Magic Stones
Description
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".
Input
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.
Output
If there exists a (possibly empty) sequence of synchronization operations, which changes all charges to the required ones, print "Yes".
Otherwise, print "No".
Samples
4
7 2 4 12
7 15 10 12
Yes
3
4 4 4
1 2 3
No
Note
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.