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:
from collections import *
from sys import stdin, stdout


class graph:
    # initialize graph
    def __init__(self, gdict=None):
        if gdict is None:
            gdict = defaultdict(list)
        self.gdict, self.edges, self.l, self.visit = gdict, defaultdict(int), defaultdict(int), defaultdict(int)

    # add edge
    def add_edge(self, node1, node2, w=None):
        self.gdict[node1].append(node2)
        self.gdict[node2].append(node1)
        # self.edges[(node1, node2)] = 1
        self.l[node1] += 1
        self.l[node2] += 1

    def bfs_util(self, i):
        self.visit, self.diam, c, flag = defaultdict(int), defaultdict(int), 0, 0
        queue, self.visit[i] = deque([i]), 1

        while queue:
            # dequeue parent vertix
            s = queue.popleft()

            # enqueue child vertices
            for i in self.gdict[s]:
                if self.visit[i] == 0:
                    queue.append(i)
                    self.visit[i] = 1
                    self.edges[s, i], self.edges[i, s] = all[-1], all[-1]
                    all.pop()
        #             self.diam[i] += self.diam[s] + 1
        # return max(self.diam, key=self.diam.get)


edges, n = [], int(input())
g = graph()

for i in range(n - 1):
    u, v = map(int, stdin.readline().split())
    g.add_edge(u, v)
    edges.append([u, v])

all, ans = [i for i in range(n - 1)][::-1], []
# print(all,max(g.l, key=g.l.get))
g.bfs_util(max(g.l, key=g.l.get))

for i, j in edges:
    ans.append(str(g.edges[i, j]))
    
stdout.write('\n'.join(ans))