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
n = int(input())
dg = 10**6
edge = [[] for i in range(n+1)]
p = []

for i in range(n-1):
    u,v = map(int,input().split())
    edge[u].append(v)
    edge[v].append(u)
    p.append(u*dg+v)

q = -1
for i in range(1,n+1):
    if len(edge[i]) >= 3:
        q = i
        break

if q == -1:
    for i in range(n-1):
        print(i)
else:
    X = 0
    mi = 3
    for e in p:
        a,b = e//dg,e%dg
        if q in (a,b):
            if X != 3:
                print(X)
                X += 1
            else:
                print(mi)
                mi += 1
        else:
            print(mi)
            mi += 1