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;
long long n;
long long a[300000];
long long b[12][12];
void read_data(void) {
  cin >> n;
  for (long long i = 0; i < n; i++) cin >> a[i];
}
void solve(void) {
  read_data();
  for (long long i = 0; i < 12; i++)
    for (long long j = 0; j < 12; j++) b[i][j] = 0;
  long long d = 0;
  long long f = 0;
  long long total = 0;
  for (long long i = n - 1; i >= 0; i--) {
    long long l = a[i] - f;
    total += l / 2;
    if (f > d)
      d = 1 - d;
    else
      d = 0;
    if (l & 1)
      f++;
    else if (f > 0)
      f--;
    if (i > 0 && (f > d)) total += ((f - d) / 2) + ((f - d) % 2);
  }
  cout << total << endl;
}
void gen_stair(void) {
  long long n = 200000;
  cout << n << endl;
  for (long long i = n; i >= 2; i--) cout << i << " ";
  cout << 1 << endl;
}
int32_t main() {
  solve();
  return 0;
}
