vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Natasha travels around Mars in the Mars rover. But suddenly it broke down, namely — the logical scheme inside it. The scheme is an undirected tree (connected acyclic graph) with a root in the vertex $1$, in which every leaf (excluding root) is an input, and all other vertices are logical elements, including the root, which is output. One bit is fed to each input. One bit is returned at the output.

There are four types of logical elements: AND ($2$ inputs), OR ($2$ inputs), XOR ($2$ inputs), NOT ($1$ input). Logical elements take values from their direct descendants (inputs) and return the result of the function they perform. Natasha knows the logical scheme of the Mars rover, as well as the fact that only one input is broken. In order to fix the Mars rover, she needs to change the value on this input.

For each input, determine what the output will be if Natasha changes this input.


-----Input-----

The first line contains a single integer $n$ ($2 \le n \le 10^6$) — the number of vertices in the graph (both inputs and elements).

The $i$-th of the next $n$ lines contains a description of $i$-th vertex: the first word "AND", "OR", "XOR", "NOT" or "IN" (means the input of the scheme) is the vertex type. If this vertex is "IN", then the value of this input follows ($0$ or $1$), otherwise follow the indices of input vertices of this element: "AND", "OR", "XOR" have $2$ inputs, whereas "NOT" has $1$ input. The vertices are numbered from one.

It is guaranteed that input data contains a correct logical scheme with an output produced by the vertex $1$.


-----Output-----

Print a string of characters '0' and '1' (without quotes) — answers to the problem for each input in the ascending order of their vertex indices.


-----Example-----
Input
10
AND 9 4
IN 1
IN 1
XOR 6 5
AND 3 7
IN 0
NOT 10
IN 1
IN 1
AND 2 8

Output
10110


-----Note-----

The original scheme from the example (before the input is changed):

[Image]

Green indicates bits '1', yellow indicates bits '0'.

If Natasha changes the input bit $2$ to $0$, then the output will be $1$.

If Natasha changes the input bit $3$ to $0$, then the output will be $0$.

If Natasha changes the input bit $6$ to $1$, then the output will be $1$.

If Natasha changes the input bit $8$ to $0$, then the output will be $1$.

If Natasha changes the input bit $9$ to $0$, then the output will be $0$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Range Minimum Query is a well-known problem: given an array of distinct integers with size $n=2^k$ and $m$ queries, find the minimum element on subsegment $[L_i,R_i]$.

One of the most efficient and famous solutions to this problem is a segment tree. A segment tree is a full binary tree with $2\cdot n-1$ nodes where the leaves contain the values of the original array and each non-leaf node contains the minimum value of its entire subtree.

Usually, a segment tree is represented as an array of integers with $2\cdot n-1$ elements. The left child of the $i^{\mbox{th}}$ node is in the $(2\cdot i+1)^{th}$ cell, and the right child is in the $(2\cdot i+2)^{th}$ cell. For example, $A=[1,1,3,1,2,3,4]$ represents the following segment tree where the first number in a node describes the array index, $\boldsymbol{i}$, in $\mbox{A}$ and the second number denotes the value stored at index $\boldsymbol{i}$ (which corresponds to the minimum value in that node's subtree):

You've just used $n$ distinct integers to construct your first segment tree and saved it as an array, $\mbox{A}$, of $2\cdot n-1$ values. Unfortunately, some evil guy came and either shuffled or altered the elements in your array. Can you use the altered data to restore the original array? If no, print NO on a new line; otherwise, print two lines where the first line contains the word YES and the second line contains $2\cdot n-1$ space-separated integers denoting the array's original values. If there are several possible original arrays, print the lexicographically smallest one.

Input Format

The first line contains a single integer, $n$, denoting the size of the array. 

The second line contains $2\cdot n-1$ space-separated integers denoting the shuffled values of the segment tree.

Constraints

$1\leq n\leq2^{18}$
$n$ is a power of two.
Each value in the segment tree is between $-10^9$ and $\mathbf{10^{9}}$.

