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:
#author: riyan

if __name__ == '__main__':
    n = int(input())
    edges = []
    adj_vec = {}
    for i in range(n - 1):
        u, v = map(int, input().split())
        edges.append([(u, v), -1])
        if u not in adj_vec.keys():
            adj_vec[u] = []
        adj_vec[u].append(v)
        if v not in adj_vec.keys():
            adj_vec[v] = []
        adj_vec[v].append(u)

    bamboo = True
    for i in range(1, n + 1):
        if len(adj_vec[i]) >= 3:
            mn = i
            bamboo = False
            break
    
    if bamboo:
        for i in range(n - 1):
            print(i)
    else:
        cnt = 0
        for i in range(n - 1):
            u, v = edges[i][0]
            if u == mn or v == mn:
                edges[i][1] = cnt
                cnt += 1
        for i in range(n - 1):
            if edges[i][1] == -1:
                edges[i][1] = cnt
                cnt += 1
            print(edges[i][1])