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 deque

q = deque()

p = 0
n = int(input())
color = [0 for i in range(n)]
mass = [[0] for i in range(n)]
for i in range(n - 1):
    x, y = map(int, input().split())
    mass[x - 1] += [[y - 1, i]]
    mass[y - 1] += [[x - 1, i]]
    mass[x - 1][0] += 1
    mass[y - 1][0] += 1
k = 0
m = []
f = 1
for i in range(n):
    if mass[i][0] == n - 1:
        for i in range(n - 1):
            print(i)
        exit()
    if mass[i][0] == 2:
        k += 1
    if mass[i][0] == 1:
        m += [mass[i][1][1]]
        if f == 1:
            p = i
        f = 0
if k == n - 2:
    for i in range(n - 1):
        print(i)
    exit()
if n == 2:
    print(0)
    print(1)
    exit()
res=[-1 for i in range (n-1)]
if len(m)>=3:
    res[m[0]]=0
    res[m[1]]=1
    res[m[2]]=2
j=3
for i in range (n-1):
    if res[i]==-1:
        print(j)
        j+=1
    else:
        print(res[i])