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())
 
G = [0]*n
V = []
for i in range(n-1):
    x,y = [int(x)-1 for x in input().split()]
    G[x] += 1
    G[y] += 1
    V.append((x,y))
 
good = -1
for i in range(n):
    if G[i] > 2:
        good = i
        break
if good == -1:
    for i in range(n-1):
        print(i)
else:
    deg = G[good]-1
    bad = 0
    for i in range(n-1):
        if good in V[i]:
            print(deg)
            deg -= 1
        else:
            print(G[good]+bad)
            bad += 1