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 PYTHON):

Solution:
from collections import Counter, defaultdict, deque
import bisect
from sys import stdin, stdout
from itertools import repeat
import math

# sys.stdin = open('input')

def inp():
    return map(int, raw_input().split())

def main():
        n = inp()[0]
        ans = [i for i in range(n-1)]
        G = defaultdict(list)
        for i in range(n-1):
            a, b = inp()
            a -= 1
            b -= 1
            G[a].append(i)
            G[b].append(i)
        need = []
        for i in range(n):
            if len(need) == 3:
                continue
            if len(G[i])==1:
                need.append(G[i][0])
        if len(need) == 3:
            # print need[0],ans[0], ans[need[0]]
            ans = [-1] * (n-1)
            ans[need[0]] = 0
            ans[need[1]] = 1
            ans[need[2]] = 2
            now = 3
            for i in range(n-1):
                if ans[i]==-1:
                    ans[i]=now
                    now+=1
        print '\n'.join(map(str, ans))

main()