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 PYTHON):

Solution:
from sys import stdin, stdout
from itertools import repeat
def main():
    n = int(stdin.readline())
    dat = map(int, stdin.read().split(), repeat(10, 2 * n - 2))
    d = [0] * n
    p = [-1] * n
    for i in xrange(n - 1):
        x, y = dat[i*2] - 1, dat[i*2+1] - 1
        d[x] += 1
        d[y] += 1
        p[x] = p[y] = i
    c = 0
    a = [-1] * (n - 1)
    for i in xrange(n):
        if d[i] == 1 and a[p[i]] == -1:
            a[p[i]] = c
            c += 1
    for i in xrange(n - 1):
        if a[i] == -1:
            a[i] = c
            c += 1
    stdout.write('\n'.join(map(str, a)))
main()