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:
if __name__ == "__main__":
    n = int(input())
    l = [0 for i in range(n+1)]
    deg3 = -1
    edges = []
    for i in range(n-1):
        u,v = map(int, input().split())
        edges.append([u,v])
        l[u]+=1
        l[v]+=1
        if deg3 == -1:
            if l[u] == 3:
                deg3 = u
            if l[v] == 3:
                deg3 = v
    #tree has a node with degree more than 2
    if deg3 != -1:
        nC = 3
        deg3C = 0
        for i in edges:
            u,v = i
            if (u == deg3 or v == deg3) and deg3C != 3:
                print(deg3C)
                deg3C+=1
            else:
                print(nC)
                nC+=1
    else:
        nC = 0
        for i in edges:
            print(nC)
            nC+=1