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:
n = int(input())
tree = [[] for _ in range(n + 1)]
enum = dict()
for i in range(n - 1):
    u, v = map(int, input().split())
    tree[u].append(v)
    tree[v].append(u)
    enum[(u, v)] = enum[(v, u)] = i
found = False
ans = list(range(n - 1))
free = set(range(n - 1))
for start in range(1, n + 1):
    if len(tree[start]) > 2:
        fork = tree[start][:3]
        found = True
        ans[enum[(start, fork[2])]] = 0
        ans[enum[(start, fork[0])]] = 1
        ans[enum[(start, fork[1])]] = 2
        free.remove(enum[(start, fork[2])])
        free.remove(enum[(start, fork[0])])
        free.remove(enum[(start, fork[1])])
        break
if found:
    for i, w in zip(free, range(3, n - 1)):
        ans[i] = w
print(*ans, sep='\n')