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())

G = [[] for _ in range(n)]
edges = []

for edge in range(n-1):
    u,v = map(int, input().split())
    u-=1
    v-=1
    G[u].append((u,v))
    G[v].append((u,v))
    edges.append((u,v))

for node in range(n):
    if len(G[node]) >= 3:
        special = G[node][:3]
        out = []
        count = 3
        for edge in edges:
            if edge in special:
                out.append(str(special.index(edge)))
                continue
            out.append(str(count))
            count += 1
        print("\n".join(out))
        exit(0)

out = []
for i in range(n-1):
    out.append(str(i))
print("\n".join(out))