$3.$ Bobby and Jack like to play a guessing game called "Guess the food." First Bobby thinks of a food. Then Jack has to ask a set of questions to figure out what food Bobby picked. Each question asks about some food's characteristic, and then Bobby answers "yes" or $"$no$."$

$```$

Jack: $"$Is the food crispy?"

Bobby: $"$No$"$

Jack: $"$Is the food sweet?"

Bobby: "Yes"

Jack: "Are there chocolate chips in the food?"

Bobby: "Yes"

Jack: $"$Is the food flat and round?"

Bobby: "Yes"

Jack: "Then I guess chocolate chip cookie."

Bobby: "Correct!"

$```$

The "viable set" is the set of all food items with characteristics consistent with Bobby's questions so far. Jack will keep asking questions until the viable set only has one food. At that point Jack makes his guess. In each question, Jack will pick a characteristic of the food in the viable set to ask about. He never asks the same characteristic twice.

Given all of the food and their characteristics Bobby and Jack know, what is the maximum number of "yes" answers before Jack can guess? Utilize a hashtable in your solution. You can use Java STL hashtable, book codes can be copied to write the hashtable, cite your sources. No other plagiarism allowed. Submit your Java files.

INPUT FORMAT

The first line of input contains the number of food, $\backslash ((2\backslash$leq N $\backslash$leq $1002\backslash$leq N $\backslash$leq $100)\backslash ).$ Each of the next $\backslash ($ N $\backslash )$ lines describes a food item. The line starts with the food name, then an integer $\backslash ($ K$(1\backslash$leq K $\backslash$leq $1001\backslash$leq K $\backslash$leq $100)\backslash ),$ then $\backslash ($ K $\backslash )$ characteristics of that food. Food names and characteristics are strings, size $20$ max. No two food items have exactly the same characteristics.

OUTPUT FORMAT

Output the maximum number of "yes" answers before game ends.

SAMPLE INPUT:

$4$

cookie $2$ sweet soft

pizza $5$ cheesy salty soft awesome saucy

chips $3$ cheesy salty crispy

ramen $2$ salty awesome

SAMPLE OUTPUT:

$3$

In this example, Jack can ask a maximum of $3$ "yes" questions, for example, to guess "pizza" or "chips"

in java programming, Please do not use duplicate code thank you for your help!