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:


class Node:
    def __init__(self, val):
        self.left = None
        self.right = None
        self.value = val

class Tree:
    def __init__(self, n):
        self.root = None
        self.size = n

def mex(u, v):
    if max(u) > max(v):
        return u
    return v

def main():

    n = int(input())
    v = dict()

    # пропускаем первый элемент
    ans = [-1]
    # tree = Tree(n)
    for i in range(1, n):
        v[i] = []
        ans.append(-1)
    
    for i in range(1, n):
        a, b = [int(v) for v in input().split()]
        
        if not a in v:
            v[a] = []
        v[a].append(i)

        if not b in v:
            v[b] = []
        v[b].append(i)
        # print(i)

    # print(ans)

    mx = (0,0)
    for i in range(1, n):
        # print(i, mx, (len(v[i]), i))
        mx = max(mx, (len(v[i]), i))
        # print(i, mx, (len(v[i]), i))

    cur = 0
    for i in v[mx[1]]:
        ans[i] = cur
        cur += 1

    # print(ans)

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


if __name__ == "__main__":
    main()