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>
#define FOR(i,bg,ed) for(ll i=(bg);i<(ed);i++)
#define REP(i,n) FOR(i,0,n)
#define MOD 1000000007
//#define int long long
using namespace std;
typedef long long ll;
typedef vector<vector<ll>> mat;
const int INF = 1e9;

int dp[100001], color[100001];
vector<int> e[100001];

void paint(int v, int d, int c)
{
    if (!color[v]) color[v] = c;
    if (dp[v] >= d || d == 0) return;
    dp[v] = d;
    for (auto u : e[v]) paint(u, d - 1, c);
}

signed main()
{
    int N, M, Q, a, b;
    cin >> N >> M;

    REP(i,M) {
        cin >> a >> b;
        e[a].push_back(b);
        e[b].push_back(a);
    }

    cin >> Q;
    int v[Q], d[Q], c[Q];
    REP(i,Q) {
        cin >> v[i] >> d[i] >> c[i];
    }

    for (int i=Q-1; i>=0; i--) paint(v[i], d[i], c[i]);
    REP(i,N) cout << color[i + 1] << endl;
}
