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 PYTHON):

Solution:
import sys

def findcross(sp) :
    l = [0 for i in sp]+[0, 0]
    fin = [0 for i in sp]
    nbgraal = 2
    graal = -1
    for j in sp :
        #print(j[0], j[1], l)
        l[int(j[0])] += 1
        l[int(j[1])] += 1
        if l[int(j[0])] >= 3 :
            graal = int(j[0])
            break
        if l[int(j[1])] >= 3 :
            graal = int(j[1])
            break
    #print(l)
    for k in range(len(l)) :
        if l[k] >= 3 :
            graal = k
    nbamettre = len(sp) - 1

    for k in range(len(sp)) :
        if((int(sp[k][0]) == graal or int(sp[k][1]) == graal) and nbgraal >= 0) :
            fin[k] = nbgraal
            nbgraal -= 1
        else :
            #print("hey",nbamettre)
            fin[k] = nbamettre
            nbamettre -= 1
    print("\n".join(map(str,fin)))

nbtest = sys.stdin.readline()
ligne = []
for i in range(int(nbtest) - 1) :
    ligne.append(sys.stdin.readline().rstrip().split(" "))
    #print(ligne)
findcross(ligne)