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 dp[1000000][2];
const long long MOD = 1e9 + 7;
int main() {
  long long n, bl = 0, wh = 0;
  cin >> n;
  for (int i = 0; i < n; i++) {
    long long num;
    cin >> num;
    if (i % 2 == 0) {
      bl += num / 2;
      wh += (num - 1) / 2 + 1;
    } else {
      wh += num / 2;
      bl += (num - 1) / 2 + 1;
    }
  }
  cout << min(wh, bl);
  return 0;
}
