Problem Statement

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. $|X| \lt |Y|$ and $X_1X_2\ldots X_{|X|} = Y_1Y_2\ldots Y_{|X|}$. 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

Output

Print a way to fill the grid that satisfies the conditions in the following format, where $A_{ij}$ is the character written at the $i$-th row and $j$-th column:

A_{11}A_{12}\dots A_{1N}
\vdots
A_{N1}A_{N2}\dots A_{NN}

If there are multiple ways to satisfy the conditions, any of them will be accepted.