B - Counting Arrays /

問題文

1 から N までの番号がついた N 個の数列が与えられます。

制約

• 1 \leq N \leq 2 \times 10^5
• 1 \leq L_i \leq 2 \times 10^5 (1 \leq i \leq N)
• 0 \leq a_{i,j} \leq 10^{9} (1 \leq i \leq N, 1 \leq j \leq L_i)
• すべての数列の要素の個数の和、すなわち \sum_{i=1}^N L_i2 \times 10^5 を超えない。
• 入力はすべて整数である。

入力

N
L_1 a_{1,1} a_{1,2} \dots a_{1,L_1}
L_2 a_{2,1} a_{2,2} \dots a_{2,L_2}
\vdots
L_N a_{N,1} a_{N,2} \dots a_{N,L_N}


入力例 1

4
2 1 2
2 1 1
2 2 1
2 1 2


出力例 1

3


• 数列 1 : (1, 2)
• 数列 2 : (1, 1)
• 数列 3 : (2, 1)
• 数列 4 : (1, 2)

このうち数列 1 と数列 4 は同じ数列で、それ以外は互いに異なる数列なので全部で 3 種類の数列があります。

入力例 2

5
1 1
1 1
1 2
2 1 1
3 1 1 1


出力例 2

4


• 数列 1 : (1)
• 数列 2 : (1)
• 数列 3 : (2)
• 数列 4 : (1, 1)
• 数列 5 : (1, 1, 1)

入力例 3

1
1 1


出力例 3

1


Score : 200 points

Problem Statement

You are given N sequences numbered 1 to N.
Sequence i has a length of L_i and its j-th element (1 \leq j \leq L_i) is a_{i,j}.

Sequence i and Sequence j are considered the same when L_i = L_j and a_{i,k} = a_{j,k} for every k (1 \leq k \leq L_i).
How many different sequences are there among Sequence 1 through Sequence N?

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq L_i \leq 2 \times 10^5 (1 \leq i \leq N)
• 0 \leq a_{i,j} \leq 10^{9} (1 \leq i \leq N, 1 \leq j \leq L_i)
• The total number of elements in the sequences, \sum_{i=1}^N L_i, does not exceed 2 \times 10^5.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
L_1 a_{1,1} a_{1,2} \dots a_{1,L_1}
L_2 a_{2,1} a_{2,2} \dots a_{2,L_2}
\vdots
L_N a_{N,1} a_{N,2} \dots a_{N,L_N}


Output

Print the number of different sequences.

Sample Input 1

4
2 1 2
2 1 1
2 2 1
2 1 2


Sample Output 1

3


Sample Input 1 contains four sequences:

• Sequence 1 : (1, 2)
• Sequence 2 : (1, 1)
• Sequence 3 : (2, 1)
• Sequence 4 : (1, 2)

Except that Sequence 1 and Sequence 4 are the same, these sequences are pairwise different, so we have three different sequences.

Sample Input 2

5
1 1
1 1
1 2
2 1 1
3 1 1 1


Sample Output 2

4


Sample Input 2 contains five sequences:

• Sequence 1 : (1)
• Sequence 2 : (1)
• Sequence 3 : (2)
• Sequence 4 : (1, 1)
• Sequence 5 : (1, 1, 1)

Sample Input 3

1
1 1


Sample Output 3

1