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:
#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=tf-8
#

"""
"""

from collections import defaultdict
from operator import itemgetter

import sys
input = sys.stdin.readline

def solve(n):
    n_edge = [0]*(n+1)
    edges = []
    for i in range(n-1):
        a, b = map(int,input().split())
        n_edge[a] += 1
        n_edge[b] += 1
        edges.append((a,b))
    if n <= 3:
        for j in range(0,n-1):
            print(j)
    else:
        x = list(enumerate(n_edge))[1:]
        y = list(filter(lambda i:i[1]==1,x))[:3]
        z = set(map(itemgetter(0),y))
        l = len(y)
        cnt1 = 0
        cnt2 = l
        for i in range(1,n):
            if cnt1 < l and (edges[i-1][0] in z or edges[i-1][1] in z):
                print(cnt1)
                cnt1+=1
            else:
                print(cnt2)
                cnt2+=1


def main():
    n = int(input())
    solve(n)


if __name__ == "__main__":
    main()