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:
# maa chudaaye duniya
n = int(input())
graph = [[] for i in range(n+1)]
taken = [False for i in range(n-1)]

xx = []
mp_unit = {}
mp = {}
for i in range(n-1):
    xg = input()
    xx.append(xg)
    a, b = map(int, xg.split())
    graph[a].append(b)
    graph[b].append(a)
    mp[xg] = 1

count = 0
ans = []
for i in range(1, n+1):
    if len(graph[i]) == 1:
        count += 1
if count <= 2:
    for i in range(n-1):
        ans.append(i)
else:
    for i in range(1, n+1):
        if len(graph[i]) == 1:
            branch = str(i) + ' ' + str(graph[i][0])
            b2 = str(graph[i][0]) + ' ' + str(i)
            if branch in mp:
                mp[branch] = 10**7
            else:
                mp[b2] = 10**7
    id = count
    im = 0
    for i in xx:
        if mp[i] != 10**7:
            ans.append(id)
            id += 1
        else:
            ans.append(im)
            im += 1
for i in ans:
    print(i)