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
def li():return [int(i) for i in input().rstrip('\n').split()]
def st():return input().rstrip('\n')
def val():return int(input().rstrip('\n'))
def li2():return [i for i in input().rstrip('\n')]
def li3():return [int(i) for i in input().rstrip('\n')]

from collections import *
n = val()
g = defaultdict(set)

l = []
ans = [-1 for i in range(n)]
camein = [set() for i in range(n + 10)]
if n == 2:
    print(0)
    exit()
elif n == 3:
    print(0,1)
    exit()
done = 1
curr = 0
for i in range(n - 1):
    a,b = li()
    g[a].add(b)
    g[b].add(a)
    if done:
        camein[a].add(i)
        camein[b].add(i)
        if len(camein[a]) == 3:
            for k in camein[a]:
                ans[k] = curr
                curr += 1
                if curr == 3:break
            done = 0
            break
        elif len(camein[b]) == 3:
            for k in camein[b]:
                ans[k] = curr
                curr += 1
                if curr == 3:break
            done = 0
            break
for i in range(n - 1):
    if ans[i] != -1:print(ans[i])
    else:
        print(curr)
        curr += 1