Given an unrooted tree structure as in the picture below, we chop it into pieces in the following way: pick the smallest numbered leaf, and remove the edge connecting that leaf to the tree. Then repeat this process until nothing is left of the tree.

To record this process, we write list the edges of the tree
in the order they were chopped off, and write each edge as
“`u` `v`” where
`u` is the leaf and `v` is its connecting vertex. So for the figure
above we get:

u v 3 5 4 1 5 1 1 2 6 2 2 7

Unfortunately, we lost the first column of data of this
extremely important list so we only have the “`v`” column. Can you help us reconstruct the
“`u`” column? The vertices of the tree
are always numbered from 1 up to the number of vertices.

The first line of input contains an integer $n$ ($1
\le n \le 200\, 000$) giving the length of the list. The
next $n$ lines each
contain an integer between 1 and $n+1$ (inclusive), describing the
`v` column of the list.

If the `u` column can be uniquely
determined, write $n$
lines of integers giving the `u` column
of the list. If the `u` column can not
be uniquely determined (either because no tree exists which
results in the given `v` column, or
because many different such trees exist), write a single line
containing the word “`Error`”.

This problem has somewhat large amounts of input and output. We recommend you to make sure that your output is properly buffered, otherwise your solution may be too slow.

Sample Input 1 | Sample Output 1 |
---|---|

6 5 1 1 2 2 7 |
3 4 5 1 6 2 |

Sample Input 2 | Sample Output 2 |
---|---|

2 1 2 |
Error |