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:
def f():
    n = int(input())
    neibor = [0]*(n+1)
    orders = dict()
    for i in range(n-1):
        u, v = [int(s) for s in input().split()]
        if neibor[u] > 0:
            neibor[u] = n+1
        else:
            neibor[u] = v
        if neibor[v] > 0:
            neibor[v] = n+1
        else:
            neibor[v] = u
        orders[(u,v)] = i

    leaves = []
    for i in range(1,n+1):
        if neibor[i] <= n:
            leaves.append(i)
    if len(leaves)<=2:
        # one line
        for i in range(n-1):
            print(i)
        return
    # len(leaves) >=3
    ans = [-1]*(n-1)
    for i in range(3):
        u = leaves[i]
        v = neibor[u]
        if (u,v) in orders:
            ans[orders[(u,v)]] = i
        else:
            ans[orders[(v,u)]] = i
    i = 3
    for j in range(n-1):
        if ans[j] >= 0:
            continue
        ans[j] = i
        i += 1
    for a in ans:
        print(a)

f()