Morris' Blog 我在摸索我存在的意義、生命的意義、內涵及價值。 沒有真正神手般的厲害，套用模式是大部分的情況。 沒那麼厲害的我存在的意義為何，襯托出神的存在？ 有時候不能怪別人不給我機會，我已經開始省思， 為什麼我沒有給別人機會的原因，而是全要靠別人。 有時候我認為我與眾不同，那是因為我做不到很多人能辦到的事情。 我聽不到、玩不起來、說得不夠明瞭、理解得不夠多， 我缺少的語文能力，就是一切一切無能的判定。 為此，我不曉得能做些對別人有幫助的事情。 我知道我自己是個不服輸的性格，但現在我不得不認輸。 我沒有能力，因此我必須認輸。 我到底來這世界作什麼？處處充滿不確定性， 而我總是無法出類拔萃，想當個一般人似乎也回不了頭了。 越強大的挑戰需要越強力的支持，而我的支持是什麼？ 最近嘗試與人談話，但都是失敗的結局，沒人能接受， 不需要言語，不需要溝通，一切所想都表達不出來。

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Background

   A 2D raster image is defined by a matrix of points or pixels. In a black and white raster image, each pixel (a matrix element) can be black (full) or white (empty). There are several methods known to represent a raster image. Two of them, are the "Quadtree" and the "Run Length code".
   In a Quadtree, the matrix is preferably square with a length that is a power of two. One image is represented following a recursive visit: the image is divided in four image cells (accordingly to the order shown in Figure 1) and each cell is evaluated to be Full, Empty, or Partial. When a Partial cell is found, it is recursively subdivided in four cells and the same principle is repeated again and again until the cell is completely Full or completely Empty. The structure of a quadtree is a tree of nodes and each node can have from zero to four descendents (see Figure 1).

Figure 1 - One image, the order of visit and the quadtree

   In the Run Length code, pixels are grouped in series of empty pixels, full pixels and empty pixels again, etc. In this way, the image can be represented as a series of numbers, being each number of pixels in a group (we can assume that the first group is composed of full pixels). Using the image of Figure 1 as an example, the run length code is: 0, 20, 4, 4, 9, 1, 1, 1, 4, 1, 1, 2, 4, 4, 4, 4 (considering the lower left pixel as the first one).

Problem

   Given an image in the form of a quadtree, the problem is to obtain the correspondent run length code. The image maximum size is 256*256 and the origin of coordinates is the lower left pixel.

Input

   The first line of the input contains the length of the image and the second line contains the number of nodes N to be considered (both in integer format). Each one of the following N lines describes a different node (in sequence, starting with node 1), with four fields separated by a space. Each field may be one character F (full) or E (empty) or a number that is the index of a descendent node.

Output

   One line with the run length code of the given image (integers separated by a space). Note that the first group is assumed to be Full.

Sample Input
1

8
5
E 2 F 3
E E F F
4 5 E E
F E E F
F E E E

Sample Output
0 20 4 4 9 1 1 1 4 1 1 2 4 4 4 4