apaz/codeforces-genesys huggingface dataset:
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
You are given an array of $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$. The integers are either $$$1$$$ or $$$-1$$$. You have to perform the following operation exactly once on the array $$$a$$$:

- Choose an index $$$i$$$ ($$$1 \leq i < n$$$) and flip the signs of $$$a_i$$$ and $$$a_{i+1}$$$. Here, flipping the sign means $$$-1$$$ will be $$$1$$$ and $$$1$$$ will be $$$-1$$$.

What is the maximum possible value of $$$a_1 + a_2 + \ldots + a_n$$$ after applying the above operation?

## Input Format
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 500$$$). Description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 10^5$$$), the length of the array $$$a$$$.

The next line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$a_i = 1$$$ or $$$a_i = -1$$$).

The sum of $$$n$$$ over all cases doesn't exceed $$$10^5$$$.

## Output Format
For each test case, print the maximum possible sum of the array $$$a$$$ you can get in a separate line.

## Examples
```input
4
5
-1 1 1 -1 -1
5
1 1 -1 -1 -1
2
1 1
4
1 -1 -1 1
```
```output
3
3
-2
4
```

## Note
In the first case, we can choose index $$$4$$$ and flip the signs of $$$a_4$$$ and $$$a_5$$$. After this operation, the sum will be $$$-1+1+1+1+1 = 3$$$. We can't make the sum larger than this.

In the third case, the only option is to choose the index $$$1$$$.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
You are given two binary strings $$$a$$$ and $$$b$$$ of length $$$n$$$. In each move, the string $$$a$$$ is modified in the following way.

- An index $$$i$$$ ($$$1 \leq i \leq n$$$) is chosen uniformly at random. The character $$$a_i$$$ will be flipped. That is, if $$$a_i$$$ is $$$0$$$, it becomes $$$1$$$, and if $$$a_i$$$ is $$$1$$$, it becomes $$$0$$$.

What is the expected number of moves required to make both strings equal for the first time?

A binary string is a string, in which the character is either $$$\tt{0}$$$ or $$$\tt{1}$$$.

## Input Format
The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^5$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 10^6$$$) — the length of the strings.

The second line of each test case contains the binary string $$$a$$$ of length $$$n$$$.

The third line of each test case contains the binary string $$$b$$$ of length $$$n$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^6$$$.

## Output Format
For each test case, output a single line containing the expected number of moves modulo $$$998\,244\,353$$$.

Formally, let $$$M = 998\,244\,353$$$. It can be shown that the answer can be expressed as an irreducible fraction $$$\frac{p}{q}$$$, where $$$p$$$ and $$$q$$$ are integers and $$$q \not \equiv 0 \pmod{M}$$$. Output the integer equal to $$$p \cdot q^{-1} \bmod M$$$. In other words, output such an integer $$$x$$$ that $$$0 \le x < M$$$ and $$$x \cdot q \equiv p \pmod{M}$$$.

## Examples
```input
4
1
0
1
2
00
00
4
1000
1110
5
01001
10111
```
```output
1
0
665496254
665496277
```

## Note
In the first test case, index $$$1$$$ is chosen randomly and $$$a_1$$$ is flipped. After the move, the strings $$$a$$$ and $$$b$$$ are equal. The expected number of moves is $$$1$$$.

The strings $$$a$$$ and $$$b$$$ are already equal in the second test case. So, the expected number of moves is $$$0$$$.

The expected number of moves for the third and fourth test cases are $$$\frac{56}{3}$$$ and $$$\frac{125}{3}$$$ respectively.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Mocha likes arrays, and Serval gave her an array consisting of positive integers as a gift.

Mocha thinks that for an array of positive integers $$$a$$$, it is good iff the greatest common divisor of all the elements in $$$a$$$ is no more than its length. And for an array of at least $$$2$$$ positive integers, it is beautiful iff all of its prefixes whose length is no less than $$$2$$$ are good.

