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
import bisect
# import heapq
from math import ceil,floor,factorial

def c(a,b):
    return int((factorial(a))/((factorial(b)*factorial(a-b))))

RI = lambda : [int(x) for x in sys.stdin.readline().split()]
ri = lambda : sys.stdin.readline().strip()
mod = 10**9+7
# for _ in range(int(ri())):

n = int(ri())

ans = [0]*(n-1)
lis = [[] for i in range(n)]
index = [[] for i in range(n)]
for _ in range(n-1):
    a,b = RI()
    a-=1
    b-=1
    lis[a].append(b)
    lis[b].append(a)
    index[b].append(_)
    index[a].append(_)
pos = -1
for i in range(len(lis)):
    if len(lis[i]) >= 3  :
        pos = i
        break
flag = [-1] * (n-1)
ite  = 1
if pos != -1:
    for i in range(len(index[pos])):
        ans[index[pos][i]] = ite
        flag[index[pos][i]] = 1
        ite+=1
    for i in range(n):
        if pos != i :
            for j in range(len(lis[i])):
                if flag[index[i][j]] == -1:
                    ans[index[i][j]] = ite
                    ite+=1
                    flag[index[i][j]] = 1

else:
    for i in range(n):
        for j in range(len(lis[i])):
            if flag[index[i][j]] == -1:
                ans[index[i][j]] = ite
                ite+=1
                flag[index[i][j]] = 1

for i in range(len(ans)):
    print(ans[i]-1)