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 $$$a$$$ of $$$n$$$ integers $$$a_1, a_2, a_3, \ldots, a_n$$$.

You have to answer $$$q$$$ independent queries, each consisting of two integers $$$l$$$ and $$$r$$$.

- Consider the subarray $$$a[l:r]$$$ $$$=$$$ $$$[a_l, a_{l+1}, \ldots, a_r]$$$. You can apply the following operation to the subarray any number of times (possibly zero)-   Choose two integers $$$L$$$, $$$R$$$ such that $$$l \le L \le R \le r$$$ and $$$R - L + 1$$$ is odd.  Replace each element in the subarray from $$$L$$$ to $$$R$$$ with the XOR of the elements in the subarray $$$[L, R]$$$.
- The answer to the query is the minimum number of operations required to make all elements of the subarray $$$a[l:r]$$$ equal to $$$0$$$ or $$$-1$$$ if it is impossible to make all of them equal to $$$0$$$.

You can find more details about XOR operation here.

## Input Format
The first line contains two integers $$$n$$$ and $$$q$$$ $$$(1 \le n, q \le 2 \cdot 10^5)$$$  — the length of the array $$$a$$$ and the number of queries.

The next line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ $$$(0 \le a_i \lt 2^{30})$$$  — the elements of the array $$$a$$$.

The $$$i$$$-th of the next $$$q$$$ lines contains two integers $$$l_i$$$ and $$$r_i$$$ $$$(1 \le l_i \le r_i \le n)$$$  — the description of the $$$i$$$-th query.

## Output Format
For each query, output a single integer  — the answer to that query.

## Examples
```input
7 6
3 0 3 3 1 2 3
3 4
4 6
3 7
5 6
1 6
2 2
```
```output
-1
1
1
-1
2
0
```

## Note
In the first query, $$$l = 3, r = 4$$$, subarray = $$$[3, 3]$$$. We can apply operation only to the subarrays of length $$$1$$$, which won't change the array; hence it is impossible to make all elements equal to $$$0$$$.

In the second query, $$$l = 4, r = 6$$$, subarray = $$$[3, 1, 2]$$$. We can choose the whole subarray $$$(L = 4, R = 6)$$$ and replace all elements by their XOR $$$(3 \oplus 1 \oplus 2) = 0$$$, making the subarray $$$[0, 0, 0]$$$.

In the fifth query, $$$l = 1, r = 6$$$, subarray = $$$[3, 0, 3, 3, 1, 2]$$$. We can make the operations as follows:

1. Choose $$$L = 4, R = 6$$$, making the subarray $$$[3, 0, 3, 0, 0, 0]$$$.
2. Choose $$$L = 1, R = 5$$$, making the subarray $$$[0, 0, 0, 0, 0, 0]$$$.

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: 1.0 seconds
Memory limit: 256.0 MB

# Problem
For given integers $$$n$$$ and $$$m$$$, let's call a pair of arrays $$$a$$$ and $$$b$$$ of integers good, if they satisfy the following conditions:

- $$$a$$$ and $$$b$$$ have the same length, let their length be $$$k$$$.
- $$$k \ge 2$$$ and $$$a_1 = 0, a_k = n, b_1 = 0, b_k = m$$$.
- For each $$$1 < i \le k$$$ the following holds: $$$a_i \geq a_{i - 1}$$$, $$$b_i \geq b_{i - 1}$$$, and $$$a_i + b_i \neq a_{i - 1} + b_{i - 1}$$$.

Find the sum of $$$|a|$$$ over all good pairs of arrays $$$(a,b)$$$. Since the answer can be very large, output it modulo $$$10^9 + 7$$$.

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

The only line of each test case contains two integers $$$n$$$ and $$$m$$$ $$$(1 \leq n, m \leq 5 \cdot 10^6)$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$5 \cdot 10^6$$$ and the sum of $$$m$$$ over all test cases does not exceed $$$5 \cdot 10^6$$$.

## Output Format
For each test case, output a single integer  — the sum of $$$|a|$$$ over all good pairs of arrays $$$(a,b)$$$ modulo $$$10^9 + 7$$$.