For example:

- $$$[3,6]$$$ is not good, because $$$\gcd(3,6)=3$$$ is greater than its length $$$2$$$.
- $$$[1,2,4]$$$ is both good and beautiful, because all of its prefixes whose length is no less than $$$2$$$, which are $$$[1,2]$$$ and $$$[1,2,4]$$$, are both good.
- $$$[3,6,1]$$$ is good but not beautiful, because $$$[3,6]$$$ is not good.

Now Mocha gives you the gift array $$$a$$$ of $$$n$$$ positive integers, and she wants to know whether array $$$a$$$ could become beautiful by reordering the elements in $$$a$$$. It is allowed to keep the array $$$a$$$ unchanged.

## Input Format
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1\leq t\leq 500$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2\leq n\leq 100$$$) — the length of array $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1\leq a_1,a_2,\ldots,a_n\leq 10^6$$$) — the elements of array $$$a$$$.

## Output Format
For each test case, print Yes if it is possible to reorder the elements in $$$a$$$ to make it beautiful, and print No if not.

You can output Yes and No in any case (for example, strings yEs, yes, Yes and YES will be recognized as a positive response).

## Examples
```input
6
2
3 6
3
1 2 4
3
3 6 1
3
15 35 21
4
35 10 35 14
5
1261 227821 143 4171 1941
```
```output
No
Yes
Yes
No
Yes
Yes
```

## Note
In the first test case, neither $$$[3,6]$$$ nor $$$[6,3]$$$ are beautiful, so it's impossible to obtain a beautiful array by reordering the elements in $$$a$$$.

In the second test case, $$$[1,2,4]$$$ is already beautiful. Keeping the array $$$a$$$ unchanged can obtain a beautiful array.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Serval has a string $$$s$$$ that only consists of 0 and 1 of length $$$n$$$. The $$$i$$$-th character of $$$s$$$ is denoted as $$$s_i$$$, where $$$1\leq i\leq n$$$.

Serval can perform the following operation called Inversion Magic on the string $$$s$$$:

- Choose an segment $$$[l, r]$$$ ($$$1\leq l\leq r\leq n$$$). For $$$l\leq i\leq r$$$, change $$$s_i$$$ into 1 if $$$s_i$$$ is 0, and change $$$s_i$$$ into 0 if $$$s_i$$$ is 1.

For example, let $$$s$$$ be 010100 and the segment $$$[2,5]$$$ is chosen. The string $$$s$$$ will be 001010 after performing the Inversion Magic.

Serval wants to make $$$s$$$ a palindrome after performing Inversion Magic exactly once. Help him to determine whether it is possible.

A string is a palindrome iff it reads the same backwards as forwards. For example, 010010 is a palindrome but 10111 is not.

## Input Format
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1\leq t\leq 10^4$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2\leq n\leq 10^5$$$) — the length of string $$$s$$$.

The second line of each test case contains a binary string $$$s$$$ of length $$$n$$$. Only characters 0 and 1 can appear in $$$s$$$.

It's guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.

## Output Format
For each test case, print Yes if $$$s$$$ can be a palindrome after performing Inversion Magic exactly once, and print No if not.

You can output Yes and No in any case (for example, strings yEs, yes, Yes and YES will be recognized as a positive response).

## Examples
```input
3
4
1001
5
10010
7
0111011
```
```output
Yes
Yes
No
```

## Note
In the first test case, Serval can perform Inversion Magic on the segment $$$[1,4]$$$. The string $$$s$$$ will be 0110 after the magic.

In the second test case, Serval can perform Inversion Magic on the segment $$$[1,3]$$$. The string $$$s$$$ will be 01110 after the magic.

In the third test case, Serval can't make $$$s$$$ a palindrome by performing Inversion Magic exactly once.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Serval loves Brain Power and his brain power problem.

