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 getInt(): return int(input())
def getVars(): return map(int, input().split())
def getList(): return list(map(int, input().split()))
def getStr(): return input().strip()
## -------------------------------

def foo(k, ii):
    global d, res3, res, num
    if k not in d:
        d[k] = []
    d[k].append(ii)
    if len(d[k]) == 3 and len(res3) == 0:
        res3 = d[k].copy()
        

n = getInt()
res3 = []

d = {}
num = n-2
for i in range(n-1):
    u, v = getVars()
    foo(u, i)
    foo(v, i)

num = n-2
num3 = 0
for i in range(n-1):
    if i in res3:
        print(num3)
        num3+=1
    else:
        print(num)
        num -= 1