Output Format

Print NO if this array could not be constructed by shuffling some segment tree. Otherwise, print YES on the first line, and $2\cdot n-1$ space-separated integers describing the respective values of the original array on the second line. If there are several possible answers, print the lexicographically smallest one.

Sample Input 0

4
3 1 3 1 2 4 1

Sample Output 0

YES
1 1 3 1 2 3 4 

Explanation 0 

This is the same segment tree shown in the Problem Statement above.

Sample Input 1

2
1 1 1

Sample Output 1

NO 

Explanation 1 

A segment tree with three nodes would consist of a root, a left child, and a right child. Because all three numbers in this array are the same and the leaves of the segment tree must be $n$ distinct integers, it's not possible to reconstruct the original array.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Polo the Penguin and Lucky Numbers

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Everybody knows that lucky numbers are positive integers that contain only lucky digits 4 and 7 in their decimal representation. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.

Polo the Penguin have two positive integers *l* and *r* (*l*<=&lt;<=*r*), both of them are lucky numbers. Moreover, their lengths (that is, the number of digits in the decimal representation without the leading zeroes) are equal to each other.

Let's assume that *n* is the number of distinct lucky numbers, each of them cannot be greater than *r* or less than *l*, and *a**i* is the *i*-th (in increasing order) number of them. Find *a*1·*a*2<=+<=*a*2·*a*3<=+<=...<=+<=*a**n*<=-<=1·*a**n*. As the answer can be rather large, print the remainder after dividing it by 1000000007 (109<=+<=7).

Input Specification:
The first line contains a positive integer *l*, and the second line contains a positive integer *r* (1<=≤<=*l*<=&lt;<=*r*<=≤<=10100000). The numbers are given without any leading zeroes.

It is guaranteed that the lengths of the given numbers are equal to each other and that both of them are lucky numbers.

Output Specification:
In the single line print a single integer — the answer to the problem modulo 1000000007 (109<=+<=7).

Demo Input:
['4\n7\n', '474\n777\n']

Demo Output:
['28\n', '2316330\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Palo Alto is an unusual city because it is an endless coordinate line. It is also known for the office of Lyft Level 5.

Lyft has become so popular so that it is now used by all $m$ taxi drivers in the city, who every day transport the rest of the city residents — $n$ riders.

Each resident (including taxi drivers) of Palo-Alto lives in its unique location (there is no such pair of residents that their coordinates are the same).

The Lyft system is very clever: when a rider calls a taxi, his call does not go to all taxi drivers, but only to the one that is the closest to that person. If there are multiple ones with the same distance, then to taxi driver with a smaller coordinate is selected.

But one morning the taxi drivers wondered: how many riders are there that would call the given taxi driver if they were the first to order a taxi on that day? In other words, you need to find for each taxi driver $i$ the number $a_{i}$ — the number of riders that would call the $i$-th taxi driver when all drivers and riders are at their home?

The taxi driver can neither transport himself nor other taxi drivers.


-----Input-----

The first line contains two integers $n$ and $m$ ($1 \le n,m \le 10^5$) — number of riders and taxi drivers.

The second line contains $n + m$ integers $x_1, x_2, \ldots, x_{n+m}$ ($1 \le x_1 < x_2 < \ldots < x_{n+m} \le 10^9$), where $x_i$ is the coordinate where the $i$-th resident lives. 

The third line contains $n + m$ integers $t_1, t_2, \ldots, t_{n+m}$ ($0 \le t_i \le 1$). If $t_i = 1$, then the $i$-th resident is a taxi driver, otherwise $t_i = 0$.

It is guaranteed that the number of $i$ such that $t_i = 1$ is equal to $m$.


-----Output-----

Print $m$ integers $a_1, a_2, \ldots, a_{m}$, where $a_i$ is the answer for the $i$-th taxi driver. The taxi driver has the number $i$ if among all the taxi drivers he lives in the $i$-th smallest coordinate (see examples for better understanding).


-----Examples-----
Input
3 1
1 2 3 10
0 0 1 0

Output
3 
Input
3 2
2 3 4 5 6
1 0 0 0 1

Output
2 1 
Input
1 4
2 4 6 10 15
1 1 1 1 0

Output
0 0 0 1 


-----Note-----

In the first example, we have only one taxi driver, which means an order from any of $n$ riders will go to him.

