Problem Statement

You are given a tree $T$ with $N$ vertices: vertex $1$, vertex $2$, $\ldots$, vertex $N$. The $i$-th edge $(1\leq i\lt N)$ connects vertices $u_i$ and $v_i$.

For a vertex $u$ in $T$, define $f(u)$ as follows:

• $f(u)\coloneqq$ The number of pairs of vertices $v$ and $w$ in $T$ that satisfy the following two conditions:
• Vertex $w$ is contained in the path connecting vertices $u$ and $v$.
  • $v\lt w$.

Here, vertex $w$ is contained in the path connecting vertices $u$ and $v$ also when $u=w$ or $v=w$.

Find the values of $f(1),f(2),\ldots,f(N)$.

Constraints

• $2\leq N\leq2\times10^5$
• $1\leq u_i\leq N\ (1\leq i\leq N)$
• $1\leq v_i\leq N\ (1\leq i\leq N)$
• The given graph is a tree.
• All input values are integers.

Input

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}

Output

Print the values of $f(1),f(2),\ldots,f(N)$ in this order, separated by spaces.