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
def f():
    n = int(sys.stdin.readline())
    g = [list() for _ in range(n+1)]
    a=[-1]*(n)
    c = [0]*(n+1)
    s = 0
    for i in range(n-1):
        u,v = map(int,sys.stdin.readline().split())
        g[u].append(i+1)
        g[v].append(i+1)
        c[u]+= 1
        c[v]+=1
        if c[u]>=3:
            s = u
        if c[v]>=3:
            s = v
    g1(n,a,g,c,s)
def g1(n,a,g,c,s):
    if s==0:
        for i in range(n-1):
            print(i)
    else:
        for i in range(0,3):
            a[g[s][i]] = i
        v = 3
        for i in range(1,n):
            if a[i]==-1:
                a[i]=v
                v+=1
            print(a[i])
f()