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:
n = int(input())
a = [0]*n
pos = -1
c = []
for i in range(0, n-1):
    u, v = map(int, input().split())
    c.append([u, v])
for i in range(0, n-1):
    a[c[i][0]-1] += 1
    a[c[i][1]-1] += 1
    if a[c[i][0]-1] >= 3:
        pos = c[i][0]
        break
    if a[c[i][1]-1] >= 3:
        pos = c[i][1]
        break
ans = [-1]*(n-1)
count = 3
if pos != -1:
    for i in range(0, n-1):
        if c[i][0] == pos or c[i][1] == pos:
            ans[i] = (count-1)
            count -= 1
            if count == 0:
                break
count = 3
if pos == -1:
    count -= 3
for i in range(0, n-1):
    if ans[i] == -1:
        ans[i] = count
        count += 1
for i in range(0, n-1):
    print(ans[i])