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())
t = []
yy = False
hh = 0
C = [0]*(n+1)
for i in range(n-1):
    a,b = map(int, input().split())
    t.append((a,b))
    C[a] += 1
    C[b] += 1
    if not yy:
        if C[a] > 2:
            hh = a
            yy = True
        if C[b] > 2:
            hh = b
            yy = True

if not yy:
    for i in range(0,n-1):
        print(i)
else:
    a1 = 0
    a2 = 3
    for i in range(n-1):
        if t[i][0] != hh and t[i][1] != hh:
            print(a2)
            a2 += 1
        else:
            print(a1)
            a1 += 1
            if a1>2:
                hh = -1