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())

if n == 2:
    a, b = [int(i) for i in input().split()]
    print(0)
    exit(0)

r = [[] for i in range(n - 1)]
K = [0 for i in range(n)]
for i in range(n - 1):
    a, b = [int(i) for i in input().split()]
    r[i] = [a - 1, b - 1]
    K[a - 1] += 1
    K[b - 1] += 1

s = set()
for i in range(len(K)):
    if K[i] == 1:
        s.add(i)
        if len(s) > 3:
            break

k = 0
if len(s) <= 2:
    l = 2
    f = 2
else:
    l = 3
    f = 3
for a, b in r:
    if (a in s or b in s) and k < f:
        print(k)
        k += 1
    else:
        print(l)
        l += 1