## Examples
```input
4
1 1
1 2
2 2
100 100
```
```output
8
26
101
886336572
```

## Note
In the first testcase, the good pairs of arrays are

- $$$([0, 1], [0, 1])$$$, length = $$$2$$$.
- $$$([0, 1, 1], [0, 0, 1])$$$, length = $$$3$$$.
- $$$([0, 0, 1], [0, 1, 1])$$$, length = $$$3$$$.

Hence the sum of the lengths would be $$${2 + 3 + 3} = 8$$$.

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: 512.0 MB

# Problem
You are given an expression of the form $$$a{+}b$$$, where $$$a$$$ and $$$b$$$ are integers from $$$0$$$ to $$$9$$$. You have to evaluate it and print the result.

## Input Format
The first line contains one integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases.

Each test case consists of one line containing an expression of the form $$$a{+}b$$$ ($$$0 \le a, b \le 9$$$, both $$$a$$$ and $$$b$$$ are integers). The integers are not separated from the $$$+$$$ sign.

## Output Format
For each test case, print one integer — the result of the expression.

## Examples
```input
4
4+2
0+0
3+7
8+9
```
```output
6
0
10
17
```

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: 512.0 MB

# Problem
You have a matrix $$$2 \times 2$$$ filled with distinct integers. You want your matrix to become beautiful. The matrix is beautiful if the following two conditions are satisfied:

- in each row, the first element is smaller than the second element;
- in each column, the first element is smaller than the second element.

You can perform the following operation on the matrix any number of times: rotate it clockwise by $$$90$$$ degrees, so the top left element shifts to the top right cell, the top right element shifts to the bottom right cell, and so on:

Determine if it is possible to make the matrix beautiful by applying zero or more operations.

## Input Format
The first line contains one integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

Each test case consists of two lines. Each of those lines contains two integers — the elements of the corresponding row of the matrix. In each matrix, all four elements are distinct integers from $$$1$$$ to $$$100$$$.

## Output Format
For each test case, print YES if the matrix can become beautiful, or NO otherwise. You may print each letter in any case (YES, yes, Yes will all be recognized as positive answer, NO, no and nO will all be recognized as negative answer).

## Examples
```input
6
1 3
5 7
8 10
3 4
8 10
4 3
6 1
9 2
7 5
4 2
1 2
4 3
```
```output
YES
YES
NO
YES
YES
NO
```

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: 512.0 MB

# Problem
An array $$$a$$$ consisting of $$$k$$$ integers is strictly increasing if $$$a_1 < a_2 < \dots < a_k$$$. For example, the arrays $$$[1, 3, 5]$$$, $$$[1, 2, 3, 4]$$$, $$$[3, 5, 6]$$$ are strictly increasing; the arrays $$$[2, 2]$$$, $$$[3, 7, 5]$$$, $$$[7, 4, 3]$$$, $$$[1, 2, 2, 3]$$$ are not.

For a strictly increasing array $$$a$$$ of $$$k$$$ elements, let's denote the characteristic as the number of different elements in the array $$$[a_2 - a_1, a_3 - a_2, \dots, a_k - a_{k-1}]$$$. For example, the characteristic of the array $$$[1, 3, 4, 7, 8]$$$ is $$$3$$$ since the array $$$[2, 1, 3, 1]$$$ contains $$$3$$$ different elements: $$$2$$$, $$$1$$$ and $$$3$$$.

You are given two integers $$$k$$$ and $$$n$$$ ($$$k \le n$$$). Construct an increasing array of $$$k$$$ integers from $$$1$$$ to $$$n$$$ with maximum possible characteristic.

## Input Format
The first line contains one integer $$$t$$$ ($$$1 \le t \le 819$$$) — the number of test cases.

Each test case consists of one line containing two integers $$$k$$$ and $$$n$$$ ($$$2 \le k \le n \le 40$$$).

## Output Format
For each test case, print $$$k$$$ integers — the elements of the strictly increasing array $$$a$$$ with the maximum possible characteristic. If there are multiple answers, print any of them.

