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:
from collections import Counter
import sys

reader = (tuple(map(int, line.split())) for line in sys.stdin)

am = int(input())
bran = list()
for i in range(am - 1):
    bran.append(next(reader))

num_barn = enumerate(bran)


result = []
c = Counter()
for br in bran:
    c[br[0]] += 1
    c[br[1]] += 1
i = 0
best = c.most_common(1)[0]
if best[1] >= 3:
    for br in num_barn:
        if br[1][0] == best[0] or br[1][1] == best[0]:
            result.append((br[0], i))
            i += 1
            if len(result) >= 3:
                break
for j in range(0, am - 1):
    if len(result) != 0 and result[0][0] == j:

        print(result[0][1])
        # print(result)
        result.pop(0)
    else:
        print(i)
        i += 1