Problem Statement

We have a tree with $N$ vertices and $N-1$ edges, where the vertices are numbered $1, 2, \dots, N$ and the edges are numbered $1, 2, \dots, N-1$. Edge $i$ connects Vertices $a_i$ and $b_i$. Each vertex in the tree has an integer written on it. Let $c_i$ be the integer written on Vertex $i$. Initially, $c_i = 0$.

You will be given $Q$ queries. The $i$-th query, consisting of integers $t_i$, $e_i$, and $x_i$, is as follows:

• If $t_i = 1$: for each Vertex $v$ reachable from Vertex $a_{e_i}$ without visiting Vertex $b_{e_i}$ by traversing edges, replace $c_v$ with $c_v + x_i$.
• If $t_i = 2$: for each Vertex $v$ reachable from Vertex $b_{e_i}$ without visiting Vertex $a_{e_i}$ by traversing edges, replace $c_v$ with $c_v + x_i$.

After processing all queries, print the integer written on each vertex.

Constraints

• All values in input are integers.
• $2 \le N \le 2 \times 10^5$
• $1 \le a_i, b_i \le N$
• The given graph is a tree.
• $1 \le Q \le 2 \times 10^5$
• $t_i \in \{1, 2\}$
• $1 \le e_i \le N-1$
• $1 \le x_i \le 10^9$

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
\vdots
a_{N-1} b_{N-1}
Q
t_1 e_1 x_1
\vdots
t_Q e_Q x_Q

Output

Print the values $c_1, c_2, \dots, c_N$ after processing all queries, each in its own line.