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.math.BigInteger;
import java.util.*;


public class Main {

	 static class FastReader 
	    { 
	        final private int BUFFER_SIZE = 1 << 16; 
	        private DataInputStream din; 
	        private byte[] buffer; 
	        private int bufferPointer, bytesRead; 
	  
	        public FastReader() 
	        { 
	            din = new DataInputStream(System.in); 
	            buffer = new byte[BUFFER_SIZE]; 
	            bufferPointer = bytesRead = 0; 
	        } 
	  
	        public FastReader(String file_name) throws IOException 
	        { 
	            din = new DataInputStream(new FileInputStream(file_name)); 
	            buffer = new byte[BUFFER_SIZE]; 
	            bufferPointer = bytesRead = 0; 
	        } 
	  
	        public String readLine() throws IOException 
	        { 
	            byte[] buf = new byte[64]; // line length 
	            int cnt = 0, c; 
	            while ((c = read()) != -1) 
	            { 
	                if (c == '\n') 
	                    break; 
	                buf[cnt++] = (byte) c; 
	            } 
	            return new String(buf, 0, cnt); 
	        } 
	  
	        public int nextInt() throws IOException 
	        { 
	            int ret = 0; 
	            byte c = read(); 
	            while (c <= ' ') 
	                c = read(); 
	            boolean neg = (c == '-'); 
	            if (neg) 
	                c = read(); 
	            do
	            { 
	                ret = ret * 10 + c - '0'; 
	            }  while ((c = read()) >= '0' && c <= '9'); 
	  
	            if (neg) 
	                return -ret; 
	            return ret; 
	        } 
	  
	        public long nextLong() throws IOException 
	        { 
	            long ret = 0; 
	            byte c = read(); 
	            while (c <= ' ') 
	                c = read(); 
	            boolean neg = (c == '-'); 
	            if (neg) 
	                c = read(); 
	            do { 
	                ret = ret * 10 + c - '0'; 
	            } 
	            while ((c = read()) >= '0' && c <= '9'); 
	            if (neg) 
	                return -ret; 
	            return ret; 
	        } 
	  
	        public double nextDouble() throws IOException 
	        { 
	            double ret = 0, div = 1; 
	            byte c = read(); 
	            while (c <= ' ') 
	                c = read(); 
	            boolean neg = (c == '-'); 
	            if (neg) 
	                c = read(); 
	  
	            do { 
	                ret = ret * 10 + c - '0'; 
	            } 
	            while ((c = read()) >= '0' && c <= '9'); 
	  
	            if (c == '.') 
	            { 
	                while ((c = read()) >= '0' && c <= '9') 
	                { 
	                    ret += (c - '0') / (div *= 10); 
	                } 
	            } 
	  
	            if (neg) 
	                return -ret; 
	            return ret; 
	        } 
	  
	        private void fillBuffer() throws IOException 
	        { 
	            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
	            if (bytesRead == -1) 
	                buffer[0] = -1; 
	        } 
	  
	        private byte read() throws IOException 
	        { 
	            if (bufferPointer == bytesRead) 
	                fillBuffer(); 
	            return buffer[bufferPointer++]; 
	        } 
	  
	        public void close() throws IOException 
	        { 
	            if (din == null) 
	                return; 
	            din.close(); 
	        } 
	    } 
	
		public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
		public static long mod = (long) (1e9 + 7);
		public static long[][] dp;
	    public static List<Pair>[] edges ;
		public static List<Pair> pre;
		static FastReader sc = new FastReader();
		public static void main(String[] args) throws IOException {
		
			int n = sc.nextInt();
			edges = new ArrayList[n+1];
			for(int i=0;i<=n;++i) edges[i] = new ArrayList<>();
		
			
			  for(int i=0;i<n-1;++i) {
				  int u = sc.nextInt();
				  int v = sc.nextInt();
				  edges[u].add(new Pair(v,i));
				  edges[v].add(new Pair(u,i));
			  }
			  
			   
			    int m = sc.nextInt();
			    int[] ans = new int[n+1];
			    Arrays.fill(ans, 1);
			 
			    int[][] q = new int[m+1][3];
			   
			    for(int i=1;i<=m;++i){
			      
			        int u = sc.nextInt();
			        int v = sc.nextInt();
			        int w = sc.nextInt();
			        q[i][0] = u;
			        q[i][1] = v;
			        q[i][2] = w;
			 
			     dfs(u,v,0,ans,w);
			    }
			 boolean found = true;
			    for (int i=1;i<=m && found;++i) {
			        int x = q[i][0];
			        int y = q[i][1];
			        int w = q[i][2];
			            if(!dfss(x,y,w,0,(int) 1e9,ans)){
			              found = false;
			            }
			         }
			        
			    if(found) for(int i=0;i<n-1;++i) out.print(ans[i]+" ");
			    else out.print(-1);
			    
			
			
			out.close();
		}

		
		
		private static boolean dfss(int x, int y, int w, int par, int j, int[] ans) {
			if(x == y) return (j == w);
			   for(Pair v : edges[x]){
			      if(v.first != par){
			         if(dfss(v.first,y,w,x,Math.min(j,ans[v.second]),ans)){
			            return true;
			         }
			      }
			   }
			  
			return false;
		}



		private static boolean dfs(int x, int y, int par, int[] ans,int w) {
			 if(x == y) return true;
			   for(Pair v : edges[x]){
			      if(v.first!=par){
			         if(dfs(v.first,y,x,ans,w)){
			           ans[v.second] = Math.max(ans[v.second],w);
			            return true;
			         }
			      }
			   }
			   return false;
			
		}



		static class Pair{
			int first;
			int second;
			Pair(int first,int second){
				this.first = first;
				this.second = second;
			}
		}

	}