I decided to plant vegetables in the vegetable garden. There were n seeds, so I sown n seeds one by one a day over n days. All seeds sprout and grow quickly. I can't wait for the harvest time.

One day, when I was watering the seedlings as usual, I noticed something strange. There should be n vegetable seedlings, but one more. Weeds have grown. I want to pull it out immediately, but the trouble is that all the seedlings are very similar and I can't tell the difference between vegetables and weeds.

The clue is the growth rate of vegetables. This vegetable continues to grow for a fixed length of day after sowing. However, I don't know how many centimeters this "fixed length" is. I also forgot how many days ago I sown the first seed. The seedlings are lined up in a row, but the only thing I remember is that when I sowed the seeds, I planted one seed each day, starting from the right.

Create a program that inputs the length of n + 1 seedlings and outputs the length of weeds.



input

The input consists of multiple datasets. The end of the input is indicated by a single zero line. The input is given in the following format.


n
h1 h2 h3 ... hn + 1


The first line n (4 ≤ n ≤ 100) is an integer representing the number of vegetable seedlings. The second line contains n + 1 integers separated by one space, and hi (1 ≤ hi ≤ 109) indicates the length of the i-th seedling from the left.

No input is given such that h1 h2 ... hn + 1 is an arithmetic progression.

The number of datasets does not exceed 500.

output

Outputs the length of weeds for each dataset.

Example

Input

5
1 2 3 6 4 5
6
1 3 6 9 12 15 18
4
5 7 9 11 12
0


Output

6
1
12
#include<iostream>
#include<vector>
using namespace std;
int n,h[128];
vector<int> v;
int solve(int a){
  int d = v[1] - v[0];
  for(int i = 2;i < v.size(); i++){
    if(v[i] - v[i-1] != d) return 0;
    if(i == v.size()-1){
      cout << h[a] << endl;
      return 1;
    }
  }
}
int main(void){
  while(cin >> n,n){
    for(int i = 0;i <= n; i++) cin >> h[i];
    for(int i = 0;i <= n; i++){
      v.clear();
      for(int j = 0;j <= n; j++){
	if(i == j) continue;
	v.push_back(h[j]);
      }
      if(solve(i)) break;
    }
  }
}
