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 solve(n, queries):
    node = 0
    count = [0] * (n + 1)
    for u, v in queries:
        count[u] += 1
        count[v] += 1
        if count[u] == 3:
            node = u
        if count[v] == 3:
            node = v
    
    j = 0
    ans = [-1] * len(queries)
    for i, pair in enumerate(queries):
        if node in pair:
            ans[i] = j
            j += 1
    for i in range(len(queries)):
        if ans[i] != -1:
            continue
        ans[i] = j
        j += 1
    for i in ans:
        print(i)


def smain():
    inp = lambda: [int(x) for x in input().split()]
    n =  int(input())
    queries = [inp() for _ in range(n - 1)]
    solve(n, queries)


if __name__ == '__main__':
    smain()