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 = int(input())
e = [tuple(map(int, input().split())) for _ in range(n - 1)]
g = [[] for _ in range(n + 1)]
for i, (u, v) in enumerate(e):
    g[u].append((v, i))
    g[v].append((u, i))
r = max((len(g[u]), u) for u in range(1, n + 1))[1]
ans = [0] * (n - 1)
nxt = 0
mk = [0] * (n + 1)
mk[r] = 1
q = [r]
while q:
    q2 = []
    for u in q:
        for v, i in g[u]:
            if mk[v]:
                continue
            ans[i] = nxt
            nxt += 1
            mk[v] = 1
            q2.append(v)
    q = q2
print(*ans, sep='\n')