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
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
vector<int> g[100000];
int dp[100000][15] = {};
signed main() {
  ios::sync_with_stdio(false); cin.tie(0);
  int n, m, q;
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    int a, b;
    cin >> a >> b;
    a--; b--;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  cin >> q;
  vector<int> c(q + 1);
  for (int i = 1; i <= q; i++) {
    int v, d;
    cin >> v >> d >> c[i];
    v--;
    dp[v][d] = max(dp[v][d], i);
  }
  for (int i = 10; i >= 1; i--) {
    for (int j = 0; j < n; j++) {
      for (int nbr : g[j]) {
        dp[nbr][i - 1] = max(dp[nbr][i - 1], dp[j][i]);
      }
    }
  }
  for (int i = 0; i < n; i++) {
    int t = 0;
    for (int j = 0; j <= 10; j++) {
      t = max(t, dp[i][j]);
    }
    cout << c[t] << endl;
  }
  return 0;	
}