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 sys import stdin, gettrace

if not gettrace():
    def input():
        return next(stdin)[:-1]


# def input():
#    return stdin.buffer.readline()

def main():
    n = int(input())
    adj = [[] for _ in range(n)]
    for i in range(n-1):
        u,v = map(int, input().split())
        adj[u-1].append((v-1, i))
        adj[v-1].append((u-1, i))
    next = 0
    res = [-1]*(n-1)
    for u in range(n):
        if len(adj[u]) == 1 and res[adj[u][0][1]] == -1:
            res[adj[u][0][1]] = next
            next+=1
            if next == 3:
                break
    for i in range(n-1):
        if res[i] == -1:
            res[i] = next
            next+=1
    print('\n'.join(map(str,res)))




if __name__ == "__main__":
    main()