Serval defines that a string $$$T$$$ is powerful iff $$$T$$$ can be obtained by concatenating some string $$$T'$$$ multiple times. Formally speaking, $$$T$$$ is powerful iff there exist a string $$$T'$$$ and an integer $$$k\geq 2$$$ such that $$$$$$T=\underbrace{T'+T'+\dots+T'}_{k\text{ times}}$$$$$$

For example, gogogo is powerful because it can be obtained by concatenating go three times, but power is not powerful.

Serval has a string $$$S$$$ consists of lowercase English letters. He is curious about the longest powerful subsequence of $$$S$$$, and he only needs you to find out the length of it. If all the non-empty subsequences of $$$S$$$ is not powerful, the answer is considered to be $$$0$$$.

A string $$$a$$$ is a subsequence of a string $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by the deletion of several (possibly, zero or all) characters.

## Input Format
The first line contains a single string $$$S$$$ ($$$|S|\leq 80$$$) consisting of lowercase English letters.

## Output Format
Print a single integer — the length of the longest powerful subsequence of $$$S$$$. If all the non-empty subsequences of $$$S$$$ is not powerful, print $$$0$$$.

## Examples
```input
buaa
```
```output
2
```
-----
```input
codeforcesround
```
```output
6
```
-----
```input
oooooooooooaaaaeaaiaujooooooooooooo
```
```output
24
```
-----
```input
zero
```
```output
0
```

## Note
For the first sample, all of the non-empty subsequences of buaa are listed below:

- b
- u
- a (occurred twice, buaa and buaa)
- bu
- ba (occurred twice, buaa and buaa)
- ua (occurred twice, buaa and buaa)
- aa
- bua (occurred twice, buaa and buaa )
- baa
- uaa
- buaa

Since $$$\texttt{aa} = \texttt{a} + \texttt{a}$$$, aa is a powerful subsequence. It can be shown that aa is the only powerful subsequence among them. So the answer is $$$2$$$.

For the second sample, the longest powerful subsequence is codcod from codeforcesround. So the answer is $$$6$$$.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Alperen is standing at the point $$$(0,0)$$$. He is given a string $$$s$$$ of length $$$n$$$ and performs $$$n$$$ moves. The $$$i$$$-th move is as follows:

- if $$$s_i = \texttt{L}$$$, then move one unit left;
- if $$$s_i = \texttt{R}$$$, then move one unit right;
- if $$$s_i = \texttt{U}$$$, then move one unit up;
- if $$$s_i = \texttt{D}$$$, then move one unit down.

If Alperen starts at the center point, he can make the four moves shown.

Alperen's path in the first test case.

## Input Format
The first line of the input contains an integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of testcases.

The first line of each test case contains an integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the length of the string.

The second line of each test case contains a string $$$s$$$ of length $$$n$$$ consisting of characters $$$\texttt{L}$$$, $$$\texttt{R}$$$, $$$\texttt{D}$$$, and $$$\texttt{U}$$$, denoting the moves Alperen makes.

## Output Format
For each test case, output "YES" (without quotes) if Alperen passes the candy, and "NO" (without quotes) otherwise.

You can output the answer in any case (for example, the strings "yEs", "yes", "Yes" and "YES" will be recognized as a positive answer).

## Examples
```input
7
7
UUURDDL
2
UR
8
RRRUUDDD
3
LLL
4
DUUR
5
RUDLL
11
LLLLDDRUDRD
```
```output
YES
YES
NO
NO
YES
YES
NO
```

## Note
In the first test case, Alperen follows the path $$$$$$(0,0) \overset{\texttt{U}}{\to} (0,1) \overset{\texttt{U}}{\to} (0,2) \overset{\texttt{U}}{\to} (0,3) \overset{\texttt{R}}{\to} (1,3) \overset{\texttt{D}}{\to} (1,2) \overset{\texttt{D}}{\to} \color{green}{\mathbf{(1,1)}} \overset{\texttt{L}}{\to} (0,1).$$$$$$ Note that Alperen doesn't need to end at the candy's location of $$$(1,1)$$$, he just needs to pass it at some point.

