You're given an sequence $$$a$$$ of size $$$n$$$.

Determine if there is a sequence $$$b$$$ that satisfies all the following conditions:

• $$$b$$$ is a subsequence of $$$a$$$;
• There's an index $$$i(1\leq i \leq n)$$$,if we note $$$c=\underbrace{[[a_1,...a_{i-1},a_{i+1},...,a_n],[a_1,...a_{i-1},a_{i+1},...,a_n],...,[a_1,...a_{i-1},a_{i+1},...,a_n]]}_{n\cdot (n-1)elements}$$$,$$$b$$$ is not a subsequence of $$$c$$$.

A subsequence of a given sequence is a sequence that can be derived from the given sequence by deleting some or no elements without changing the order of the remaining elements. For example,$$$[1,2]$$$ and $$$[1,1]$$$ are subsequences of $$$[1,2,1]$$$ but $$$[2,2]$$$ and $$$[3]$$$ are not.

For two positive integers $$$x,y$$$,define $$$con(x,y)$$$ as the number obtained by connecting the decimal representation of $$$x$$$ with $$$y$$$, where $$$x$$$ is on the left and $$$y$$$ is on the right.For example $$$con(20,23)=2023,con(2,33)=233$$$.

You're given two integers $$$n,k$$$.You can choose an array $$$a$$$ of positive integers of size $$$n$$$,which satisfies $$$\Sigma_{i=1}^{n}a_i=k$$$.

Define the score as the number of prime numbers among all $$$con(a_i, a_j)(1\leq i,j\leq n)$$$.Find the minimum score you can get.

You're given an string $$$s$$$ of size $$$n$$$ composed of lowercase letters.

Define $$$f(C)$$$ as the character obtained by shifting the character $$$C$$$ to the left.Formally,$$$f(a)=z,f(b)=a,...,f(z)=y$$$.

You can do the following operation any number of times:

• choose two different indexes $$$i,j(1 \leq i,j \leq n)$$$,then make $$$s_i:=f(s_i)$$$ and $$$s_j:=f(s_j)$$$;

Find the minimum number of operations to make all characters in $$$s$$$ to $$$a$$$.If you can not make all characters in $$$s$$$ to $$$a$$$,output $$$-1$$$ instead.

A snake queue can be formed as an $$$n \cdot n$$$ grid graph.

When someone enter this queue, he is in position $$$(1,1)$$$.

Assume someone is in $$$(i,j)$$$ currently(and $$$(i,j)$$$ is not the endpoint of the queue),one second later:

• If $$$i$$$ is odd and $$$j \neq n$$$,he'll move to $$$(i,j+1)$$$;
• If $$$i$$$ is odd and $$$j = n$$$,he'll move to $$$(i+1,j)$$$;
• If $$$i$$$ is even and $$$j \neq 1$$$,he'll move to $$$(i,j-1)$$$;
• If $$$i$$$ is even and $$$j = 1$$$,he'll move to $$$(i+1,j)$$$.

There're $$$n \cdot n$$$ people.The $$$i_{th}$$$ person has a number $$$a_i$$$ in hi hand.In the $$$j_{th}(1\leq j \leq n^2)$$$ second,the $$$j_{th}$$$ person will enter this queue.

For example,$$$n=3$$$ and $$$a=[11,22,33,44,55,66,77,88,99]$$$,the following images show the status of the snake queue at certain times:

The status in the $$$2_{nd},5_{th}$$$ and $$$8_{th}$$$ second,respectively.

You need to answer the $$$q$$$ queries.The $$$i_{th}$$$ query gives two integers $$$t_i,x_i$$$,which means you need to answer the sum of the numbers of all the people in the $$$x_{th}$$$ column in the $$$t_{th}$$$ second.

You're given a permutation $$$p$$$ of size $$$n$$$ and a piece of pseudocode:

    sum:=0
    for i:=1 to n 
        sort(1,i)        #sort p[1],p[2],...p[i] in ascending order
        for j:=1 to n
            if(j is odd) sum:=sum+p[j]
            else         sum:=sum-p[j]

Output the final value of the variable $$$sum$$$.

Since you are a good friend of Jaber and Eyad, they are asking for your help to solve this problem.

You are given a graph consisting of $$$n$$$ nodes, which initially has no edges. For each node $$$i$$$, there's a string $$$s_i$$$ of lowercase Latin letters written on it.

You have to process $$$q$$$ queries of two types:

• 1 u v : it means add an edge between node $$$u$$$ and node $$$v$$$.
• 2 u t : it means for node $$$u$$$ and string $$$t$$$, output the sum of $$$cnt_v$$$ over all nodes $$$v$$$ which belong to the same component as $$$u$$$,where $$$cnt_v$$$ is the number of times $$$s_v$$$ occurs in $$$t$$$ as a substring.