Interactive Tree Discovery

You are given a rooted tree with $n$ nodes, with node $1$ as the root. Your task is to determine the structure of the tree by making a series of queries.

There are two types of queries available:
1. Query Type 1: ? 1 u v
    This query returns the distance between nodes $u$ and $v$.
2. Query Type 2: ? 2 u
    This query returns two pieces of information about the subtree rooted at node $u$: first, the size of the subtree, and then a list of all nodes in this subtree (in arbitrary order).

Once you are confident about the tree structure, output the parent of every node (excluding the root) in the format:

$\displaystyle !\ fa[2]\ fa[3]\ \ldots\ fa[n]$

You must ensure that the interactive protocol does not produce more than $10^5$ numbers in total.

inputFormat

The first line contains a single integer $n$, which is the number of nodes in the tree.

For the purposes of offline simulation (and testing), the second line contains $n-1$ integers: $fa[2], fa[3], \ldots, fa[n]$, indicating the parent of each node from $2$ to $n$.

outputFormat

Output a single line in the following format:

$\displaystyle !\ fa[2]\ fa[3]\ \ldots\ fa[n]$

Here, $fa[i]$ is the parent of node $i$ in the tree.

sample

3
1 1

! 1 1