Praveen went crazy yesterday and created an arbitrary matrix consisting of 0, 1 or 2. There was no rule observed in forming this matrix. But then he made up some rules himself.

If there are adjacent $1's$, they are said to be connected. Similarly, if there are adjacent $2's$, they are said to be connected. Here adjacent means all the surrounding positions along with the diagonal positions.

Now given a matrix of 0, 1 or 2, do your computation according to the following rules:

1. If there is a path from any position in top row to any position in bottom row consisting only of 1, then print 1.
2. If there is a path from any position in first column to any position in last column consisting only of 2, then print 2.
3. If both Rule 1 & Rule 2 are true, print $AMBIGUOUS$.
4. If none of Rule 1, Rule 2 or Rule 3 satisfies, print 0.

Input format

First line of input contains a positive integer N, the size of matrix. Then N line follows, each containing N integers which are either 0, 1 or 2.

Output format

Print a single line containing the output according to the rule mentioned. Clearly, the output can only be 0, 1, 2 or $AMBIGUOUS$.

Input constraint

$1 <= N <= 100$

Example

4

0 0 0 0

2 0 1 0

0 2 1 2

0 1 2 0

Here the output is 2, as there is a connected path of 2 from first column to last column.