CF1154B Make Them Equal

You are given a sequence $ a_1, a_2, \dots, a_n $ consisting of $ n $ integers. You can choose any non-negative integer $ D $ (i.e. $ D \ge 0 $ ), and for each $ a_i $ you can: - add $ D $ (only once), i. e. perform $ a_i := a_i + D $ , or - subtract $ D $ (only once), i. e. perform $ a_i := a_i - D $ , or - leave the value of $ a_i $ unchanged. It is possible that after an operation the value $ a_i $ becomes negative. Your goal is to choose such minimum non-negative integer $ D $ and perform changes in such a way, that all $ a_i $ are equal (i.e. $ a_1=a_2=\dots=a_n $ ). Print the required $ D $ or, if it is impossible to choose such value $ D $ , print -1. For example, for array $ [2, 8] $ the value $ D=3 $ is minimum possible because you can obtain the array $ [5, 5] $ if you will add $ D $ to $ 2 $ and subtract $ D $ from $ 8 $ . And for array $ [1, 4, 7, 7] $ the value $ D=3 $ is also minimum possible. You can add it to $ 1 $ and subtract it from $ 7 $ and obtain the array $ [4, 4, 4, 4] $ .

The first line of the input contains one integer $ n $ ( $ 1 \le n \le 100 $ ) — the number of elements in $ a $ . The second line of the input contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le 100 $ ) — the sequence $ a $ .

Print one integer — the minimum non-negative integer value $ D $ such that if you add this value to some $ a_i $ , subtract this value from some $ a_i $ and leave some $ a_i $ without changes, all obtained values become equal. If it is impossible to choose such value $ D $ , print -1.