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
from sys import stdin, stdout
n = int(input())
edges = []
g = [[] for i in range(n)]
x = -1
for i in range(n - 1):
    u, v = map(int, sys.stdin.readline().split(' '))
    u -= 1
    v -= 1
    if (u > v):
        u, v = v, u
    g[u].append(v)
    g[v].append(u)
    if (len(g[u]) > 2):
        x = u
    if (len(g[v]) > 2):
        x = v
    edges.append((u, v))

ans = { }
if (x == -1):
    for i in range(n - 1):
        print(i)
else:
    i = 0
    for v in g[x]:
        if (v > x):
            ans[x, v] = i
        else:
            ans[v, x] = i
        i += 1
    for e in edges:
        if e in ans:
            print(ans[e])
        else:
            print(i)
            i += 1