Spliting a tree

You are given a tree $T$ with $N$ vertices numbered $1,2,\cdots,N$.

Choose a vertex $v$ and a nonnegative integer $k$. Remove every vertex whose distance from $v$ is at most $k$, together with every edge incident to a removed vertex. The distance between two vertices is the number of edges on the unique simple path connecting them.

For every vertex $v$, find the minimum $k$ such that the remaining graph has at least two connected components. If no such $k$ exists, the answer for $v$ is $-1$.

The empty graph has zero connected components.

The input is given from Standard Input in the following format:

$N$ $u_1\ v_1$ $u_2\ v_2$ $\vdots$ $u_{N-1}\ v_{N-1}$

For every $i$ ($1 \leq i \leq N-1$), there is an edge connecting vertices $u_i$ and $v_i$.

Let $A_i$ be the answer for vertex $i$. Print $A_1,A_2,\cdots,A_N$ on one line, separated by spaces.

• $1 \leq N \leq 500\,000$.
• $1 \leq u_i,v_i \leq N$ ($1 \leq i \leq N-1$).
• $u_i \neq v_i$ ($1 \leq i \leq N-1$).
• The given graph is a tree.