In the second test case, Alperen follows the path $$$$$$(0,0) \overset{\texttt{U}}{\to} (0,1) \overset{\texttt{R}}{\to} \color{green}{\mathbf{(1,1)}}.$$$$$$

In the third test case, Alperen follows the path $$$$$$(0,0) \overset{\texttt{R}}{\to} (1,0) \overset{\texttt{R}}{\to} (2,0) \overset{\texttt{R}}{\to} (3,0) \overset{\texttt{U}}{\to} (3,1) \overset{\texttt{U}}{\to} (3,2) \overset{\texttt{D}}{\to} (3,1) \overset{\texttt{D}}{\to} (3,0) \overset{\texttt{D}}{\to} (3,-1).$$$$$$

In the fourth test case, Alperen follows the path $$$$$$(0,0) \overset{\texttt{L}}{\to} (-1,0) \overset{\texttt{L}}{\to} (-2,0) \overset{\texttt{L}}{\to} (-3,0).$$$$$$

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Let's denote the $$$f(x)$$$ function for a string $$$x$$$ as the number of distinct characters that the string contains. For example $$$f(\texttt{abc}) = 3$$$, $$$f(\texttt{bbbbb}) = 1$$$, and $$$f(\texttt{babacaba}) = 3$$$.

Given a string $$$s$$$, split it into two non-empty strings $$$a$$$ and $$$b$$$ such that $$$f(a) + f(b)$$$ is the maximum possible. In other words, find the maximum possible value of $$$f(a) + f(b)$$$ such that $$$a + b = s$$$ (the concatenation of string $$$a$$$ and string $$$b$$$ is equal to string $$$s$$$).

## Input Format
The input consists of multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$2 \leq n \leq 2\cdot10^5$$$) — the length of the string $$$s$$$.

The second line contains the string $$$s$$$, consisting of lowercase English letters.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot10^5$$$.

## Output Format
For each test case, output a single integer  — the maximum possible value of $$$f(a) + f(b)$$$ such that $$$a + b = s$$$.

## Examples
```input
5
2
aa
7
abcabcd
5
aaaaa
10
paiumoment
4
aazz
```
```output
2
7
2
10
3
```

## Note
For the first test case, there is only one valid way to split $$$\texttt{aa}$$$ into two non-empty strings $$$\texttt{a}$$$ and $$$\texttt{a}$$$, and $$$f(\texttt{a}) + f(\texttt{a}) = 1 + 1 = 2$$$.

For the second test case, by splitting $$$\texttt{abcabcd}$$$ into $$$\texttt{abc}$$$ and $$$\texttt{abcd}$$$ we can get the answer of $$$f(\texttt{abc}) + f(\texttt{abcd}) = 3 + 4 = 7$$$ which is maximum possible.

For the third test case, it doesn't matter how we split the string, the answer will always be $$$2$$$.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Given an array $$$a_1, a_2, \dots, a_n$$$, you need to handle a total of $$$q$$$ updates and queries of two types:

- $$$1$$$ $$$l$$$ $$$r$$$ — for each index $$$i$$$ with $$$l \leq i \leq r$$$, update the value of $$$a_i$$$ to the sum of the digits of $$$a_i$$$.
- $$$2$$$ $$$x$$$ — output $$$a_x$$$.

## Input Format
The first line of the input contains an integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of testcases.

The first line of each test case contains two integers $$$n$$$ and $$$q$$$ ($$$1 \le n, q \le 2 \cdot 10^5$$$) — the size of the array and the number of queries, respectively.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$).

The next $$$q$$$ lines of each test case are of two forms:

- $$$1$$$ $$$l$$$ $$$r$$$ ($$$1 \leq l \leq r \leq n$$$) — it means, for each index $$$i$$$ with $$$l \leq i \leq r$$$, you should update the value of $$$a_i$$$ to the sum of its digits.
- $$$2$$$ $$$x$$$ ($$$1 \leq x \leq n$$$) — it means you should output $$$a_x$$$.

