waclaw

문제

Waclaw Sierpinski was a Polish mathematician who liked playing with triangles. One day he started drawing triangles using the following procedure: 

• Draw an equilateral triangle T. 
• Connect the midpoints of its sides with line segments. Denote the new equilateral triangles with T1, T2, T3 and T4, as illustrated in the first figure below. 
• Repeat the previous step on triangles T1, T2 and T3. New triangles are: T11, T12, T13, T14, T21, T22, T23, T24, T31, T32, T33, T34. 
• Continue the procedure on all triangles ending in 1, 2 or 3. The resulting fractal is called the Sierpinski triangle. 

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We say that a triangle A is leaning on the triangle B if B does not contain A and if one entire side of A is a part of some side of B. For example, the triangle T23 is leaning on T24 and T4, but not on T2 or T32. Note that A leaning on B does not imply that B is leaning on A. 

Write a program that, given a triangle A, which is a part of the Sierpinski triangle, finds all triangles B such that A is leaning on B. 

입력

The first and only line of input contains a sequence of characters representing the given triangle, as described above. The sequence will contain between 2 and 50 characters, inclusive. 

출력

Output all triangles that the given triangle is leaning on, each on a separate line, in any order.