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 N = 2e6 + 51 + 51, MOD = 1e9 + 7, mod = 998244353, INF = 3e18;
mt19937 Flash_new_51(51515);
using vi = vector<long long>;
using vp = vector<pair<long long, long long>>;
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long n, sum = 0, w = 0;
  cin >> n;
  for (long long i = 0; i < n; i++) {
    long long x;
    cin >> x;
    sum += x;
    w += x / 2;
    if (x % 2 && i % 2) w++;
  }
  cout << min(sum - w, w);
}
