Contest Score Weight Selection

There are N contestants participating in a contest which is held in 2 rounds. The i^th contestant scores A_i points in round one and B_i points in round two. In each round, a positive integer weight is assigned — X for round one and Y for round two. The final score for the i^th contestant is computed as:

You, as the contest organizer, can freely choose the weights X and Y (both must be positive integers). However, Squeaky, a bribing mouse, wants you to pick the weights in such a way that for every pair of contestants with indices i < j, the following holds:

In other words, the scores must be strictly decreasing from the first contestant to the last. Is it possible to choose positive integers X and Y to satisfy this condition? If yes, output Yes, otherwise output No.

inputFormat

The input consists of three lines:

• The first line contains a single integer N (the number of contestants).
• The second line contains N integers A₁, A₂, ..., A_N separated by spaces.
• The third line contains N integers B₁, B₂, ..., B_N separated by spaces.

You can assume that all input numbers are integers and that N ≥ 2.

outputFormat

Output a single string: Yes if it is possible to choose positive integers X and Y so that for every 1 ≤ i < j ≤ N, S_i > S_j holds; otherwise, output No.

sample

3
3 2 1
1 2 3

Yes