In the second example, the first taxi driver lives at the point with the coordinate $2$, and the second one lives at the point with the coordinate $6$. Obviously, the nearest taxi driver to the rider who lives on the $3$ coordinate is the first one, and to the rider who lives on the coordinate $5$ is the second one. The rider who lives on the $4$ coordinate has the same distance to the first and the second taxi drivers, but since the first taxi driver has a smaller coordinate, the call from this rider will go to the first taxi driver.

In the third example, we have one rider and the taxi driver nearest to him is the fourth one.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Red and Blue Balls

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
User ainta has a stack of *n* red and blue balls. He can apply a certain operation which changes the colors of the balls inside the stack.
 -  While the top ball inside the stack is red, pop the ball from the top of the stack. -  Then replace the blue ball on the top with a red ball. -  And finally push some blue balls to the stack until the stack has total of *n* balls inside. 
If there are no blue balls inside the stack, ainta can't apply this operation. Given the initial state of the stack, ainta wants to know the maximum number of operations he can repeatedly apply.

Input Specification:
The first line contains an integer *n* (1<=≤<=*n*<=≤<=50) — the number of balls inside the stack.

The second line contains a string *s* (|*s*|<==<=*n*) describing the initial state of the stack. The *i*-th character of the string *s* denotes the color of the *i*-th ball (we'll number the balls from top to bottom of the stack). If the character is "R", the color is red. If the character is "B", the color is blue.

Output Specification:
Print the maximum number of operations ainta can repeatedly apply.

Please, do not write the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Demo Input:
['3\nRBR\n', '4\nRBBR\n', '5\nRBBRR\n']

Demo Output:
['2\n', '6\n', '6\n']

Note:
The first example is depicted below.

The explanation how user ainta applies the first operation. He pops out one red ball, changes the color of the ball in the middle from blue to red, and pushes one blue ball.

The explanation how user ainta applies the second operation. He will not pop out red balls, he simply changes the color of the ball on the top from blue to red.

From now on, ainta can't apply any operation because there are no blue balls inside the stack. ainta applied two operations, so the answer is 2.

The second example is depicted below. The blue arrow denotes a single operation.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Takahashi has N cards. The i-th of these cards has an integer A_i written on it.
Takahashi will choose an integer K, and then repeat the following operation some number of times:
 - Choose exactly K cards such that the integers written on them are all different, and eat those cards. (The eaten cards disappear.)
For each K = 1,2, \ldots, N, find the maximum number of times Takahashi can do the operation.

-----Constraints-----
 -  1 \le N \le 3 \times 10^5 
 -  1 \le A_i \le N 
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N
A_1 A_2 \ldots A_N

-----Output-----
Print N integers.
The t-th (1 \le t \le N) of them should be the answer for the case K=t.

-----Sample Input-----
3
2 1 2

-----Sample Output-----
3
1
0

For K = 1, we can do the operation as follows:
 - Choose the first card to eat.
 - Choose the second card to eat.
 - Choose the third card to eat.
For K = 2, we can do the operation as follows:
 - Choose the first and second cards to eat.
For K = 3, we cannot do the operation at all. Note that we cannot choose the first and third cards at the same time.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
James has a tree with $n$ nodes $n-1$ edges where the $i^{{th}}$ edge has a length, $w_i$. He wants to play a game involving $n$ moves. During each move, he performs the following steps:

Randomly chooses some node $x_i$ from the tree. Each node has an equal probability of being chosen.
Calculates the distance from node $x_i$ to each node reachable from $x_i$ using one or more edges.
Deletes node $x_i$.

For example, the diagram below shows what happens when we choose a random node and delete it from the tree:

After $n$ moves, the tree is empty and the game ends.

James defines the magic number, $m$, as the sum of all numbers calculated in step $2$ of each move. Let $E_{m}$ be the expected value of $m$.

Give the tree's edges and their respective lengths, calculate and the print the value of $(E_m\times n!)\ \text{mod}\ (10^9+9)$. It is guaranteed that $E_m\times n!$ is an integer.

