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문제

이진 트리는 매우 중요한 기본 자료 구조이다. 아래 그림은 루트 노드가 유일한 이진 트리이다. 모든 노드는 최대 2개의 자식 노드를 가질 수 있으며, 왼쪽 자식이 순서가 먼저이다. 노드 n개로 이루어진 이진 트리를 BT라고 하자. BT의 노드는 1부터 n까지 유일한 번호가 매겨져 있다.

아래 그림에 나와있는 BT의 루트는 3번 노드이다. 1번 노드는 오른쪽 자식만 가지고 있고, 4와 7은 왼쪽 자식만 가지고 있다. 3과 6은 왼쪽과 오른쪽 자식을 모두 가지고 있다. 나머지 노드는 모두 자식이 없으며, 이러한 노드는 리프 노드라고 부른다.

BT의 모든 노드를 순회하는 방법은 전위 순회(preorder), 중위 순회(inorder), 후위 순회(postorder)로 총 세 가지가 있다. 이 세 방법은 아래에 C 스타일의 의사 코드로 나와 있다. BT의 노드 v에 대해서, v.left는 왼쪽 자식, v.right는 오른쪽 자식을 나타낸다. v가 왼쪽 자식이 없으면 v.left는 ∅와 같고, 오른쪽 자식이 없으면 v.right는 ∅와 같다.

BT를 전위 순회, 중위 순회한 결과가 주어진다. 즉, 위의 함수 중 preorder(root node of BT)와 inorder(root node of BT)를 호출해서 만든 리스트가 주어진다. 두 순회한 결과를 가지고 다시 BT를 만들 수 있다. BT의 전위, 중위 순회한 결과가 주어졌을 때, 후위 순회했을 때의 결과를 구하는 프로그램을 작성하시오.

예를 들어, 위의 그림을 전위 순회하면 3,6,5,4,8,7,1,2, 중위 순회하면 5,6,8,4,3,1,2,7이 된다. 이를 이용해 후위 순회하면 5,8,4,6,2,1,7,3이 된다.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스의 첫째 줄에는 노드의 개수 n이 주어진다. (1 ≤ n ≤ 1,000) BT의 모든 노드에는 1부터 n까지 서로 다른 번호가 매겨져 있다. 다음 줄에는 BT를 전위 순회한 결과, 그 다음 줄에는 중위 순회한 결과가 주어진다. 항상 두 순회 결과로 유일한 이진 트리가 만들어지는 경우만 입력으로 주어진다.

출력

각 테스트 케이스마다 후위 순회한 결과를 출력 한다.