## Examples
```input
7
5 9
4 12
3 3
3 4
4 4
4 6
8 11
```
```output
1 3 4 7 8
2 4 7 12
1 2 3
1 3 4
1 2 3 4
2 4 5 6
1 2 3 5 6 7 8 11
```

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: 512.0 MB

# Problem
You are given an array $$$a$$$ consisting of $$$n$$$ integers. The array is sorted if $$$a_1 \le a_2 \le \dots \le a_n$$$.

You want to make the array $$$a$$$ sorted by applying the following operation exactly once:

- choose an integer $$$x$$$, then for every $$$i \in [1, n]$$$, replace $$$a_i$$$ by $$$|a_i - x|$$$.

Find any value of $$$x$$$ that will make the array sorted, or report that there is no such value.

## Input Format
The first line contains one integer $$$t$$$ ($$$1 \le t \le 2 \cdot 10^4$$$) — the number of test cases.

Each test case consists of two lines. The first line contains one integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$). The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^8$$$).

Additional constraint on the input: the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

## Output Format
For each test case, print any integer $$$x$$$ ($$$0 \le x \le 10^9$$$) that makes the array sorted. It can be shown that if such an integer $$$x$$$ exists, there is at least one such integer between $$$0$$$ and $$$10^9$$$.

If there is no such integer, then print $$$-1$$$. If there are multiple suitable values of $$$x$$$, print any of them.

## Examples
```input
8
5
5 3 3 3 5
4
5 3 4 5
8
1 2 3 4 5 6 7 8
6
10 5 4 3 2 1
3
3 3 1
3
42 43 42
2
100000000 99999999
6
29613295 52036613 75100585 78027446 81409090 73215
```
```output
4
-1
0
42
2
-1
100000000
40741153
```

## Note
In the first test case, after using $$$x = 4$$$, the array becomes $$$[1, 1, 1, 1, 1]$$$.

In the third test case, after using $$$x = 0$$$, the array becomes $$$[1, 2, 3, 4, 5, 6, 7, 8]$$$.

In the fourth test case, after using $$$x = 42$$$, the array becomes $$$[32, 37, 38, 39, 40, 41]$$$.

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
Beppa and her circle of geek friends keep up to date on a group chat in the instant messaging app SwerChat$$$^{\text{TM}}$$$.

The group has $$$n$$$ members, excluding Beppa. Each of those members has a unique ID between $$$1$$$ and $$$n$$$. When a user opens a group chat, SwerChat$$$^{\text{TM}}$$$ displays the list of other members of that group, sorted by decreasing times of last seen online (so the member who opened the chat most recently is the first of the list). However, the times of last seen are not displayed.

Today, Beppa has been busy all day: she has only opened the group chat twice, once at 9:00 and once at 22:00. Both times, she wrote down the list of members in the order they appeared at that time. Now she wonders: what is the minimum number of other members that must have been online at least once between 9:00 and 22:00?

Beppa is sure that no two members are ever online at the same time and no members are online when Beppa opens the group chat at 9:00 and 22:00.

## Input Format
Each test contains multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10\,000$$$) — the number of test cases. The descriptions of the $$$t$$$ test cases follow.

The first line of each test case contains an integer $$$n$$$ ($$$1 \leq n \leq 10^5$$$) — the number of members of the group excluding Beppa.

The second line contains $$$n$$$ integers $$$a_1, \, a_2, \, \dots, \, a_n$$$ ($$$1 \le a_i \le n$$$) — the list of IDs of the members, sorted by decreasing times of last seen online at 9:00.

The third line contains $$$n$$$ integers $$$b_1, \, b_2, \, \dots, \, b_n$$$ ($$$1 \le b_i \le n$$$) — the list of IDs of the members, sorted by decreasing times of last seen online at 22:00.

For all $$$1\le i < j\le n$$$, it is guaranteed that $$$a_i \ne a_j$$$ and $$$b_i \ne b_j$$$.

It is also guaranteed that the sum of the values of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

## Output Format
For each test case, print the minimum number of members that must have been online between 9:00 and 22:00.

