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