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 io
import os

from collections import Counter, defaultdict, deque


def solve(N, edges):
    g = defaultdict(lambda: defaultdict(int))
    for i, (u, v) in enumerate(edges):
        g[u][v] = i
        g[v][u] = i
    maxDeg, maxNode = max((len(g[u]), u) for u in g.keys())

    if maxDeg <= 2:
        return "\n".join(map(str, range(N - 1)))
    else:
        out = [None for i in range(N - 1)]
        curr = 0
        for v, index in g[maxNode].items():
            out[index] = curr
            curr += 1
            if curr == 3:
                break

        for i in range(N - 1):
            if out[i] is None:
                out[i] = curr
                curr += 1

        return "\n".join(map(str, out))


if __name__ == "__main__":
    input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

    N, = [int(x) for x in input().split()]
    edges = [[int(x) for x in input().split()] for i in range(N - 1)]
    ans = solve(N, edges)
    print(ans)