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 <iostream>
#include <vector>
using namespace std;
vector<int> v[100010];
int n,m,k;
int a[100010],b[100010],c[100010];
int d[100010];
int r[100010]={0};
void dfs(int x,int y,int col)
{
	//cout <<x<<" "<<y<<" "<<col<<" "<<d[x]<<"\n{\n";
	if (y<=d[x]) return;
	else d[x]=y;
	if (!r[x]) r[x]=col;
	if (!y) return;
	else
	{
		for (int i=0;i<v[x].size();i++)
		{
			int xi=v[x][i];
			dfs(xi,y-1,col);
		}
		//cout <<"}\n";
	}
}
int main()
{
	cin >>n>>m;
	for (int i=0;i<m;i++)
	{
		int x,y;
		cin >>x>>y;
		x--,y--;
		v[x].push_back(y);
		v[y].push_back(x);
	}
	cin >>k;
	for (int i=0;i<k;i++) cin >>a[i]>>b[i]>>c[i],a[i]--;
	fill(d,d+n,-1);
	for (int i=k-1;i>=0;i--) dfs(a[i],b[i],c[i]);
	for (int i=0;i<n;i++) cout <<r[i]<<"\n";
	return 0;
} 