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())
l = []
m = [0] * (n + 1)
chk = [0] * (n + 1)

for _ in range(n - 1):
    a, b = map(int, input().split())

    if a > b:
        a, b = b, a

    m[a] += 1
    m[b] += 1

    l.append([a, b, -1])

if n == 2:
    print(0)
else:
    for x in range(1, n + 1):
        if m[x] == 1:
            chk[x] = 1

    cnt = 0
    cnt2 = n -2

    for x in range(n - 1):
        if chk[l[x][0]] == 1 or chk[l[x][1]] == 1:
            l[x][2] = cnt
            cnt += 1
        else:
            l[x][2] = cnt2
            cnt2 -= 1

    for x in l:
        print(x[2])