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;
int i, i0, n, m, ans, a[300005];
int main() {
  long long ans = 0, d = 0, p = 0;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  a[0] = INT_MAX;
  for (int i = 1, i0 = n; i <= n; i++) {
    while (a[i0] < i) i0--;
    if (i0 - i + 1 <= 0) break;
    if (a[i] - i + 1 <= 0) break;
    ans += (i0 - i) / 2;
    p += (i0 - i) % 2;
    ans += (a[i] - i) / 2;
    p += (a[i] - i) % 2;
    d++;
  }
  printf("%lld\n", ans + min(d, p));
  return 0;
}