## Examples
```input
4
5
1 4 2 5 3
4 5 1 2 3
6
1 2 3 4 5 6
1 2 3 4 5 6
8
8 2 4 7 1 6 5 3
5 6 1 4 8 2 7 3
1
1
1
```
```output
2
0
4
0
```

## Note
In the first test case, members $$$4, 5$$$ must have been online between 9:00 and 22:00.

In the second test case, it is possible that nobody has been online between 9:00 and 22:00.

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 at your grandparents' house and you are playing an old video game on a strange console. Your controller has only two buttons and each button has a number written on it.

Initially, your score is $$$0$$$. The game is composed of $$$n$$$ rounds. For each $$$1\le i\le n$$$, the $$$i$$$-th round works as follows.

On the screen, a symbol $$$s_i$$$ appears, which is either $$$\texttt{+}$$$ (plus) or $$$\texttt{-}$$$ (minus). Then you must press one of the two buttons on the controller once. Suppose you press a button with the number $$$x$$$ written on it: your score will increase by $$$x$$$ if the symbol was $$$\texttt{+}$$$ and will decrease by $$$x$$$ if the symbol was $$$\texttt{-}$$$. After you press the button, the round ends.

After you have played all $$$n$$$ rounds, you win if your score is $$$0$$$.

Over the years, your grandparents bought many different controllers, so you have $$$q$$$ of them. The two buttons on the $$$j$$$-th controller have the numbers $$$a_j$$$ and $$$b_j$$$ written on them. For each controller, you must compute whether you can win the game playing with that controller.

## Input Format
The first line contains a single integer $$$n$$$ ($$$1 \le n \le 2\cdot 10^5$$$) — the number of rounds.

The second line contains a string $$$s$$$ of length $$$n$$$ — where $$$s_i$$$ is the symbol that will appear on the screen in the $$$i$$$-th round. It is guaranteed that $$$s$$$ contains only the characters $$$\texttt{+}$$$ and $$$\texttt{-}$$$.

The third line contains an integer $$$q$$$ ($$$1 \le q \le 10^5$$$) — the number of controllers.

The following $$$q$$$ lines contain two integers $$$a_j$$$ and $$$b_j$$$ each ($$$1 \le a_j, b_j \le 10^9$$$) — the numbers on the buttons of controller $$$j$$$.

## Output Format
Output $$$q$$$ lines. On line $$$j$$$ print $$$\texttt{YES}$$$ if the game is winnable using controller $$$j$$$, otherwise print $$$\texttt{NO}$$$.

## Examples
```input
8
+-+---+-
5
2 1
10 3
7 9
10 10
5 3
```
```output
YES
NO
NO
NO
YES
```
-----
```input
6
+-++--
2
9 7
1 1
```
```output
YES
YES
```
-----
```input
20
+-----+--+--------+-
2
1000000000 99999997
250000000 1000000000
```
```output
NO
YES
```

## Note
In the first sample, one possible way to get score $$$0$$$ using the first controller is by pressing the button with numnber $$$1$$$ in rounds $$$1$$$, $$$2$$$, $$$4$$$, $$$5$$$, $$$6$$$ and $$$8$$$, and pressing the button with number $$$2$$$ in rounds $$$3$$$ and $$$7$$$. It is possible to show that there is no way to get a score of $$$0$$$ using the second controller.

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
The "Parmigiana di melanzane" is a typical Italian dish. Alessandro and Bianca have very different tastes when it comes to it: Alessandro loves to eat Parmigiana with seafood, but Bianca thinks it is an atrocity! To decide which ingredients to include in the dish they prepare, they play the following game.

There are $$$n$$$ possible ingredients, labeled from $$$1$$$ to $$$n$$$. The higher the label, the closer the ingredient is to being seafood. The ingredients are connected by $$$n - 1$$$ edges, in such a way as to form a tree. Alessandro and Bianca take turns, with Alessandro going first. They alternately choose a terminal ingredient $$$x$$$, that is an ingredient currently connected to at most one other ingredient, and remove it from the tree. If the terminal ingredient $$$x$$$ was chosen by Alessandro, it goes in the recipe; if it was chosen by Bianca, it is discarded.

