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
input = sys.stdin.readline

n = int(input())
verts = [-1] * n
for e in range(n - 1):
    a, b = map(int, input().split())

    for v in (a-1, b-1):
        if verts[v] == -1:
            verts[v] = e
        else:
            verts[v] = -2

good = set()
for e in verts:
    if e > -1:
        good.add(e)

out = []
smol = 0
tol = 0

for e in range(n-1):
    if e in good:
        tol += 1

for e in range(n - 1):
    if e in good:
        out.append(smol)
        smol += 1
    else:
        out.append(tol)
        tol += 1
print('\n'.join(map(str,out)))