Kitchen Garden

I decided to plant vegetables in my vegetable garden. n seeds were available, so I sowed n seeds, one per day, over n days. All the seeds sprouted and are growing very well. We are looking forward to the harvest time.

One day, as I was watering the seedlings as usual, I noticed something strange. There were supposed to be n vegetable seedlings, but there was one too many. A weed has grown up. I want to pull it out immediately, but the trouble is that all the seedlings look so similar that I can't tell the difference between the vegetable and the weed.

The clue is the growth rate of the vegetable. The vegetable continues to grow at a fixed length per day, ever since it was sown. However, we do not know how many centimeters this "fixed length" is. I also forgot how many days ago I sowed the first seed. The seedlings are lined up in a row, and the only thing I remember is that when I sowed the seeds, I sowed them one by one every day, starting from the right.

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

Input

The input consists of multiple data sets. The end of the input is indicated by a line with a single zero. 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 a single space, and h_i (1 ≤ h_i ≤ 10⁹) indicates the length of the i-th seedling from the left.

No input can be given such that h₁ h₂ ... h_n+1 is an identity sequence.

The number of datasets does not exceed 500.

Output

Output the length of the weed for each dataset.

Sample Input

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

Sample Output

6
1
12

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