Division of Property#8772
Sema and Yura have baskets of apples, with a total of different types of apples. In the -th basket, there are c_i apples, and the type of the -th apple in the -th basket is denoted as a_{ij}.
They have had a disagreement and wish to divide the baskets such that:
Each person receives at least one basket.
No type of apple appears in both Sema's and Yura's baskets.
Your task is to help them divide the baskets accordingly.
The first line contains two integers and (2 \leq n \leq 10^5, 1 \leq m \leq 10^5) — representing the number of baskets and the number of apple types, respectively.
The following lines describe the baskets. Each basket's description consists of two lines. The first line contains a single integer c_i (1 \leq c_i \leq 2 \cdot 10^5), indicating the number of apples in the basket. The second line lists c_i integers a_{i1}, a_{i2}, , a_{ic_i} (1 \leq a_{ij} \leq m) — representing the types of apples in that basket.
It is guaranteed that the total sum of all c_i does not exceed 2 \cdot 10^5.
Print «YES» if it is possible to divide the baskets as required, or «NO» if it is not.
If the answer is «YES», also provide a second line with integers, either or . If the -th number is , the -th basket should be assigned to Sema; if , to Yura.
If there are multiple valid solutions, you may print any of them.
Example 1
Example 2