D

Dominator

In graph theory, a node X dominates a node Y if every path from the predefined start node to Y must go through X. If Y is not reachable from the start node then node Y does not have any dominator. By definition, every node reachable from the start node dominates itself. In this problem, you will be given a directed graph and you have to find the dominators of every node where the 0^th node is the start node.

As an example, for the graph shown right, 3 dominates 4 since all the paths from 0 to 4 must pass through 3. 1 doesn't dominate 3 since there is a path 0-2-3 that doesn't include 1.

Input

The first line of input will contain T (≤ 100) denoting the number of cases.

Each case starts with an integer N (0 < N < 100) that represents the number of nodes in the graph. The next N lines contain N integers each. If the j^th(0 based) integer of i^th(0 based) line is 1, it means that there is an edge from node i to node j and similarly a 0 means there is no edge.

Output

For each case, output the case number first. Then output 2N+1 lines that summarizes the dominator relationship between every pair of nodes. If node A dominates node B, output 'Y' in cell (A, B), otherwise output 'N'. Cell (A, B) means cell at A^th row and B^th column. Surround the output with |, + and – to make it more legible. Look at the samples for exact format.

Sample Input	Output for Sample Input
2 5 0 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1	Case 1: +---------+ |Y|Y|Y|Y|Y| +---------+ |N|Y|N|N|N| +---------+ |N|N|Y|N|N| +---------+ |N|N|N|Y|Y| +---------+ |N|N|N|N|Y| +---------+ Case 2: +-+ |Y| +-+

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Problem Setter: Sohel Hafiz, Special Thanks: Kazi Rakibul Hossain, Jane Alam Jan