Note

Due to a bug in the system, you might see accepted verdict in this problem even if you don't pass all the test cases. Please ignore that verdict, only the score you get is important in the ranklist.

Input Format

The first line contains an integer, $n$, denoting the number of nodes. 

Each of the $n-1$ subsequent lines contains three space-separated integers describing the respective values of $u_i$, $v_i$, and $w_i$, meaning that there is an edge of length $w_i$ connecting nodes $u_i$ and $v_i$.  

Constraints

$1\leq n\leq5000$
$1\leq u_i,v_i\leq n$
$1\leq w_i\leq10^9$

Subtasks

For $30\%$ of the max score $n\leq10$
For ${60\%}$ of the max score $n\leq400$

Output Format

Print a single integer denoting the value of $(E_m\times n!)\ \text{mod}\ (10^9+9)$.

Sample Input
3
2 1 2
3 2 3

Sample Output
50

Explanation

Let $d(u,v)$ be the distance between node ${u}$ and node ${v}$. Here are the ${6}$ different variants:

$(x_1,x_2,x_3)=(1,2,3)$

$(x_1,x_2,x_3)=(2,1,3)$

$(x_1,x_2,x_3)=(1,3,2)$. $m=7+3+0=10$

$(x_1,x_2,x_3)=(2,3,1)$. $m=0+5+0=5$
$(x_1,x_2,x_3)=(3,1,2)$. $m=2+0+8=10$
$(x_1,x_2,x_3)=(3,2,1)$. $m=0+2+8=10$

The expected value of the magic number is $E_m=\frac{50}{6}$. We then print the value of $(E_m\times n!)\ \text{mod}\ (10^9+9)=(\frac{50}{6}\times3!)\ \text{mod}\ (10^9+9)=50$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Lukáš really likes orienteering, a sport that requires locating control points in rough terrain. To entertain the NWERC participants Lukáš wants to organize an orienteering race. However, it would be too harsh for the participants to be outdoors in this cold Swedish November weather, so he decided to jump on the new trend of indoor races, and set the race inside the B building of Linköping University.

Lukáš has already decided on the locations of the control points. He has also decided on the exact length of the race, so the only thing remaining is to decide in which order the control points should be visited such that the length of the total race is as he wishes. Because this is not always possible, he asks you to write a program to help him.

Note from the organizer: the NWERC indoorienteering race for this year has been cancelled since we neglected to apply for an orienteering permit in time from the university administration. (We still need you to solve the problem so that we can organize it for next year.)

-----Input-----
The input consists of:
 - one line with two integers $n$ ($2\leq n \leq 14$) and $L$ ($1 \leq L \leq 10^{15}$), the number of control points and the desired length of the race, respectively;
 - $n$ lines with $n$ integers each. The $j$th integer on the $i$th line, $d_{ij}$, denotes the distance between control point $i$ and $j$ ($1\leq d_{ij} \leq L$ for $i \not= j$, and $d_{ii} = 0$). For all $1 \leq i,j,k \leq N$ it is the case that $d_{ij} = d_{ji}$ and $d_{ij} \leq d_{ik} + d_{kj}$.

-----Output-----
Output one line with “possible” if it is possible to visit all control points once in some order and directly return to the first one such that the total distance is exactly $L$, and “impossible” otherwise.

-----Examples-----
Sample Input:
4 10
0 3 2 1
3 0 1 3
2 1 0 2
1 3 2 0
Sample Output:
possible

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Let $x_0, \ldots , x_{n-1}$ denote $n$ boolean variables (i.e., variables taking only values $0$ and $1$). A binary decision diagram (BDD) over these variables is a diagrammatic representation of a boolean function $f(x_0, \ldots , x_{n-1})$ as inputs.

A BDD is a rooted binary tree such that all internal vertices $v$ have precisely two children. The edges connecting an internal vertex $v$ with its children are labelled with a $0$ or $1$ (exactly one of each). Each leaf vertex is also labelled with a $0$ or $1$. We note that a BDD may consist of a single vertex, which is considered to be both the root and a leaf vertex.

