Problem Statement

Consider a binary tree with $N$ vertices numbered $1, 2, \\ldots, N$. Here, a binary tree is a rooted tree where each vertex has at most two children. Specifically, each vertex in a binary tree has at most one left child and at most one right child.

Determine whether there exists a binary tree rooted at Vertex $1$ satisfying the conditions below, and present such a tree if it exists.

• The depth-first traversal of the tree in pre-order is $(P_1, P_2, \\ldots, P_N)$.
• The depth-first traversal of the tree in in-order is $(I_1, I_2, \\ldots, I_N)$.

Constraints

• $2 \\leq N \\leq 2 \\times 10^5$
• $N$ is an integer.
• $(P_1, P_2, \\ldots, P_N)$ is a permutation of $(1, 2, \\ldots, N)$.
• $(I_1, I_2, \\ldots, I_N)$ is a permutation of $(1, 2, \\ldots, N)$.

Input

Input is given from Standard Input in the following format:

$N$ $P_1$ $P_2$ $\\ldots$ $P_N$ $I_1$ $I_2$ $\\ldots$ $I_N$

Output

If there is no binary tree rooted at Vertex $1$ satisfying the conditions in Problem Statement, print $\-1$.
Otherwise, print one such tree in $N$ lines as follows. For each $i = 1, 2, \\ldots, N$, the $i$-th line should contain $L_i$ and $R_i$, the indices of the left and right children of Vertex $i$, respectively. Here, if Vertex $i$ has no left (right) child, $L_i$ ($R_i$) should be $0$.
If there are multiple binary trees rooted at Vertex $1$ satisfying the conditions, any of them will be accepted.

$L_1$ $R_1$ $L_2$ $R_2$ $\\vdots$ $L_N$ $R_N$

Sample Input 1

6
1 3 5 6 4 2
3 5 1 4 6 2

Sample Output 1

3 6
0 0
0 5
0 0
0 0
4 2

The binary tree rooted at Vertex $1$ shown in the following image satisfies the conditions.

Sample Input 2

2
2 1
1 2

Sample Output 2

-1

No binary tree rooted at Vertex $1$ satisfies the conditions, so $\-1$ should be printed.