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 int N = 2e5 + 2;
const int M = 1e5 + 2;
const int mod = 998244353;
const int inf = 1e9;
const long long INF = 1e16;
void data() {}
template <typename T>
void scerr(T nums) {
  for (auto it : nums) cerr << it << " | ";
  cerr << "\n";
}
long long n, a, cntA, cntB;
int main() {
  data();
  scanf("%lld", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &a);
    if (i & 1) {
      cntA += (a / 2) + (a % 2);
      cntB += (a / 2);
    } else {
      cntB += (a / 2) + (a % 2);
      cntA += (a / 2);
    }
  }
  printf("%lld", min(cntA, cntB));
}
