ASCII diamonds can be drawn with integer side lengths. Each layer of this diamond is drawn with a single ASCII alphabet, starting with ‘a’ and ending with ‘z’ (starting from the center) and continues in cyclic order.

Any one of these ASCII diamonds can be used to draw an infinite plane by using this as a tile. For example ASCII diamond of length 5 can be used to draw such an infinite grid. Only first 20 row and 60 columns are shown below:

Here rows and columns are numbered starting from zero. By specifying the topmost row (row₁), leftmost column (col₁), bottommost row (row₂) and rightmost column (col₂) we can specify a portion of such an infinite grid (also shown in figure above).

Given the side length of the tile to be used, the topmost row (row₁), leftmost column (col₁), bottommost row (row₂) and rightmost column (col₂) you have to print the pattern within these four boundaries (inclusive).

Input

Input contains at most 125 sets of inputs. But not all cases are extreme.

Each set of input contains five integers: N (0<N£20000), row₁, col₁, row₂, col₂ (0£ row₁ £ row₂ £ 20000, 0 £ col₁ £ col₂ £ 20000, 0£ (row₂- row₁+1)* (col₂- col₁+1) £ 40000). Here N denotes that the side length of the tiles used to draw the plane should be N. The meaning of row₁, col₁, row₂, col₂ are given in the problem statement. The first sample input corresponds to the figure above.

Input is terminated by a line where the first integer is zero.

Output

For each line of input produce (row₂- row₁+2) lines of output. First line contains serial of output. Each of the next lines contain (col₂- col₁+1) characters. These lines describe the patterns within the specified rows and columns. Look at the output for sample input for details. The output file size is less than 1 MB.

Sample Input                              Output for Sample Input

Problem setter: Shahriar Manzoor, Special Thanks: Sohel Hafiz, Md. Arifuzzaman Arif

考慮將座標映射到左上角的菱形，然後再轉換到菱形的左上角部分(切成四等份的左上角)。

最後用數學計算，決定要輸出哪個字元。