Nets of Dice

In mathematics, some plain words have special meanings. The word "net" is one of such technical terms. In mathematics, the word "net" is sometimes used to mean a plane shape which can be folded into some solid shape.

The following are a solid shape (Figure 1) and one of its net (Figure 2).

Figure 1: a prism	Figure 2: a net of a prism

Nets corresponding to a solid shape are not unique. For example, Figure 3 shows three of the nets of a cube.

Figure 3: examples of nets of a cube

In this problem, we consider nets of dice. The definition of a die is as follows.

1. A die is a cube, each face marked with a number between one and six.
2. Numbers on faces of a die are different from each other.
3. The sum of two numbers on the opposite faces is always 7.

Usually, a die is used in pair with another die. The plural form of the word "die" is "dice".

Some examples of proper nets of dice are shown in Figure 4, and those of improper ones are shown in Figure 5.

Figure 4: examples of proper nets of dice

Figure 5: examples of improper nets

The reasons why each example in Figure 5 is improper are as follows.

(a) The sum of two numbers on the opposite faces is not always 7.

(b) Some faces are marked with the same number.

(c) This is not a net of a cube. Some faces overlap each other.

(d) This is not a net of a cube. Some faces overlap each other and one face of a cube is not covered.

(e) This is not a net of a cube. The plane shape is cut off into two parts. The face marked with '2' is isolated.

(f) This is not a net of a cube. The plane shape is cut off into two parts.

(g) There is an extra face marked with '5'.

Notice that there are two kinds of dice. For example, the solid shapes formed from the first two examples in Figure 4 are mirror images of each other.

Any net of a die can be expressed on a sheet of 5x5 mesh like the one in Figure 6. In the figure, gray squares are the parts to be cut off. When we represent the sheet of mesh by numbers as in Figure 7, squares cut off are marked with zeros.

Figure 6: 5x5 mesh	Figure 7: representation by numbers

Your job is to write a program which tells the proper nets of a die from the improper ones automatically.

Input

The input consists of multiple sheets of 5x5 mesh.

N

Mesh0

Mesh1

...

MeshN-1

N is the number of sheets of mesh. Each Mesh_i gives a sheet of mesh on which a net of a die is expressed. Mesh_i is in the following format.

F00	F01	F02	F03	F04
F10	F11	F12	F13	F14
F20	F21	F22	F23	F24
F30	F31	F32	F33	F34
F40	F41	F42	F43	F44

Each F_ij is an integer between 0 and 6. They are separated by a space character.

Output

For each Mesh_i, the truth value, true or false, should be output, each in a separate line. When the net of a die expressed on the Mesh_i is proper, output "true". Otherwise, output "false".

Sample Input

6
0 0 0 0 0
0 0 0 0 6
0 2 4 5 3
0 0 1 0 0
0 0 0 0 0
0 0 3 0 0
0 0 2 0 0
0 0 4 1 0
0 0 0 5 0
0 0 0 6 0
0 0 0 3 0
0 0 2 5 0
0 4 1 0 0
0 0 6 0 0
0 0 0 0 0
0 6 2 0 0
0 0 4 0 0
0 1 5 0 0
0 0 3 0 0
0 0 0 0 0
0 0 0 0 6
0 2 4 5 3
0 0 1 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 6
0 2 4 5 3
0 0 0 0 0
0 0 0 0 0
0 0 0 1 0

Output for the Sample Input

true
true
false
false
false
false

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