human
A graph G = (V, E) is a data structure where V is a finite set of vertices and E is a binary relation on V represented by a set of edges. Fig. 1 illustrates an example of a graph (or graphs).

Fig. 1

A free tree is a connnected, acyclic, undirected graph. A rooted tree is a free tree in which one of the vertices is distinguished from the others. A vertex of a rooted tree is called "node."

Your task is to write a program which reports the following information for each node u of a given rooted tree T:

* node ID of u
* parent of u
* depth of u
* node type (root, internal node or leaf)
* a list of chidlren of u


If the last edge on the path from the root r of a tree T to a node x is (p, x), then p is the parent of x, and x is a child of p. The root is the only node in T with no parent.

A node with no children is an external node or leaf. A nonleaf node is an internal node

The number of children of a node x in a rooted tree T is called the degree of x.

The length of the path from the root r to a node x is the depth of x in T.

Here, the given tree consists of n nodes and evey node has a unique ID from 0 to n-1.

Fig. 2 shows an example of rooted trees where ID of each node is indicated by a number in a circle (node). The example corresponds to the first sample input.

Fig. 2

Note

You can use a left-child, right-sibling representation to implement a tree which has the following data:

* the parent of u
* the leftmost child of u
* the immediate right sibling of u

Constraints

* 1 ≤ n ≤ 100000

Input

The first line of the input includes an integer n, the number of nodes of the tree.

In the next n lines, the information of each node u is given in the following format:

id k c1 c2 ... ck

where id is the node ID of u, k is the degree of u, c1 ... ck are node IDs of 1st, ... kth child of u. If the node does not have a child, the k is 0.

Output

Print the information of each node in the following format ordered by IDs:

node id: parent = p, depth = d, type, [c1...ck]

p is ID of its parent....
The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is Python program to print the information of each node in the following format ordered by IDs:
.

class Tree:
    def __init__(self,n):
        self.ver=[[] for _ in range(n)]
        self.par=[-1 for _ in range(n)]
    
    def unite(self,x,y):
        self.ver[x].append(y)
        self.ver[y].append(x)

        self.par[y]=x

    def getdepth(self,i):
        ret=0
        while True:
            if self.par[i]==-1:
                return ret
            else:
                i=self.par[i]
                ret+=1

        
N=int(input())
T=Tree(N)
for _ in range(N):
    i,m,*chi=map(int,input().split())
    for j in chi:
        T.unite(i,j)

# print(T.ver)
# print(T.par)

for i in range(N):
    ans=''
    ans+='node %i: '%i
    ans+='parent = %i, '%T.par[i]
    ans+='depth = %i, '%T.getdepth(i)

    kind=''
    if T.par[i]==-1:
        kind+='root'
    elif len(T.ver[i])==1:
        kind+='leaf'
    else:
        kind+='internal node'
    ans+=kind+', '
    ans+=str(list(v for v in T.ver[i] if v!=T.par[i]))
    print(ans)