The taste of the Parmigiana is measured as the maximum label of an ingredient in the recipe. Alessandro wants to maximize the taste, while Bianca wants to minimize the taste. If both play optimally, what is the taste of the Parmigiana?

## Input Format
The first line contains an integer $$$n$$$ ($$$2\le n \le 100\,000$$$) — the number of ingredients.

Each of the following $$$n-1$$$ lines contain two integers $$$u_i$$$ and $$$v_i$$$ ($$$1 \le u_i, v_i \le n$$$, $$$u_i \ne v_i$$$) — the ingredients that the $$$i$$$-th edge connects.

It is guaranteed that the edges form a tree (i.e., any pair of ingredients is connected by the edges, possibly indirectly).

## Output Format
Print the value of the taste if both Alessandro and Bianca play optimally.

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

## Note
In the first sample, Alessandro can choose terminal ingredient $$$4$$$ in the first turn. This ingredient is added to the recipe. Since $$$4$$$ is the maximum label of an ingredient, the taste is $$$4$$$ regardless of the choices that follow.

In the second sample, Bianca can make sure that neither ingredient $$$4$$$ nor $$$5$$$ are included in the recipe, in which case Alessandro can include $$$3$$$. Thus, the taste is $$$3$$$.

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: 5.0 seconds
Memory limit: 256.0 MB

# Problem
You are given a string $$$s$$$ with length $$$n-1$$$ whose characters are either $$$\texttt{<}$$$ or $$$\texttt{>}$$$.

Count the permutations $$$p_1, \, p_2, \, \dots, \, p_n$$$ of $$$1, \, 2, \, \dots, \, n$$$ such that, for all $$$i = 1, \, 2, \, \dots, \, n - 1$$$, if $$$s_i$$$ is $$$\texttt{<}$$$ then $$$p_i < p_{i+1}$$$ and if $$$s_i$$$ is $$$\texttt{>}$$$ then $$$p_i > p_{i+1}$$$.

Since this number can be very large, compute its logarithm in base $$$2$$$.

## Input Format
The first line contains a single integer $$$n$$$ ($$$2 \le n \le 100\,000$$$).

The second line contains a string $$$s$$$ of length $$$n-1$$$; each character of $$$s$$$ is either $$$\texttt{<}$$$ or $$$\texttt{>}$$$.

## Output Format
Print the logarithm in base $$$2$$$ of the number of permutations satisfying the constraints described in the statement.

Your answer is considered correct if its absolute or relative error does not exceed $$$10^{-6}$$$. Formally, let your answer be $$$x$$$ and let the correct answer be $$$y$$$. Your answer is accepted if and only if $$$\frac{|x - y|}{\max{(1, |y|)}} \le 10^{-6}$$$.

## Examples
```input
2
<
```
```output
0.0000000000
```
-----
```input
3
<>
```
```output
1.0000000000
```
-----
```input
5
><<<
```
```output
2.0000000000
```
-----
```input
10
<><<<<<>>
```
```output
9.8281364842
```

## Note
In the first sample, there is only one valid permutation, that is $$$[2, 1]$$$. Since $$$\log_2(1)=0$$$, the correct output is $$$0$$$.

In the second sample, there are $$$2$$$ valid permutations, that are $$$[3, 1, 2]$$$ and $$$[2, 1, 3]$$$. Since $$$\log_2(2)=1$$$, the correct output is $$$1$$$.

In the third sample, there are $$$4$$$ valid permutations, that are $$$[1, 5, 4, 3, 2]$$$, $$$[2, 5, 4, 3, 1]$$$, $$$[3, 5, 4, 2, 1]$$$, $$$[4, 5, 3, 2, 1]$$$. Since $$$\log_2(4)=2$$$, the correct output is $$$2$$$.

In the fourth sample, there are $$$909$$$ valid permutations. Notice that $$$\log_2(909)=9.828136484194\ldots$$$

Now solve the problem and return the code.