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 PYTHON):

Solution:
from sys import stdin, stdout

n = input()
inp = stdin.readlines()
out = [0 for i in xrange(n - 1)]

if n == 2:
    print 0
    exit()

if n == 3:
    print 0
    print 1
    exit()

g = [[] for i in xrange(n + 1)]
deg = [0 for i in xrange(n + 1)]

edges = []

cand = -1

for line in inp:
    u, v = map(int, line.strip().split())
    g[u].append(v)
    g[v].append(u)
    deg[u] += 1
    deg[v] += 1
    if u > v: u, v = v, u
    edges.append((u, v))

    if deg[u] >= 3: cand = u
    if deg[v] >= 3: cand = v

ans = [-1 for i in xrange(len(edges))]

if cand != -1:
    e = [(), (), ()]
    for i in xrange(3):
        v = g[cand][i]
        if cand > v: e[i] = (v, cand)
        else: e[i] = (cand, v)

    for i in xrange(len(edges)):
        if edges[i] == e[0]:
            ans[i] = 0
        if edges[i] == e[1]:
            ans[i] = 1
        if edges[i] == e[2]:
            ans[i] = 2

    cur = 3
    for i in xrange(len(ans)):
        if ans[i] == -1:
            ans[i] = cur
            cur += 1

    out = [str(num) for num in ans]
else:
    out = [str(i) for i in xrange(n - 1)]

stdout.write("\n".join(out))