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:
def main():
    n = int(input())
    order = []
    tree = {}
    for i in range(1,n+1):
        tree[i] = []

    edges = {}
    for i in range(n-1):
        u,v = map(int,input().split())
        tree[u].append(v)
        tree[v].append(u)
        order.append((u,v))
    
    found = False
    for i in tree.keys():
        if len(tree[i]) >= 3:
            found = True
            node = i
            break

    ans = []
    if not found:
        for i in range(n-1):
            ans.append(i)
    else:
        curr = n-2
        count = 0
        while order:
            u,v = order.pop(0)
            if count < 3:
                if u == node or v == node:
                    ans.append(count)
                    count += 1
                else:
                    ans.append(curr)
                    curr -= 1
            else:
                ans.append(curr)
                curr -= 1

    for i in ans:
        print(i)


main()