Given is a tree with $N$ vertices. The vertices are numbered $1,2,\ldots ,N$, and the $i$\-th edge is an undirected edge connecting Vertices $u_i$ and $v_i$. For each integer $i\,(1 \leq i \leq N)$, find $\sum_{j=1}^{N}dis(i,j)$. Here, $dis(i,j)$ denotes the minimum number of edges that must be traversed to go from Vertex $i$ to Vertex $j$.

Input is given from Standard Input in the following format: >$N$\ >$u_1$ $v_1$\ >$u_2$ $v_2$\ >$\vdots$\ >$u_{N-1}$ $v_{N-1}$ #### Constraints - $2 \leq N \leq 2 \times 10^5$ - $1 \leq u_i \lt v_i \leq N$ - The given graph is a tree. - All values in input are integers.

Print $N$ lines. The $i$\-th line should contain $\sum_{j=1}^{N}dis(i,j)$.

***For Sample #1:*** We have: $dis(1,1)+dis(1,2)+dis(1,3)=0+1+2=3$, $dis(2,1)+dis(2,2)+dis(2,3)=1+0+1=2$, $dis(3,1)+dis(3,2)+dis(3,3)=2+1+0=3$.

AtCoder [ABC220F]