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
sys.setrecursionlimit(1000000)
input = sys.stdin.readline

n = int(input())
g = [[] for _ in range(n)]

for i in range(n-1):
    u, v = map(int, input().split())
    u, v = u-1, v-1
    g[u].append([v, i])
    g[v].append([u, i])

#print(g)
#print(len(g[1]))
ans = [-1]*(n-1)
k = 0
for i in range(n):
    if len(g[i]) >= 3:
        for u, ei in g[i]:
            ans[ei] = k
            k += 1
        break

for i in range(n-1):
    if ans[i] ==  -1:
        ans[i] = k
        k += 1

for i in range(n-1):
    print(ans[i])