There is at least one query of the second type.

The sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

The sum of $$$q$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

## Output Format
For each test case, output the answers of queries of the second type, in the order they are given.

## Examples
```input
3
5 8
1 420 69 1434 2023
1 2 3
2 2
2 3
2 4
1 2 5
2 1
2 3
2 5
2 3
9999 1000
1 1 2
2 1
2 2
1 1
1
2 1
```
```output
6
15
1434
1
6
7
36
1
1
```

## Note
In the first test case, the following process occurs:

- Initially, $$$a = [1, 420, 69, 1434, 2023]$$$.
- The operation is performed for $$$l=2$$$, $$$r=3$$$, yielding $$$[1, \color{red}{6}, \color{red}{15}, 1434, 2023]$$$.
- We are queried for $$$x=2$$$, $$$x=3$$$, and $$$x=4$$$, and output $$$6$$$, $$$15$$$, and $$$1434$$$.
- The operation is performed for $$$l=2$$$, $$$r=5$$$, yielding $$$[1, \color{red}{6}, \color{red}{6}, \color{red}{12}, \color{red}{7}]$$$.
- We are queried for $$$x=1$$$, $$$x=3$$$, and $$$x=5$$$, and output $$$1$$$, $$$6$$$, and $$$7$$$.

Now solve the problem and return the code.
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
The only difference between the easy and hard versions are the locations you can teleport to.

Consider the points $$$0,1,\dots,n+1$$$ on the number line. There is a teleporter located on each of the points $$$1,2,\dots,n$$$. At point $$$i$$$, you can do the following:

- Move left one unit: it costs $$$1$$$ coin.
- Move right one unit: it costs $$$1$$$ coin.
- Use a teleporter at point $$$i$$$, if it exists: it costs $$$a_i$$$ coins. As a result, you can choose whether to teleport to point $$$0$$$ or point $$$n+1$$$. Once you use a teleporter, you can't use it again.

You have $$$c$$$ coins, and you start at point $$$0$$$. What's the most number of teleporters you can use?

## Input Format
The input consists of multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases. The descriptions of the test cases follow.

The first line of each test case contains two integers $$$n$$$ and $$$c$$$ ($$$1 \leq n \leq 2\cdot10^5$$$; $$$1 \leq c \leq 10^9$$$)  — the length of the array and the number of coins you have respectively.

The following line contains $$$n$$$ space-separated positive integers $$$a_1,a_2,\dots,a_n$$$ ($$$1 \leq a_i \leq 10^9$$$) — the costs to use the teleporters.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot10^5$$$.

## Output Format
For each test case, output the maximum number of teleporters you can use.

## Examples
```input
10
5 6
1 1 1 1 1
8 32
100 52 13 6 9 4 100 35
1 1
5
4 5
4 3 2 1
5 9
2 3 1 4 1
5 8
2 3 1 4 1
4 3
2 3 4 1
4 9
5 4 3 3
2 14
7 5
5 600000000
500000000 400000000 300000000 200000000 100000000
```
```output
2
3
0
1
3
2
1
1
2
2
```

## Note
In the first test case, you can move one unit to the right, use the teleporter at index $$$1$$$ and teleport to point $$$n+1$$$, move one unit to the left and use the teleporter at index $$$5$$$. You are left with $$$6-1-1-1-1 = 2$$$ coins, and wherever you teleport, you won't have enough coins to use another teleporter. You have used two teleporters, so the answer is two.

In the second test case, you go four units to the right and use the teleporter to go to $$$n+1$$$, then go three units left and use the teleporter at index $$$6$$$ to go to $$$n+1$$$, and finally, you go left four times and use the teleporter. The total cost will be $$$4+6+3+4+4+9 = 30$$$, and you used three teleporters.

In the third test case, you don't have enough coins to use any teleporter, so the answer is zero.

Now solve the problem and return the code.