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:
from collections import deque

import sys
input = sys.stdin.readline
n = int(input())
g = [[] for x in range(n)]
ed = {}
el = []
for ei in range(n-1):
    s, e = [int(x) for x in input().strip().split()]
    el.append((s, e))
    g[s-1].append(e-1)
    g[e-1].append(s-1)
nc = [0]*n
v = [0]*n
d = deque()
for node in range(n):
    nc[node] = len(g[node])
    if nc[node] == 1:
        d.append(node)
ce = 0
while d:
    nn = d.popleft()
    v[nn] = 1
    nc[nn] -= 1
    for ni in g[nn]:
        if not v[ni]:
            nc[ni] -= 1
            if nc[ni] == 1:
                d.append(ni)
            ed[(ni+1, nn+1)] = ce
            ed[(nn+1, ni+1)] = ce
            ce += 1
for eli in el:
    print(ed[eli])