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
import math

def get_array(): return list(map(int, sys.stdin.readline().strip().split()))
def read():  return int(input())
def reads(): return map(int, sys.stdin.readline().strip().split())
def input(): return sys.stdin.readline().strip() #strip() avoid reading '\n'

to = [0] * 102000
st = [0] * 102000
res = [0] * 102000
idx = [0] * 102000
#-- main --#

n = read()

for i in range(1, n):
    x, y = reads()
    to[x] += 1
    to[y] += 1
    idx[x] = i
    idx[y] = i
tot = 0
for i in range(1, n + 1):
    if to[i] == 1 and st[idx[i]] == 0:
        res[idx[i]] = tot
        st[idx[i]] = 1
        tot += 1
for i in range(1, n):
    if st[i] == 0:
        res[i]= tot
        tot += 1
for i in range(1, n):
    print(res[i], end = ' ')