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>
using namespace std;
int main(){

    int n;
    while(cin>>n,n){

        int a[120]={0};
        for(int i=0;i<=n;i++)cin>>a[i];

        for(int i=0;i<=n;i++){
            bool flg = true;
            int b[120];
            for(int j=0,t=0;j<=n;j++){
                if(j==i)continue;
                b[t] = a[j];
                t++;
            }
            int value = b[1] - b[0];
            for(int j=1;j<n;j++){
                if(b[j]-b[j-1]!=value){
                    flg = false;
                    break;
                }
            }
            if(flg){
                cout<<a[i]<<endl;
                break;
            }
        }


    }
    return 0;
}