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
 
def input():
    return sys.stdin.readline()
 
def iinput():
    return int(input())
 
def rinput():
    return input().split()
 
def rlinput():
    return [int(i) for i in input().split()]
 
def main():
    #q = rlinput() rinput() iinput() input()
    n = iinput()
    w = []
    q = [[] for i in range(n)]
    for i in range(n - 1):
        u, v = rlinput()
        q[u - 1].append(i)
        q[v - 1].append(i)   
    for i in range(n):
        if len(q[i]) == 1:
            w.append(i)
    if len(w) < 3:
        for i in range(n - 1):
            print(i)
    else:
        o = 3
        for i in range(n - 1):
            if i == q[w[0]][0]:
                print(0)
            elif i == q[w[1]][0]:
                print(1)
            elif i == q[w[2]][0]:
                print(2)
            else:
                print(o)
                o += 1
for i in range(1):
    main()