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:
def listint():
    a = input().split()
    for i in range(len(a)):
        a[i] = int(a[i])-1
    return a

def main():
    n = int(input())
    graph = []
    for i in range(n-1):
        graph.append(listint())
    nodes = []
    for i in range(n):
        nodes.append(0)
    for i in range(n-1):
        nodes[graph[i][0]] = nodes[graph[i][0]] +1
        nodes[graph[i][1]] = nodes[graph[i][1]] +1
    ans = []
    for i in range(n-1):
        ans.append(-1)
    for i in range(n):
        if nodes[i] >= 3:
            p = 0
            for j in range(n-1):
                if graph[j][0] == i:
                    ans[j] = p
                    p = p+1
                if graph[j][1] == i:
                    ans[j] = p
                    p = p+1
            for j in range(n-1):
                if ans[j] == -1:
                    ans[j] = p
                    p = p+1
            return ans
    for i in range(n-1):
        ans[i] = i
    return ans
ans = main()
for i in range(len(ans)):
    print(ans[i])