Problem: There are n railway stations in Berland. They are connected to each other by n-1 railway sections. The railway network is connected, i.e. can be represented as an undirected tree.

You have a map of that network, so for each railway section you know which stations it connects.

Each of the n-1 sections has some integer value of the scenery beauty. However, these values are not marked on the map and you don't know them. All these values are from 1 to 10^6 inclusive.

You asked m passengers some questions: the j-th one told you three values:

  * his departure station a_j; 
  * his arrival station b_j; 
  * minimum scenery beauty along the path from a_j to b_j (the train is moving along the shortest path from a_j to b_j). 



You are planning to update the map and set some value f_i on each railway section — the scenery beauty. The passengers' answers should be consistent with these values.

Print any valid set of values f_1, f_2, ..., f_{n-1}, which the passengers' answer is consistent with or report that it doesn't exist.

Input

The first line contains a single integer n (2 ≤ n ≤ 5000) — the number of railway stations in Berland.

The next n-1 lines contain descriptions of the railway sections: the i-th section description is two integers x_i and y_i (1 ≤ x_i, y_i ≤ n, x_i ≠ y_i), where x_i and y_i are the indices of the stations which are connected by the i-th railway section. All the railway sections are bidirected. Each station can be reached from any other station by the railway.

The next line contains a single integer m (1 ≤ m ≤ 5000) — the number of passengers which were asked questions. Then m lines follow, the j-th line contains three integers a_j, b_j and g_j (1 ≤ a_j, b_j ≤ n; a_j ≠ b_j; 1 ≤ g_j ≤ 10^6) — the departure station, the arrival station and the minimum scenery beauty along his path.

Output

If there is no answer then print a single integer -1.

Otherwise, print n-1 integers f_1, f_2, ..., f_{n-1} (1 ≤ f_i ≤ 10^6), where f_i is some valid scenery beauty along the i-th railway section.

If there are multiple answers, you can print any of them.

Examples

Input


4
1 2
3 2
3 4
2
1 2 5
1 3 3


Output


5 3 5


Input


6
1 2
1 6
3 1
1 5
4 1
4
6 1 3
3 4 1
6 5 2
1 2 5


Output


5 3 1 2 1 


Input


6
1 2
1 6
3 1
1 5
4 1
4
6 1 1
3 4 3
6 5 3
1 2 4


Output


-1

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public class Sol{
	public static List<Integer> adj[];
	public static int query[][];
	public static int get[][] = new int[5000][5000];
	public static int edge[];
	public static int par[];
	public static int depth[];
	public static int n, m, D;
	public static void main(String[] args) throws IOException{
		FastIO sc = new FastIO(System.in);
		PrintWriter out = new PrintWriter(System.out);
		boolean poss = true;
		n = sc.nextInt();
		par = new int[n];
		depth = new int[n];
		edge = new int[n-1];
		adj = new ArrayList[n];
		for(int i=0; i<n; ++i) {
			adj[i] = new ArrayList<>();
		}
		int idx = 0;
		for(int i=0; i<n-1; ++i) {
			int a = sc.nextInt()-1;
			int b = sc.nextInt()-1;
			adj[a].add(b);
			adj[b].add(a);
			get[a][b] = idx;
			get[b][a] = idx;
			idx++;
			edge[i] = -1;
		}
		depth[0] = 0;
		par[0] = 0;
		DFS(0, 0);
		int m = sc.nextInt();
		query = new int[m][3];
		for(int i=0; i<m; ++i) {
			query[i][0] =sc.nextInt()-1;
			query[i][1] = sc.nextInt()-1;
			query[i][2] = sc.nextInt();
		}
		ColumnSort(query, 2);
		for(int i=m-1; i>=0; --i) {
			boolean change = false;
			int num = query[i][2];
			int curr1 = query[i][0];
			int curr2 = query[i][1];
			while(curr1!=curr2) {
				if(depth[curr1]>depth[curr2]) {
					idx = get[curr1][par[curr1]];
					if(edge[idx]==-1||edge[idx]==num) {
						edge[idx] = num;
						change = true;
					}
					curr1 = par[curr1];
				}else {
					idx = get[curr2][par[curr2]];
					if(edge[idx]==-1||edge[idx]==num) {
						edge[idx] = num;
						change = true;
					}
					curr2 = par[curr2];
				}
			}
			if(!change) poss = false;
		}
		if(!poss) {
			out.println(-1);
		}else {
			for(int i=0; i<n-1; ++i) {
				out.print(Math.max(edge[i], 1) + " ");
			}
			out.println();
		}
		out.close();
	}
	public static void DFS(int curr, int p) {
		for(int i: adj[curr]) {
			if(i==p) continue;
			par[i] = curr;
			depth[i] = depth[curr]+1;
			DFS(i, curr);
		}
	}
    public static void ColumnSort(int arr[][], int col) { 
        Arrays.sort(arr, new Comparator<int[]>() { 
            @Override 
          public int compare(int[] entry1,  
                             int[] entry2) { 
            	Integer a = entry1[col];
            	Integer b = entry2[col];
            	return a.compareTo(b);
          } 
        }); 
    } 
	static class FastIO {
		 
		// Is your Fast I/O being bad?
 
		InputStream dis;
		byte[] buffer = new byte[1 << 17];
		int pointer = 0;
 
		public FastIO(String fileName) throws IOException {
			dis = new FileInputStream(fileName);
		}
 
		public FastIO(InputStream is) throws IOException {
			dis = is;
		}
 
		int nextInt() throws IOException {
			int ret = 0;
 
			byte b;
			do {
				b = nextByte();
			} while (b <= ' ');
			boolean negative = false;
			if (b == '-') {
				negative = true;
				b = nextByte();
			}
			while (b >= '0' && b <= '9') {
				ret = 10 * ret + b - '0';
				b = nextByte();
			}
 
			return (negative) ? -ret : ret;
		}
 
		long nextLong() throws IOException {
			long ret = 0;
 
			byte b;
			do {
				b = nextByte();
			} while (b <= ' ');
			boolean negative = false;
			if (b == '-') {
				negative = true;
				b = nextByte();
			}
			while (b >= '0' && b <= '9') {
				ret = 10 * ret + b - '0';
				b = nextByte();
			}
 
			return (negative) ? -ret : ret;
		}
 
		byte nextByte() throws IOException {
			if (pointer == buffer.length) {
				dis.read(buffer, 0, buffer.length);
				pointer = 0;
			}
			return buffer[pointer++];
		}
 
		String next() throws IOException {
			StringBuffer ret = new StringBuffer();
 
			byte b;
			do {
				b = nextByte();
			} while (b <= ' ');
			while (b > ' ') {
				ret.appendCodePoint(b);
				b = nextByte();
			}
 
			return ret.toString();
		}
 
	}
}