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:
n = int(input())
adj = [ [] for _ in range(n) ]
edg = []
for i in range(0,n-1):
    V = list( map(int,input().split()) )
    u,v = V[0]-1,V[1]-1
    adj[u].append(v)
    adj[v].append(u)
    edg.append( (u,v) )
ans = []
for i in range(0,n-1):
    ans.append(-1)
cnt = 0
for i in range(0,n-1):
    if ( len(adj[ edg[i][0] ])==1 or len(adj[ edg[i][1] ])==1 ) and cnt<3 :
        ans[i] = cnt
        cnt += 1
for i in range(0,n-1):
    if ans[i]==-1:
        ans[i] = cnt
        cnt += 1
for i in range(0,n-1):
    print(ans[i])