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())
info = [list(map(int, input().split())) for i in range(n - 1)]

tree = [[] for i in range(n)]
memo = {}
for i in range(n - 1):
    a, b = info[i]
    a -= 1
    b -= 1
    if a > b:
        a, b = b, a
    tree[a].append(b)
    tree[b].append(a)
    memo[a * 1000000 + b] = i
ans = [-1] * (n - 1)
pos = 0
for i in range(n):
    if len(tree[i]) == 1:
        a, b = i, tree[i][0]
        if a > b:
            a, b = b, a
        ans[memo[a * 1000000 + b]] = pos
        pos += 1
for i in range(n - 1):
    if ans[i] == -1:
        ans[i] = pos
        pos += 1
if n == 2:
    print(0)
    exit()
for i in ans:
    print(i)