Problem: You are given a tree consisting of n nodes. You want to write some labels on the tree's edges such that the following conditions hold:

  * Every label is an integer between 0 and n-2 inclusive. 
  * All the written labels are distinct. 
  * The largest value among MEX(u,v) over all pairs of nodes (u,v) is as small as possible. 



Here, MEX(u,v) denotes the smallest non-negative integer that isn't written on any edge on the unique simple path from node u to node v.

Input

The first line contains the integer n (2 ≤ n ≤ 10^5) — the number of nodes in the tree.

Each of the next n-1 lines contains two space-separated integers u and v (1 ≤ u,v ≤ n) that mean there's an edge between nodes u and v. It's guaranteed that the given graph is a tree.

Output

Output n-1 integers. The i^{th} of them will be the number written on the i^{th} edge (in the input order).

Examples

Input


3
1 2
1 3


Output


0
1


Input


6
1 2
1 3
2 4
2 5
5 6


Output


0
3
2
4
1

Note

The tree from the second sample:

<image>

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.BigInteger;
public class GFG {
    static class edge{
        int s,d,w;
        public edge(int s,int d,int w)
        {
            this.s=s;
            this.d=d;
            this.w=w;
        }
    }
    
    static class graph{
        int v;
        LinkedList<edge> li[];
        boolean visit[];
        boolean visit1[];
        int arr[];
        public graph(int v)
        {
            this.v=v;
            visit=new boolean[v];
            visit1=new boolean[v];
            arr=new int[v];
            li=new LinkedList[v];
            for(int i=0;i<v;i++)
            li[i]=new  LinkedList<>();
        }
        public void addedge(int x,int y,int w)
        {
            edge e=new edge(x,y,w);
            li[x].add(e);
            edge e1=new edge(y,x,w);
            li[y].add(e1);
        }
        public void removeedge(int x,int y,int w)
        {
            Iterator<edge> it =li[x].iterator();
        while (it.hasNext()) {
            if (it.next().d == y) {
                it.remove();
                break;
            }
        }
           Iterator<edge> it1 =li[y].iterator();
        while (it1.hasNext()) {
            if (it1.next().d == x) {
                it1.remove();
                return;
            }
        }
        }
        public boolean hasEdge(int i, int j) {
        return li[i].contains(j);
    }
        public void ans(int arr[][])
        {
            int res[]=new int[v-1];
            int p=0;
            for(int i=0;i<v-1;i++)
            {
                if(li[arr[i][0]].size()==1||li[arr[i][1]].size()==1){
                res[i]=p;p++;}
            }
            for(int i=0;i<v-1;i++)
            {
                if(li[arr[i][0]].size()!=1&&li[arr[i][1]].size()!=1){
                res[i]=p;p++;}
            }
            for(int i:res)
            System.out.println(i);
        }
    }
        public static void main (String[] args)throws IOException {
		Reader sc=new Reader();
		int n=sc.nextInt();
		//int m=sc.nextInt();
		//int k=sc.nextInt();
		graph g=new graph(n);
		int k=0;
		int arr[][]=new int[n-1][2];
		for(int i=0;i<n-1;i++)
		{
		    int x=sc.nextInt();
		    int y=sc.nextInt();
		    g.addedge(x-1,y-1,0);
		    arr[i][0]=x-1;arr[i][1]=y-1;
		}
		g.ans(arr);
	}	
	static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(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(); 
        } 
    } 
  
}