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())

from collections import defaultdict
deg = defaultdict(int)
uvl = []
for _ in range(n-1):
    u,v = map(int,input().split())
    uvl.append((u-1,v-1))
    deg[u-1] += 1
    deg[v-1] += 1

nidx = 0

ansl = [-1 for i in range(n-1)]

for idx, (u,v) in enumerate(uvl):
    if deg[u] == 1 or deg[v] == 1:
        ansl[idx] = nidx
        nidx += 1

for i in range(n-1):
    if ansl[i] == -1:
        ansl[i] = nidx
        nidx += 1

for a in ansl:
    print(a)