Given input $(x_0, \ldots , x_{n-1})$, the boolean function represented by the BDD is evaluated as follows.
 - let $v$ be the root vertex
 - let $i \leftarrow 0$
 - while $v$ is not a leaf do
 - replace $v$ with the child vertex of $v$ by traversing the edge labelled $x_ i$
 - increase $i$ by $1$
 - output the label of leaf vertex $v$

Consider the function $f(x_0,x_1,x_2)$ represented by the BDD above. To evaluate $f(1,0,1)$, we start from the root, we descend along edges labelled $1$, $0$, and then $1$. We reach a leaf vertex labelled $1$, so $f(1,0,1) = 1$.

A BDD is minimal if there is no way to replace any subtree of an internal vertex of the BDD by a single leaf vertex to get a new BDD defining the same boolean function. The BDD depicted above is minimal. It is a fact that for each boolean function $f$, there is a unique minimal BDD that represents the boolean function.

In this problem, you are given an $n$-variable boolean function specified by a list of the $2^n$ different values the function should take for various inputs. Compute the number of vertices in the minimal BDD representing this function.

-----Input-----
The first line of input consists of a single integer $1 \leq n \leq 18$. Then one more line follows that contains $2^n$ values (either $0$ or $1$) describing an $n$-variable boolean function.

We think of these values as being indexed from $0$ to $2^n-1$. The $i$th such value represents $f(x_0, \ldots , x_{n-1})$ where $x_ j$ is the $j$th least-significant bit of the binary representation of $i$. In other words, $x_ j$ is the coefficient of $2^j$ in the binary expansion of $i$.

The third sample input below corresponds to the BDD depicted above.

-----Output-----
Output consists of a single integer $m$ that is the number of vertices in the unique minimal BDD representing the boolean function from the input.

-----Examples-----
Sample Input 1:
2
1 1 0 1
Sample Output 1:
5

Sample Input 2:
2
0 0 0 0
Sample Output 2:
1

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
An airline called Divided Airlines has recently made the news due to their tendency to overbook their flights rather aggressively. For some flights, they even resorted to dragging passengers out from the plane! This was of course not very popular, so they decided to “resolve” the issue by making the seating assignments very chaotic (airlines do like unnecessary complexity). 

A particular flights has $n$ passengers. The seats are divided into $r$ rows each containing $c$ seats. Every passenger $i$ is assigned to some particular seat located at row $a_ i$ and column $b_ i$. However, some passengers may be assigned to the same seat.

Of course, passengers are usually okay with sitting somewhere else than their assigned seat, but they may still want to be somewhat close to their original seat. Perhaps they want to be able to speak to their friends, or sit close to their overhead luggage. More specifically, passenger $i$ accepts sitting at most $s_ i$ rows away from the row on their ticket.

Due to budget reasons, you decided to travel on a Divided flight. As expected, all the passengers assigned to an overbooked seat started to fight with each other, moving around in complex ways and causing a long delay. You proposed a fair resolution: you will construct a seat assignment which takes into account how far the passengers accepts to sit from their assigned seats so that as many passengers as possible get a seat. Now, all that remains is to actually find this assignment.

-----Input-----
The input consists of:
 - one line with the integers $n$, $r$ and $c$ ($1 \le n, r, c \le 10^5$), the number of passengers, rows and columns in the flight.
 - $n$ lines with the integers $a_ i, b_ i$ and $s_ i$ ($1 \le a_ i \le r$, $1 \le b_ i \le c$, $0 \le s_ i \le r$). The $i$’th line has the assigned row $a_ i$ and column $b_ i$, and maximum distance $s_ i$ of the $i$’th passenger. The maximum distance is given in rows.

-----Output-----
Output the maximum number of passengers that can be assigned a seat in an optimal assignment.

-----Examples-----
Sample Input 1:
3 2 1
1 1 0
1 1 1
2 1 0
Sample Output 1:
2

Sample Input 2:
3 3 1
1 1 0
1 1 1
1 1 2
Sample Output 2:
3

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.