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 math
import sys
from collections import defaultdict, Counter
from itertools import groupby

#input = sys.stdin.readline
rt = lambda: map(int, input().split())
ri = lambda: int(input())
rl = lambda: list(map(int, input().split()))


def main():
    n = ri()
    deg = [0] * n
    edges = []
    for _ in range(n-1):
        u, v = rt()
        edges.append((u-1, v-1))
        deg[u-1] += 1
        deg[v-1] += 1
    if max(deg) <= 2:
        print('\n'.join(map(str, range(n-1))))
    else:
        d3 = 0
        while deg[d3] < 3:
            d3 += 1

        all = set(range(n-1))
        res = [-1] * (n-1)

        # assign 0, 1, 2
        index = 0
        for val in range(3):
            while edges[index][0] != d3 and edges[index][1] != d3:
                index += 1
            res[index] = val
            index += 1
            all.remove(val)

        index = 0
        for val in all:
            while res[index] != -1:
                index += 1
            res[index] = val

        print('\n'.join(map(str, res)))






if __name__ == '__main__':
    main()