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
import collections
n = int(sys.stdin.readline())
adj = {}
res = []
for _ in range(n-1):
    u,v = map(int,sys.stdin.readline().split())
    res.append((min(u,v),max(u,v)))
    if adj.get(u) == None:
        adj[u] = [v]
    else:
        adj[u].append(v)
    if adj.get(v) == None:
        adj[v] = [u]
    else:
        adj[v].append(u)
        
maxx = 0
for j in adj:
    l = len(adj[j])
    if maxx<l:
        maxx = l
        root_node = j

visited = {}
queue = collections.deque([root_node]) 
visited[root_node] = 1
mex_val = 0
answer = {}
while len(queue)!=0:
    head = queue.popleft()
#     print(head)
    for ed in adj[head]:
        if visited.get(ed) == None:
            answer[(min(head,ed),max(head,ed))] = mex_val
            mex_val+=1
            visited[ed] = 1
            queue.append(ed)
for item in res:
    # print(answer[item])
    sys.stdout.write(str(answer[item]))
    sys.stdout.write("\n")