E. Vasya and a Tree
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Vasya has a tree consisting of $$$n$$$ vertices with root in vertex $$$1$$$. At first all vertices has $$$0$$$ written on it.

Let $$$d(i, j)$$$ be the distance between vertices $$$i$$$ and $$$j$$$, i.e. number of edges in the shortest path from $$$i$$$ to $$$j$$$. Also, let's denote $$$k$$$-subtree of vertex $$$x$$$ — set of vertices $$$y$$$ such that next two conditions are met:

  • $$$x$$$ is the ancestor of $$$y$$$ (each vertex is the ancestor of itself);
  • $$$d(x, y) \le k$$$.

Vasya needs you to process $$$m$$$ queries. The $$$i$$$-th query is a triple $$$v_i$$$, $$$d_i$$$ and $$$x_i$$$. For each query Vasya adds value $$$x_i$$$ to each vertex from $$$d_i$$$-subtree of $$$v_i$$$.

Report to Vasya all values, written on vertices of the tree after processing all queries.

Input

The first line contains single integer $$$n$$$ ($$$1 \le n \le 3 \cdot 10^5$$$) — number of vertices in the tree.

Each of next $$$n - 1$$$ lines contains two integers $$$x$$$ and $$$y$$$ ($$$1 \le x, y \le n$$$) — edge between vertices $$$x$$$ and $$$y$$$. It is guarantied that given graph is a tree.

Next line contains single integer $$$m$$$ ($$$1 \le m \le 3 \cdot 10^5$$$) — number of queries.

Each of next $$$m$$$ lines contains three integers $$$v_i$$$, $$$d_i$$$, $$$x_i$$$ ($$$1 \le v_i \le n$$$, $$$0 \le d_i \le 10^9$$$, $$$1 \le x_i \le 10^9$$$) — description of the $$$i$$$-th query.

Output

Print $$$n$$$ integers. The $$$i$$$-th integers is the value, written in the $$$i$$$-th vertex after processing all queries.

Examples
Input
5
1 2
1 3
2 4
2 5
3
1 1 1
2 0 10
4 10 100
Output
1 11 1 100 0
Input
5
2 3
2 1
5 4
3 4
5
2 0 4
3 10 1
1 2 3
2 3 10
1 1 7
Output
10 24 14 11 11
Note

In the first exapmle initial values in vertices are $$$0, 0, 0, 0, 0$$$. After the first query values will be equal to $$$1, 1, 1, 0, 0$$$. After the second query values will be equal to $$$1, 11, 1, 0, 0$$$. After the third query values will be equal to $$$1, 11, 1, 100, 0$$$.