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
sys.setrecursionlimit(10 ** 6)


############ ---- Input Functions ---- ############
def in_int():
    return (int(input()))


def in_list():
    return (list(map(int, input().split())))


def in_str():
    s = input()
    return (list(s[:len(s) - 1]))


def in_ints():
    return (map(int, input().split()))


n = in_int()


g = [[] for i in range(n+1)]
e = [-1]*(n-1)


vv = 0
mx = 0
for xx in range(n-1):
    u, v  = in_ints()

    g[u].append((v,xx))
    if len(g[u]) > mx:
        mx = len(g[u])
        vv = u

    g[v].append((u,xx))
    if len(g[v]) > mx:
        mx = len(g[v])
        vv = v


count  = 0

for v, i in g[vv]:
    if e[i] == -1:
        e[i] = count
        count +=1


for i in range(len(e)):
    if e[i] == -1:
        e[i] = count
        count += 1
    print(e[i])