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:
/**
 * BaZ :D
 */

import java.util.*;
import java.io.*;
import static java.lang.Math.*;

public class Main
{
    static MyScanner scan;
    static PrintWriter pw;
    static long MOD = 1_000_000_007;
    static long INF = 1_000_000_000_000_000_000L;
    static long inf = 2_000_000_000;
    public static void main(String[] args) {
        new Thread(null, null, "BaZ", 1 << 27) {
            public void run() {
                try {
                    solve();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }

    static int n,par[],which_edge[], val[];
    static ArrayList<Pair> adj[];
    static void solve() throws IOException
    {
        //initIo(true);
        initIo(false);
        StringBuilder sb = new StringBuilder();
        n = ni();
        val = new int[n];
        Arrays.fill(val, 1);
        adj = new ArrayList[n+1];
        for(int i=1;i<=n;++i) {
            adj[i] = new ArrayList<>();
        }
        for(int i=1;i<n;++i) {
            int u = ni(), v = ni();
            adj[u].add(new Pair(v,i));
            adj[v].add(new Pair(u,i));
        }
        int q = ni();
        Pair queries[] = new Pair[q];
        for(int i=0;i<q;++i) {
            int x = ni(), y  = ni(), z = ni();
            queries[i] = new Pair(z, x*(n+1) + y);
        }
        Arrays.sort(queries);
        //pl("Queries");
        par = new int[n+1];
        which_edge = new int[n+1];
        int ans = 0;
        for(int i=q-1;i>=0;--i) {
            int x = queries[i].y / (n+1);
            int y = queries[i].y % (n+1);
            int v = queries[i].x;
            //pl(x+" "+y+" "+v);
            dfs(x, x, -1);
            int curr = y;
            boolean found = false;
            while(curr!=x) {
                int edge_id = which_edge[curr];
                if(val[edge_id] > v) {
                    curr = par[curr];
                    continue;
                }
                val[edge_id] = v;
                found = true;
                curr = par[curr];
            }
            if(!found) {
                ans = -1;
                break;
            }
        }
        if(ans==0) {
            for(int i=1;i<n;++i) {
                p(val[i]);
            }
            pl();
        }
        else {
            pl(-1);
        }
        pw.flush();
        pw.close();
    }
    static void dfs(int v, int p, int edge_index) {
        par[v] = p;
        which_edge[v] = edge_index;
        for(Pair pp : adj[v]) {
            if(pp.x!=p) {
                dfs(pp.x, v, pp.y);
            }
        }
    }
    static class Pair implements Comparable<Pair>
    {
        int x,y;
        Pair(int x,int y)
        {
            this.x=x;
            this.y=y;
        }
        public int compareTo(Pair other)
        {
            if(this.x!=other.x)
                return this.x-other.x;
            return this.y-other.y;
        }
        public String toString()
        {
            return "("+x+","+y+")";
        }
    }
    static void initIo(boolean isFileIO) throws IOException {
        scan = new MyScanner(isFileIO);
        if(isFileIO) {
            pw = new PrintWriter("/Users/amandeep/Desktop/output.txt");
        }
        else {
            pw = new PrintWriter(System.out, true);
        }
    }
    static int ni() throws IOException
    {
        return scan.nextInt();
    }
    static long nl() throws IOException
    {
        return scan.nextLong();
    }
    static double nd() throws IOException
    {
        return scan.nextDouble();
    }
    static String ne() throws IOException
    {
        return scan.next();
    }
    static String nel() throws IOException
    {
        return scan.nextLine();
    }
    static void pl()
    {
        pw.println();
    }
    static void p(Object o)
    {
        pw.print(o+" ");
    }
    static void pl(Object o)
    {
        pw.println(o);
    }
    static void psb(StringBuilder sb)
    {
        pw.print(sb);
    }
    static void pa(String arrayName, Object arr[])
    {
        pl(arrayName+" : ");
        for(Object o : arr)
            p(o);
        pl();
    }
    static void pa(String arrayName, int arr[])
    {
        pl(arrayName+" : ");
        for(int o : arr)
            p(o);
        pl();
    }
    static void pa(String arrayName, long arr[])
    {
        pl(arrayName+" : ");
        for(long o : arr)
            p(o);
        pl();
    }
    static void pa(String arrayName, double arr[])
    {
        pl(arrayName+" : ");
        for(double o : arr)
            p(o);
        pl();
    }
    static void pa(String arrayName, char arr[])
    {
        pl(arrayName+" : ");
        for(char o : arr)
            p(o);
        pl();
    }
    static void pa(String listName, List list)
    {
        pl(listName+" : ");
        for(Object o : list)
            p(o);
        pl();
    }
    static void pa(String arrayName, Object[][] arr) {
        pl(arrayName+" : ");
        for(int i=0;i<arr.length;++i) {
            for(Object o : arr[i])
                p(o);
            pl();
        }
    }
    static void pa(String arrayName, int[][] arr) {
        pl(arrayName+" : ");
        for(int i=0;i<arr.length;++i) {
            for(int o : arr[i])
                p(o);
            pl();
        }
    }
    static void pa(String arrayName, long[][] arr) {
        pl(arrayName+" : ");
        for(int i=0;i<arr.length;++i) {
            for(long o : arr[i])
                p(o);
            pl();
        }
    }
    static void pa(String arrayName, char[][] arr) {
        pl(arrayName+" : ");
        for(int i=0;i<arr.length;++i) {
            for(char o : arr[i])
                p(o);
            pl();
        }
    }
    static void pa(String arrayName, double[][] arr) {
        pl(arrayName+" : ");
        for(int i=0;i<arr.length;++i) {
            for(double o : arr[i])
                p(o);
            pl();
        }
    }
    static class MyScanner
    {
        BufferedReader br;
        StringTokenizer st;
        MyScanner(boolean readingFromFile) throws IOException
        {
            if(readingFromFile) {
                br = new BufferedReader(new FileReader("/Users/amandeep/Desktop/input.txt"));
            }
            else {
                br = new BufferedReader(new InputStreamReader(System.in));
            }
        }
        String nextLine()throws IOException
        {
            return br.readLine();
        }
        String next() throws IOException
        {
            if(st==null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
        int nextInt() throws IOException
        {
            return Integer.parseInt(next());
        }
        long nextLong() throws IOException
        {
            return Long.parseLong(next());
        }
        double nextDouble() throws IOException
        {
            return Double.parseDouble(next());
        }
    }
}

/*
3
1 2
1 3
2
1 2 100
2 3 10
 */