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:
n = int(input())

graf = dict()
ucka = []
vcka = []


pocty = n * [0]
for i in range(n-1):
    [u, v] = [int(x) for x in input().split()]

    ucka.append(u)
    vcka.append(v)

    pocty[u-1] += 1
    pocty[v-1] += 1

hrana = None

if max(pocty)>2:
    for i in range(n):
        if pocty[i]>2:
            hrana = i+1
            break

spodne = 0
akt = 3

if hrana == None:
    for i in range(n-1):
        print(i)
else:
    for i in range(n-1):
        if (ucka[i] == hrana or vcka[i] == hrana) and spodne <3:
            print(spodne)
            spodne = spodne + 1
        else:
            print(akt)
            akt = akt+1