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:
import sys
import collections
input = sys.stdin.readline


def main():
    N = int(input())
    AB = [[int(x) for x in input().split()] for _ in range(N - 1)]
    V = [[] for j in range(N)]
    for i, (a, b) in enumerate(AB):
        V[a - 1].append([b - 1, i])
        V[b - 1].append([a - 1, i])


    f = False
    ans = [-1] * (N - 1)
    for v in V:
        if len(v) >= 3:
            f = True
            for i in range(3):
                ans[v[i][1]] = i
            break


    cnt = 0
    if f:
        cnt = 3

    for a in ans:
        if a == -1:
            print(cnt)
            cnt += 1
        else:
            print(a)




    

if __name__ == '__main__':
    main()