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>
#include<vector>
#define N 100005
using namespace std;
vector<int> G[N];
int n,m,q,dp[11][N],c[N];
int main()
{
	int i,j,k,x,y;
	scanf("%d %d",&n,&m);
	for(i=1;i<=m;i++){
		scanf("%d %d",&x,&y);
		G[x].push_back(y);
		G[y].push_back(x);
	  }
	scanf("%d",&q);
	for(i=1;i<=q;i++){
		scanf("%d %d %d",&x,&y,&c[i]);
		dp[y][x]=i;
	  }
	for(i=10;i>=1;i--)
		for(j=1;j<=n;j++){
			dp[i-1][j]=max(dp[i-1][j],dp[i][j]);
			for(k=0;k<G[j].size();k++)
				dp[i-1][G[j][k]]=max(dp[i-1][G[j][k]],dp[i][j]);
		  }
	for(i=1;i<=n;i++)
		printf("%d\n",c[dp[0][i]]);
	return 0;
}
