An underwater volcano has erupted massively in somewhere of the deep Atlantis Ocean. This large eruption led to the birth of a new volcanic island, which had a shape of square. Near the island, there are `N` countries. All of them have claimed the sovereignty over the island.

After a lot of multilateral negotiation and occasional armed conflicts, the `N` countries decided to divide the square volcanic island equally. They partitioned the island into `N` x `N` small equal-sized square chunks. Each country could get a connected region consists of exact `N` chunks.

Two chunks A and B are called "connected" if they share an edge, or there exists another chunk C connected with both A and B. A group of chunks are called "connected region" if any two of these chunks are connected.

Every country want a unique region. It means the `N` regions should be different with each other. Two regions are considered as the same if and only if one can transform into the other by an isometry (a combination of rigid motions, including translation, rotation and reflection).

In a nutshell, your task is to divide a square island with `N` x `N` chunks into `N` connected regions with different shape. You also need to draw a map to color the regions of the map so that no two edge-adjacent regions have the same color. Most of the people in these countries believed that four different colors are enough. So you can mark these regions with at most four colors, red, green, blue and yellow.

There are multiple test cases. The first line of input contains an integer `T` indicating the number of test cases. For each test case:

There is only an integer `N` (1 <= `N` <= 100).

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