Score : $600$ points

Problem Statement

Given are two integer sequences of $N$ elements each: $A_1,...,A_N$ and $B_1,...,B_N$. Determine if it is possible to do the following operation at most $N-2$ times (possibly zero) so that, for every integer $i$ from $1$ to $N$, $A_i \leq B_i$ holds:

• Choose two distinct integers $x$ and $y$ between $1$ and $N$ (inclusive), and swap the values of $A_x$ and $A_y$.

Constraints

• $2 \leq N \leq 10^5$
• $1 \leq A_i,B_i \leq 10^9$

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $...$ $A_N$

$B_1$ $B_2$ $...$ $B_N$

Output

If the objective is achievable, print Yes; if it is not, print No.

3
1 3 2
1 2 3

Yes

We should swap the values of $A_2$ and $A_3$.

3
1 2 3
2 2 2

No

6
3 1 2 6 3 4
2 2 8 3 4 3

Yes