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
def main():
    n = int(sys.stdin.readline())
    adj = [[] for i in range(n)]
    st = 0
    d = dict()
    for i in range(n-1):
        u,v = [int(j)-1 for j in sys.stdin.readline().split()]
        d[(u,v)] = "#" 
        adj[u].append(v)
        adj[v].append(u)
        if len(adj[u])>2:
            st = u
        elif len(adj[v])>2:
            st = v
    stack = [st]
    ct = 0
    visited = set()
    while(len(stack)>0):
        # print(stack)
        v = stack.pop()
        visited.add(v)
        # print(v)
        # break
        for nb in adj[v]:
            if nb not in visited:
                if (nb,v) in d:
                    d[(nb,v)] = str(ct)
                    ct+=1
                elif (v,nb) in d:
                    d[(v,nb)] = str(ct)
                    ct+=1
                stack.append(nb)
    sys.stdout.write("\n".join(list(d.values())))
main()