Taro attempts to tell digits to Hanako by putting straight bars on the floor. Taro wants to express each digit by making one of the forms shown in Figure 2.
Since Taro may not have bars of desired lengths, Taro cannot always make forms exactly as shown in Figure 2. Fortunately, Hanako can recognize a form as a digit if the connection relation between bars in the form is kept. Neither the lengths of bars nor the directions of forms affect Hanako’s perception as long as the connection relation remains the same. For example, Hanako can recognize all the awkward forms in Figure 3 as digits. On the other hand, Hanako cannot recognize the forms in Figure 4 as digits. For clarity, touching bars are slightly separated in Figures 2, 3 and 4. Actually, touching bars overlap exactly at one single point.
In the forms, when a bar touches another, the touching point is an end of at least one of them. That is, bars never cross. In addition, the angle of such two bars is always a right angle.
To enable Taro to represent forms with his limited set of bars, positions and lengths of bars can be changed as far as the connection relations are kept. Also, forms can be rotated.
Keeping the connection relations means the following.
Separated bars are not made to touch.
Touching bars are not made separate.
When one end of a bar touches another bar, that end still touches the same bar. When it touches a midpoint of the other bar, it remains to touch a midpoint of the same bar on the same side.
The angle of touching two bars is kept to be the same right angle (90 degrees and -90 degrees are considered different, and forms for 2 and 5 are kept distinguished).
Your task is to find how many times each digit appears on the floor.
The forms of some digits always contain the forms of other digits. For example, a form for 9 always contains four forms for 1, one form for 4, and two overlapping forms for 7. In this problem, ignore the forms contained in another form and count only the digit of the “largest” form composed of all mutually connecting bars. If there is one form for 9, it should be interpreted as one appearance of 9 and no appearance of 1, 4, or 7.