AT_abc479_e [ABC479E] Cut and Add

There is a tree with $ N $ vertices numbered $ 1,2,\dots,N $ . Here, $ N $ is odd. The edges are also numbered $ 1,2,\dots,N-1 $ , and edge $ i $ connects vertices $ A_i $ and $ B_i $ . Each vertex $ i $ has a variable $ x_i $ , and initially $ x_i=0 $ for every vertex $ i $ . Now, for $ i=1,2,\dots,N-1 $ in this order, perform the following operation. - First, remove edge $ i $ . As a result, the tree is split into two connected components. - For every vertex $ v $ in the connected component containing more vertices, add $ i $ to $ x_v $ . - Since $ N $ is odd, the connected component containing more vertices is uniquely determined. - Finally, restore edge $ i $ . Find the values of the variables $ x_1,x_2,\dots,x_N $ of the vertices after all operations are performed.

The input is given from Standard Input in the following format: > $ N $ $ A_1 $ $ B_1 $ $ A_2 $ $ B_2 $ $ \vdots $ $ A_{N-1} $ $ B_{N-1} $

Output the final values of the variables in the following format: > $ x_1 $ $ x_2 $ $ \dots $ $ x_N $

### Sample Explanation 1 - For $ i=1 $ , the following operation is performed. - Removing edge $ 1 $ splits the tree into a connected component with vertex $ 2 $ and a connected component with vertices $ 1,3,4,5 $ . - The larger one is the connected component with vertices $ 1,3,4,5 $ , so $ 1 $ is added to all of their variables. - As a result, the values of the variables become $ (x_1,x_2,x_3,x_4,x_5)=(1,0,1,1,1) $ . - Finally, edge $ 1 $ is restored. - For $ i=2 $ , the following operation is performed. - Removing edge $ 2 $ splits the tree into a connected component with vertex $ 5 $ and a connected component with vertices $ 1,2,3,4 $ . - The larger one is the connected component with vertices $ 1,2,3,4 $ , so $ 2 $ is added to all of their variables. - As a result, the values of the variables become $ (x_1,x_2,x_3,x_4,x_5)=(3,2,3,3,1) $ . - Finally, edge $ 2 $ is restored. - For $ i=3 $ , the following operation is performed. - Removing edge $ 3 $ splits the tree into a connected component with vertices $ 2,4 $ and a connected component with vertices $ 1,3,5 $ . - The larger one is the connected component with vertices $ 1,3,5 $ , so $ 3 $ is added to all of their variables. - As a result, the values of the variables become $ (x_1,x_2,x_3,x_4,x_5)=(6,2,6,3,4) $ . - Finally, edge $ 3 $ is restored. - For $ i=4 $ , the following operation is performed. - Removing edge $ 4 $ splits the tree into a connected component with vertex $ 3 $ and a connected component with vertices $ 1,2,4,5 $ . - The larger one is the connected component with vertices $ 1,2,4,5 $ , so $ 4 $ is added to all of their variables. - As a result, the values of the variables become $ (x_1,x_2,x_3,x_4,x_5)=(10,6,6,7,8) $ . - Finally, edge $ 4 $ is restored. The final values of the variables are $ (x_1,x_2,x_3,x_4,x_5)=(10,6,6,7,8) $ . ### Constraints - All input values are integers. - $ N $ is an odd number satisfying $ 3 \le N \le 2 \times 10^5 - 1 $ . - $ 1 \le A_i < B_i \le N $ - The given graph is a tree.