c = getchar())
    ;
  for (x = 0; isdigit(c); c = getchar()) {
    x = x * 10 + c - '0';
  }
  return x;
}
const int N = 1e6 + 5;
int n, a[N];
long long ans[2];
int main() {
  n = read();
  for (int i = 1; i <= n; i++) {
    a[i] = read();
    ans[i & 1] += a[i] >> 1;
    ans[i & 1 ^ 1] += a[i] + 1 >> 1;
  }
  printf("%I64d\n", std::min(ans[0], ans[1]));
  return 0;
}