예제 입력 1

2
4
3 2 1 4
2 3 4 1
8
3 6 5 4 8 7 1 2
5 6 8 4 3 1 2 7

예제 출력 1

2 4 1 3
5 8 4 6 2 1 7 3

힌트

[{"problem_id":"4256","problem_lang":"0","title":"\ud2b8\ub9ac","description":"<p>\uc774\uc9c4 \ud2b8\ub9ac\ub294 \ub9e4\uc6b0 \uc911\uc694\ud55c \uae30\ubcf8 \uc790\ub8cc \uad6c\uc870\uc774\ub2e4. \uc544\ub798 \uadf8\ub9bc\uc740 \ub8e8\ud2b8 \ub178\ub4dc\uac00 \uc720\uc77c\ud55c \uc774\uc9c4 \ud2b8\ub9ac\uc774\ub2e4. \ubaa8\ub4e0 \ub178\ub4dc\ub294 \ucd5c\ub300 2\uac1c\uc758 \uc790\uc2dd \ub178\ub4dc\ub97c \uac00\uc9c8 \uc218 \uc788\uc73c\uba70, \uc67c\ucabd \uc790\uc2dd\uc774 \uc21c\uc11c\uac00 \uba3c\uc800\uc774\ub2e4. \ub178\ub4dc n\uac1c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc774\uc9c4 \ud2b8\ub9ac\ub97c BT\ub77c\uace0 \ud558\uc790. BT\uc758 \ub178\ub4dc\ub294 1\ubd80\ud130 n\uae4c\uc9c0 \uc720\uc77c\ud55c \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc544\ub798 \uadf8\ub9bc\uc5d0 \ub098\uc640\uc788\ub294 BT\uc758 \ub8e8\ud2b8\ub294 3\ubc88 \ub178\ub4dc\uc774\ub2e4. 1\ubc88 \ub178\ub4dc\ub294 \uc624\ub978\ucabd \uc790\uc2dd\ub9cc \uac00\uc9c0\uace0 \uc788\uace0, 4\uc640 7\uc740 \uc67c\ucabd \uc790\uc2dd\ub9cc \uac00\uc9c0\uace0 \uc788\ub2e4. 3\uacfc 6\uc740 \uc67c\ucabd\uacfc \uc624\ub978\ucabd \uc790\uc2dd\uc744 \ubaa8\ub450 \uac00\uc9c0\uace0 \uc788\ub2e4. \ub098\uba38\uc9c0 \ub178\ub4dc\ub294 \ubaa8\ub450 \uc790\uc2dd\uc774 \uc5c6\uc73c\uba70, \uc774\ub7ec\ud55c \ub178\ub4dc\ub294 \ub9ac\ud504 \ub178\ub4dc\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/tree(2).png\" style=\"height:183px; width:250px\" \/><\/p>\r\n\r\n<p>BT\uc758 \ubaa8\ub4e0 \ub178\ub4dc\ub97c \uc21c\ud68c\ud558\ub294 \ubc29\ubc95\uc740 \uc804\uc704 \uc21c\ud68c(preorder), \uc911\uc704 \uc21c\ud68c(inorder), \ud6c4\uc704 \uc21c\ud68c(postorder)\ub85c \ucd1d \uc138 \uac00\uc9c0\uac00 \uc788\ub2e4. \uc774 \uc138 \ubc29\ubc95\uc740 \uc544\ub798\uc5d0 C \uc2a4\ud0c0\uc77c\uc758 \uc758\uc0ac \ucf54\ub4dc\ub85c \ub098\uc640 \uc788\ub2e4. BT\uc758 \ub178\ub4dc v\uc5d0 \ub300\ud574\uc11c, v.left\ub294 \uc67c\ucabd \uc790\uc2dd, v.right\ub294 \uc624\ub978\ucabd \uc790\uc2dd\uc744 \ub098\ud0c0\ub0b8\ub2e4. v\uac00 \uc67c\ucabd \uc790\uc2dd\uc774 \uc5c6\uc73c\uba74 v.left\ub294 &empty;\uc640 \uac19\uace0, \uc624\ub978\ucabd \uc790\uc2dd\uc774 \uc5c6\uc73c\uba74 v.right\ub294 &empty;\uc640 \uac19\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/treeorder.png\" style=\"height:150px; width:683px\" \/><\/p>\r\n\r\n<p>BT\ub97c \uc804\uc704 \uc21c\ud68c, \uc911\uc704&nbsp;\uc21c\ud68c\ud55c \uacb0\uacfc\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc989, \uc704\uc758 \ud568\uc218 \uc911 preorder(root node of BT)\uc640 inorder(root node of BT)\ub97c \ud638\ucd9c\ud574\uc11c \ub9cc\ub4e0 \ub9ac\uc2a4\ud2b8\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub450 \uc21c\ud68c\ud55c \uacb0\uacfc\ub97c \uac00\uc9c0\uace0 \ub2e4\uc2dc BT\ub97c \ub9cc\ub4e4 \uc218 \uc788\ub2e4. BT\uc758 \uc804\uc704, \uc911\uc704 \uc21c\ud68c\ud55c&nbsp;\uacb0\uacfc\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ud6c4\uc704&nbsp;\uc21c\ud68c\ud588\uc744 \ub54c\uc758 \uacb0\uacfc\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, \uc704\uc758 \uadf8\ub9bc\uc744 \uc804\uc704 \uc21c\ud68c\ud558\uba74 3,6,5,4,8,7,1,2, \uc911\uc704 \uc21c\ud68c\ud558\uba74 5,6,8,4,3,1,2,7\uc774 \ub41c\ub2e4. \uc774\ub97c \uc774\uc6a9\ud574 \ud6c4\uc704 \uc21c\ud68c\ud558\uba74 5,8,4,6,2,1,7,3\uc774 \ub41c\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \ub178\ub4dc\uc758 \uac1c\uc218 n\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; n &le; 1,000) BT\uc758 \ubaa8\ub4e0 \ub178\ub4dc\uc5d0\ub294 1\ubd80\ud130 n\uae4c\uc9c0 \uc11c\ub85c \ub2e4\ub978 \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\ub2e4. \ub2e4\uc74c \uc904\uc5d0\ub294 BT\ub97c \uc804\uc704 \uc21c\ud68c\ud55c \uacb0\uacfc, \uadf8 \ub2e4\uc74c \uc904\uc5d0\ub294 \uc911\uc704 \uc21c\ud68c\ud55c \uacb0\uacfc\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ud56d\uc0c1 \ub450 \uc21c\ud68c \uacb0\uacfc\ub85c \uc720\uc77c\ud55c \uc774\uc9c4 \ud2b8\ub9ac\uac00 \ub9cc\ub4e4\uc5b4\uc9c0\ub294 \uacbd\uc6b0\ub9cc \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \ud6c4\uc704 \uc21c\ud68c\ud55c \uacb0\uacfc\ub97c \ucd9c\ub825 \ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"4256","problem_lang":"1","title":"Tree","description":"<p>A binary tree is a basic and important data structure. As illustrated in Figure 1, a binary tree has a unique root node. Each node has at most two child nodes that are ordered from left to right. Let BT be a binary tree of n nodes. Nodes of BT have unique id numbers from 1 to n.&nbsp;<\/p>\r\n\r\n<p>For BT in Figure 1, the node of id 3 is the root node. The node of id 1 has only right child node, but two nodes of id 4 and id 7 have only left child nodes. Two nodes of id 3 and id 6 have left and right child nodes. The other nodes, called leaf nodes, have no child nodes.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/tree(2).png\" style=\"height:183px; width:250px\" \/><\/p>\r\n\r\n<p>Figure 1. A binary tree with 8 nodes. The dashed vertical lines from the nodes are imaginary lines to distinguish their left and right child nodes&nbsp;<\/p>\r\n\r\n<p>We have three methods to traverse all nodes of BT; preorder, inorder, and postorder traversals. These three traversals are done by the following C-style pseudo codes: For a node v of BT, we denote by v.left and v.right its left child node and right child node, respectively. If v has no left child, then v.left is equal to &empty;. If v has no right child, then v.right is equal to &empty;.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/treeorder.png\" style=\"height:150px; width:683px\" \/><\/p>\r\n\r\n<p>You are now given two lists of id numbers of BT; one is the list obtained by preorder traversal and the other is by inorder traversal, i.e., two lists obtained by calling preorder(root node of BT) and inorder(root node of BT). It is well known that BT can be reconstructed from these two lists. You need to reconstruct BT from the preorder and inorder traversal lists of BT, and output its postorder traversal list which should be the same as the result of postorder(root node of BT).&nbsp;<\/p>\r\n\r\n<p>For example, if you are given preorder traversal list of 3, 6, 5, 4, 8, 7, 1, 2 and inorder traversal list of 5, 6, 8, 4, 3, 1, 2, 7, then you should reconstruct the tree as in Figure 1, and output its postorder traversal list, which is 5, 8, 4, 6, 2, 1, 7, 3.&nbsp;<\/p>\r\n","input":"<p>Your program is to read from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case starts with integer n, the number of nodes of a rooted and ordered binary tree BT, where 1 &le; n &le; 1,000. Nodes of BT are assumed to have distinct id number from 1 to n. The next line contains a list of n numbers, i.e., a permutation of {1,2, \u22ef , n}, which is the preorder traversal list of BT. The next line contains a list of n numbers, i.e., a permutation of {1,2, \u22ef , n}, which is the inorder traversal list of the same BT. Two neighboring node id numbers in these lists have a single space between them. Note that a unique binary tree is always constructed from these preorder and inorder traversal lists.&nbsp;<\/p>\r\n","output":"<p>Your program is to write to standard output. Print exactly one line for each test case. The line should contain a permutation of n numbers of {1,2, \u22ef , n}, which is the same as the postorder traversal list of BT.&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]