题目描述

In Yinxu, the archaeological site of the late capital of the Shang Dynasty, there are $N$ divination papers written in oracle bone script, numbered $1, 2, ..., N$. Some papers may cite other papers, but no paper can cite itself. Additionally, there are no circular citations, meaning it's not possible to see the following situation: $A_1$ cites $A_2$, $A_2$ cites $A_3$, ..., $A_{K-1}$ cites $A_K$, $A_K$ cites $A_1$ (where $2 \leq K \leq N$).

As per myth, a complete set of divination papers can predict the wars and peace of the next century, and it should have a complete citation chain, i.e., $A_1$ cites $A_2$, $A_2$ cites $A_3$, ..., $A_{N-1}$ cites $A_N$, without any papers missing. Please determine whether these $N$ divination papers constitute a complete set.

输入格式

The first line contains an integer $N$, represents the number of papers. Then $N$ lines follow, the $i^{th}$ of them represents the citations of the $i^{th}$ paper: the first integer $c_i$ represents the number of its citations, followed by $c_i$ integers $p_{i,1}, p_{i,2}, ..., p_{i,c_i}$ that represent the papers that it cites.

输出格式

A single integer, $1$ if they constitute a complete set of divination papers, or $0$ otherwise.

4
0
2 1 4
2 2 4
1 1

1

4
0
1 1
2 2 4
1 1

0

提示

Sample Explanation 1

In this sample, paper $3$ cites paper $2$, paper $2$ cites paper $4$, paper $4$ cites paper $1$. Thus, we find a complete citation chain, which makes them a complete set of divination papers.

Limits

• $2 \leq N \leq 100000$;
• $0 \leq c_i \leq N-1$ for all $i \leq N$;
• $0 \leq c_1 + c_2 + ... + c_N \leq 500000$;
• $1 \leq p_{i,j} \leq N$ for all $i \leq N$ and $j \leq c_i$.
• $p_{i,j} \neq i$ for all $i \leq N$ and $j \leq c_i$.