A tree is a connected acyclic graph.

A binary tree is a tree for which each node has a left child, a right child, both, or neither, e.g.

    1
   / \
  2   3
 / \   \
4   5   6

There are three common ways to recursively traverse such a tree.

1. Pre-order: parent, left subtree, right subtree
2. Post-order: left subtree, right subtree, parent
3. In-order: left subtree, parent, right subtree

Given pre-order, post-order, and in-order traversals, determine if they can be of the same binary tree.

For example,

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

are the pre-order, post-order, and in-order traversals of the tree above.

But

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

cannot be the pre-order, post-order, and in-order traversals of the same binary tree.

The first line is the number of nodes in each traversal, 0 < N ≤ 8000.
The second line is the N space separated nodes of the pre-order traversal.
The third line is the N space separated nodes of the post-order traversal.
The fourth line is the N space separated nodes of the in-order traversal.

Each traversal is a sequence of the nodes, numbered 1 to N, without repetition.

Print "yes" if all three traversals can be of the same tree, and "no" otherwise.