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

readline = sys.stdin.readline

ns = lambda: readline().rstrip()
ni = lambda: int(readline().rstrip())
nm = lambda: map(int, readline().split())
nl = lambda: list(map(int, readline().split()))

def solve():
    n = ni()
    if n == 2:
        print(0)
        return
    edges = [tuple(nm()) for _ in range(n-1)]
    ans = [-1]*(n-1)
    G = [list() for _ in range(n)]
    for i, (u, v) in enumerate(edges):
        u -= 1; v -= 1
        G[u].append((i, v))
        G[v].append((i, u))
    c = 0
    for i in range(n):
        if len(G[i]) == 1:
            ans[G[i][0][0]] = c
            c += 1
    for i in range(n-1):
        if ans[i] < 0:
            ans[i] = c
            c += 1
    print(*ans, sep='\n')
    return

solve()

# T = ni()
# for _ in range(T):
#     solve()