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 PYTHON3):

Solution:
import functools,sys
def ip():
    
    n=int(sys.stdin.readline())
    g=[]
    for _ in range(n):
        g.append(set())
    d={}
    for j in range(n-1):
        u,v=map(int,sys.stdin.readline().split())
        u-=1
        v-=1
        d[(min(u,v),max(u,v))]=j
        g[u].add(v)
        g[v].add(u)
    k=[i for i in range(n)]
    def myfun(u,v):
        return len(g[u])-len(g[v])
    k=sorted(k,key=functools.cmp_to_key(myfun))
    ans=[0]*(n-1)
    curr=0
    #print(k)
    while curr<n-1:
        if len(k)==0:
            break
        u=k.pop()
        if len(g[u])==0:
            continue
        while g[u]:
            v=g[u].pop()
            g[v].remove(u)
            t=(min(u,v),max(u,v))
            ans[d[t]]=curr
            curr+=1
    for i in ans:
        print(i)
ip()