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():
    import sys
    input = sys.stdin.buffer.readline

    N = int(input())
    adj = [[] for _ in range(N+1)]
    E = {}
    for i in range(N-1):
        a, b = map(int, input().split())
        adj[a].append(b)
        adj[b].append(a)
        E[a*(N+1)+b] = i
        E[b*(N+1)+a] = i
    flg = 0
    ans = [-1] * (N-1)
    for v in range(1, N+1):
        if len(adj[v]) >= 3:
            for i, u in enumerate(adj[v][:3]):
                ans[E[u*(N+1)+v]] = i
            flg = 1
            break
    if flg:
        j = 3
        for i in range(N-1):
            if ans[i] == -1:
                ans[i] = j
                j += 1
    else:
        ans = list(range(N-1))
    print('\n'.join(map(str, ans)))



if __name__ == '__main__':
    main()