Squid loves painting vertices in graphs.

There is a simple undirected graph consisting of N vertices numbered 1 through N, and M edges. Initially, all the vertices are painted in color 0. The i-th edge bidirectionally connects two vertices a_i and b_i. The length of every edge is 1.

Squid performed Q operations on this graph. In the i-th operation, he repaints all the vertices within a distance of d_i from vertex v_i, in color c_i.

Find the color of each vertex after the Q operations.

Constraints

* 1 ≤ N,M,Q ≤ 10^5
* 1 ≤ a_i,b_i,v_i ≤ N
* a_i ≠ b_i
* 0 ≤ d_i ≤ 10
* 1 ≤ c_i ≤10^5
* d_i and c_i are all integers.
* There are no self-loops or multiple edges in the given graph.

Input

Input is given from Standard Input in the following format:


N M
a_1 b_1
:
a_{M} b_{M}
Q
v_1 d_1 c_1
:
v_{Q} d_{Q} c_{Q}


Output

Print the answer in N lines. In the i-th line, print the color of vertex i after the Q operations.

Examples

Input

7 7
1 2
1 3
1 4
4 5
5 6
5 7
2 3
2
6 1 1
1 2 2


Output

2
2
2
2
2
1
0


Input

14 10
1 4
5 7
7 11
4 10
14 7
14 3
6 14
8 11
5 13
8 3
8
8 6 2
9 7 85
6 9 3
6 7 5
10 3 1
12 9 4
9 6 6
8 2 3


Output

1
0
3
1
5
5
3
3
6
1
3
4
5
3
#include <bits/stdc++.h>
using namespace std;
const int Maxn = 200000 + 1000;
int e, Begin[Maxn], To[Maxn], Next[Maxn];
int N, M, Q;
inline void add_edge(int x, int y)
{
	To[++e] = y;
	Next[e] = Begin[x];
	Begin[x] = e;
}
struct query
{
	int x, y, z;
}A[Maxn];
int Color[Maxn][15];
inline void dfs(int x, int y, int z)
{
	if (y == -1) return ;
	if (Color[x][y]) return ;
	Color[x][y] = z;
	dfs(x, y - 1, z);
	for (int i = Begin[x]; i; i = Next[i])
	{
		int a = To[i];
		dfs(a, y - 1, z); 
	}
}
int main()
{
	scanf("%d%d", &N, &M);
	int x, y, z;
	for (int i = 1; i <= M; ++i)
	{
		scanf("%d%d", &x, &y);
		add_edge(x, y);
		add_edge(y, x);
	}
	scanf("%d", &Q);
	for (int i = 1; i <= Q; ++i)
		scanf("%d%d%d", &A[i].x, &A[i].y, &A[i].z);
	for (int i = Q; i >= 1; --i)
		dfs(A[i].x, A[i].y, A[i].z);
	for (int i = 1; i <= N; ++i)
		printf("%d\n", Color[i][0]);
	return 0;
}