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


n = int(input())
a = []
b = dict()
num = False
reader = (line.split() for line in sys.stdin)
for i in range(n - 1):
    a.append(next(reader))
for i in range(n - 1):
    if a[i][0] in b:
        b[a[i][0]] += 1
    else:
        b[a[i][0]] = 1
    if a[i][1] in b:
        b[a[i][1]] += 1
    else:
        b[a[i][1]] = 1
    if b[a[i][1]] == 3:
        num = a[i][1]
        break
    if b[a[i][0]] == 3:
        num = a[i][0]
        break
count = 0
count2 = 3
if not num:
    for i in range(n - 1):
        print(count)
        count += 1
else:
    for i in range(n - 1):
        if (num in a[i]) and (count < 3):
            print(count)
            count += 1
        else:
            print(count2)
            count2 += 1