History Cleanable DFA

A deterministic finite automaton (DFA) is a finite state machine that accepts or rejects finite input strings. The figure above draws one DFA as a state diagram. This automaton has three states $S_0$, $S_1$ and $S_2$, drawn as circles, and it reads a finite sequence of 0s and 1s as input. Every state has one outgoing arrow for 0 and one outgoing arrow for 1, so on reading a symbol the automaton moves from its current state to the state that arrow points at. If the automaton is in state $S_0$ and the current symbol is 1, it moves to $S_1$, written $\delta(S_0, 1) = S_1$. Extending the notation to whole strings gives statements such as $\delta(S_0, 10) = S_2$ and $\delta(S_1, 011010) = S_0$.

A DFA has a start state, drawn as an arrow coming in from nowhere, and a set of accept states, drawn as double circles. A DFA with start state $q_0$ accepts a string $w$ if and only if $\delta(q_0, w)$ is an accept state. In the figure above $S_0$ is both the start state and an accept state, and that DFA accepts exactly the binary numbers that are multiples of 3, the empty string included.

Now take a DFA $D$ with states $S_0, S_1, \dots, S_{n-1}$. A string $w$ is a history cleaner for $D$ if $\delta(S_i, w) = \delta(S_j, w)$ holds for all $i, j \in \{0, \dots, n-1\}$. In other words, whichever state the run starts from, reading $w$ leaves the DFA in one common state. $D$ is history cleanable if a history cleaner exists for it. Given a DFA whose input is a sequence of 0s and 1s, decide whether it is history cleanable.

The first line contains one integer $t$, the number of test cases ($1 \le t \le 500$). Each test case starts with a line holding one integer $n$, the number of states of a DFA with states $S_0, S_1, \dots, S_{n-1}$ ($2 \le n \le 500$). The second line of the test case holds $n$ space separated integers $a_0, a_1, \dots, a_{n-1}$ and the third line holds $n$ space separated integers $b_0, b_1, \dots, b_{n-1}$ ($0 \le a_i, b_i < n$), which means $\delta(S_i, 0) = S_{a_i}$ and $\delta(S_i, 1) = S_{b_i}$ for every $i$ with $0 \le i < n$.

For each test case print one line with the answer for that DFA. Print YES if it is history cleanable, and NO otherwise.