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;
typedef pair<int, int> pii;
#define mp(a, b) make_pair(a, b)
const int maxn = 1e5 + 10;
struct Query
{
	int v, d, c;
}a[maxn];
vector<int> E[maxn];
int n, m, q;
int c[maxn], col[maxn];
void calc(int d)
{
	for(int i = q; i; --i) 
		if(a[i].d == d)
			col[a[i].v] = max(col[a[i].v], i);
	if(d > 0)
	{
		for(int i = 1; i <= n; ++i) c[i] = col[i];
		for(int i = 1; i <= n; ++i)
			for(auto v : E[i])
				c[v] = max(c[v], col[i]);
		for(int i = 1; i <= n; ++i)
			col[i] = c[i];
	}
}
int main()
{
	scanf("%d%d", &n, &m);
	for(int i = 1; i <= m; ++i) 
	{
		int u, v;
		scanf("%d%d", &u, &v);
		E[u].push_back(v);
		E[v].push_back(u);
	}
	scanf("%d", &q);
	for(int i = 1; i <= q; ++i) scanf("%d%d%d", &a[i].v, &a[i].d, &a[i].c);
	for(int i = 10; ~i; --i) calc(i);
	for(int i = 1; i <= n; ++i)
		printf("%d\n", a[col[i]].c);
	return 0;
}