Problem Statement

You are given permutations $P = (P_1, P_2, \ldots, P_N)$ and $A = (A_1, A_2, \ldots, A_N)$ of $(1,2,\ldots,N)$.

You can perform the following operation any number of times, possibly zero:

• replace $A_i$ with $A_{P_i}$ simultaneously for all $i=1,2,\ldots,N$.

Print the lexicographically smallest $A$ that can be obtained.

What is lexicographical order? For sequences of length $N$, $A = (A_1, A_2, \ldots, A_N)$ and $B = (B_1, B_2, \ldots, B_N)$, $A$ is lexicographically smaller than $B$ if and only if: there exists an integer $i\ (1\leq i\leq N)$ such that $A_i < B_i$, and $A_j = B_j$ for all $1\leq j < i$.

Constraints

• $1\leq N\leq2\times10^5$
• $1\leq P_i\leq N\ (1\leq i\leq N)$
• $P_i\neq P_j\ (1\leq i<j\leq N)$
• $1\leq A_i\leq N\ (1\leq i\leq N)$
• $A_i\neq A_j\ (1\leq i<j\leq N)$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
P_1 P_2 \ldots P_N
A_1 A_2 \ldots A_N

Output

Let $(A_1, A_2, \ldots, A_N)$ be the lexicographically smallest $A$ that can be obtained. Print $A_1, A_2, \ldots, A_N$ in this order, separated by spaces, in one line.