E. Magic Stones
constructive algorithms; math; sortings
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 \(i\)?
The first line contains one integer \(n\) (\(2 \le n \le 10^5\)) — the number of magic stones.The second line contains integers \(c_1, c_2, \ldots, c_n\) (\(0 \le c_i \le 2 \cdot 10^9\)) — the charges of Grigory's stones.The second line contains integers \(t_1, t_2, \ldots, t_n\) (\(0 \le t_i \le 2 \cdot 10^9\)) — the charges of Andrew's stones.
If there exists a (possibly empty) sequence of synchronization operations, which changes all charges to the required ones, print ""Yes"".Otherwise, print ""No"".
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.