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:
def answer(nodeCount, edges) :
  labels = [-1] * len(edges)
  threeAboveConnectedNodeNumber = 0
  labelNumbers = [i for i in range(3, len(edges))]
  mins = [0, 1, 2]
  tree = [[] for _ in range(nodeCount+1)]
  for i in range(len(edges)) :
    u, v, li = edges[i]
    tree[u].append(li)
    if len(tree[u]) == 3 :
      for j in range(0, 3) :
        labels[tree[u][j]] = mins.pop()
      break
    tree[v].append(li)
    if len(tree[v]) == 3 :
      for j in range(0, 3) :
        labels[tree[v][j]] = mins.pop()
      break
  if len(mins) == 3 :
    labels = [i for i in range(len(edges))]
  else :
    for i in range(len(labels)) :
      if labels[i] == -1 :
        labels[i] = labelNumbers.pop()
  return "\n".join([str(i) for i in labels])

nodeCount = int(input())
edges = []
for i in range(nodeCount-1) :
  u, v = map(int, input().split())
  edges.append([u, v, i])
print(answer(nodeCount, edges))