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 sys
adj = {}
n = int(sys.stdin.readline())
temp = []
for _ in range(n-1):
    a,b = sys.stdin.readline().split()
    a = int(a); b=int(b)
    temp.append(tuple(sorted((a,b))))
    if a in adj:
        adj[a].append(b)
    else:
        adj[a] = [b]
    if b in adj:
        adj[b].append(a)
    else:
        adj[b] = [a]
m = 0
for i in adj.keys():
    if len(adj[i])>m:
        m = len(adj[i])
        root = i

mex = 0
ans = {}
for edge in adj[root]:
    ans[tuple(sorted((root,edge)))] = mex
    mex += 1
    
for i in temp:
    if i in ans:
        sys.stdout.write(str(ans[i]))
    else:
        sys.stdout.write(str(mex))
        mex += 1
    sys.stdout.write('\n')