ACSL Practice 2009

Folding six squares connected in some special ways can form a cube. For example, in the diagram below, the six squares on the left can be folded into a cube (with face ~1~ opposite face ~4~, face ~2~ opposite face ~6~, and face ~3~ opposite face ~5~) but the six squares on the right cannot be folded into a cube (faces ~3~ and ~5~ overlap).

A ~6 \times 6~ array is used to represent the six squares. Only ~6~ of the ~36~ cells are used to represent the 6 squares. A cell representing a square contains the number for the square. Other cells contain the number ~0~. Note that the same ~6~ squares can be represented in many ways. For example, the invalid six squares of the above example can be represented as follows (the one on the right is obtained after a ~90~ degree rotation of the one on the left):

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

Given a square representation, determine if the squares can be folded into a cube; if so, find the face opposite face ~1~.

Input Specification

The input consists of six lines with each line containing six integers. All but six of the input integers are zeros. The non-zero integers are ~1, 2, 3, 4, 5, 6~.

Output Specification

The output file consists of a single integer. The integer is 0 if the squares cannot be folded into a cube; otherwise, the integer is the number of the face opposite face ~1~.

Sample Input

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

Sample Output

4

Diagram