Row and Column Order

You are given two permutations $P=(P_1,P_2,\dots,P_N)$ and $Q=(Q_1,Q_2,\dots,Q_N)$ of $(1,2,\dots,N)$. Write one of the characters `0` and `1` in each cell of an $N$\-by-$N$ grid so that all of the following conditions are satisfied: * Let $S_i$ be the string obtained by concatenating the characters in the $i$\-th row from the $1$\-st to the $N$\-th column. Then, $S_{P_1} < S_{P_2} < \dots < S_{P_N}$ in lexicographical order. * Let $T_i$ be the string obtained by concatenating the characters in the $i$\-th column from the $1$\-st to the $N$\-th row. Then, $T_{Q_1} < T_{Q_2} < \dots < T_{Q_N}$ in lexicographical order. It can be proved that for any $P$ and $Q$, there is at least one way to write the characters that satisfies all the conditions. What does "$X < Y$ in lexicographical order" mean?For strings $X=X_1X_2\dots X_{|X|}$ and $Y = Y_1Y_2\dots Y_{|Y|}$, "**$X < Y$ in lexicographical order**" means that 1. or 2. below holds. Here, $|X|$ and $|Y|$ denote the lengths of $X$ and $Y$, respectively. 1. $|X| \lt |Y|$ and $X_1X_2\ldots X_{|X|} = Y_1Y_2\ldots Y_{|X|}$. 2. There exists an integer $1 \leq i \leq \min\lbrace |X|, |Y| \rbrace$ such that both of the following are true: * $X_1X_2\ldots X_{i-1} = Y_1Y_2\ldots Y_{i-1}$ * $X_i$ is less than $Y_i$. ## Constraints * $2 \leq N \leq 500$ * $P$ and $Q$ are permutations of $(1,2,\dots,N)$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $P_1$ $P_2$ $\dots$ $P_N$ $Q_1$ $Q_2$ $\dots$ $Q_N$ [samples]