CF1110E Magic Stones

Grigory has $ n $ magic stones, conveniently numbered from $ 1 $ to $ n $ . The charge of the $ i $ -th stone is equal to $ c_i $ . Sometimes Grigory gets bored and selects some inner stone (that is, some stone with index $ i $ , where $ 2 \le i \le n - 1 $ ), and after that synchronizes it with neighboring stones. After that, the chosen stone loses its own charge, but acquires the charges from neighboring stones. In other words, its charge $ c_i $ changes to $ c_i' = c_{i + 1} + c_{i - 1} - c_i $ . Andrew, Grigory's friend, also has $ n $ stones with charges $ t_i $ . Grigory is curious, whether there exists a sequence of zero or more synchronization operations, which transforms charges of Grigory's stones into charges of corresponding Andrew's stones, that is, changes $ c_i $ into $ t_i $ for all $ i $ ?

N/A

N/A

In the first example, we can perform the following synchronizations ( $ 1 $ -indexed): - First, synchronize the third stone $ [7, 2, \mathbf{4}, 12] \rightarrow [7, 2, \mathbf{10}, 12] $ . - Then synchronize the second stone: $ [7, \mathbf{2}, 10, 12] \rightarrow [7, \mathbf{15}, 10, 12] $ . In the second example, any operation with the second stone will not change its charge.