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;
#define ff first
#define ss second
vector<vector<pair<int,int>>> dt;
vector<pair<int,int>> Es;
signed main(){
    int n,m,a,b,v,d,c;
    cin >> n >> m;
    dt.resize(n);
    for(auto& x: dt)x.resize(11);
    for(int i = 0; i < m;i++){
        cin >> a >> b;a--;b--;
        Es.push_back({a, b});
    }
    int q;
    cin >> q;
    for(int i = 0; i < q; i++){
        cin >> v >> d >> c;v--;
        dt[v][d] = {i, c};
    }
    for(int d = 10; d > 0; d--){
        for(auto e: Es)
            dt[e.ff][d-1] = max(dt[e.ff][d-1], dt[e.ss][d]),
            dt[e.ss][d-1] = max(dt[e.ss][d-1], dt[e.ff][d]);
        for(auto& x: dt) x[0] = max(x[0], x[d]);
    }
    for(auto& x: dt)cout << x[0].ss << endl;
}
