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;input=sys.stdin.readline
N, = map(int, input().split())
G = [set() for _ in range(N+1)]
for i in range(N-1):
    a, b = map(int, input().split())
    G[a].add((b, i))
    G[b].add((a, i))
if N==2:
    print(0)
    sys.exit()
stack = [1]
vs = set([1])
d = [-1 for _ in range(N+1)]
cc = [0 for _ in range(N+1)]
while stack:
    v = stack.pop()
    for u, j in G[v]:
        if u in vs:
            continue
        d[u] = j
        cc[v] += 1
        vs.add(u)
        stack.append(u)
if cc[1] == 1:
    cc[1] = 0
    d[1] = G[1].pop()[1]
rs = [-1 for _ in range(N-1)]
k = 0
for i in range(1, N+1):
    if cc[i] == 0:
        rs[d[i]] = k
        k+=1
for i in range(N-1):
    if rs[i] == -1:
        rs[i] = k
        k += 1
print(*rs)