meetforever/GRPO_CL huggingface dataset:
user: You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins.
 
Given n, find the total number of full staircase rows that can be formed.

n is a non-negative integer and fits within the range of a 32-bit signed integer.

Example 1:

n = 5

The coins can form the following rows:
¤
¤ ¤
¤ ¤

Because the 3rd row is incomplete, we return 2.



Example 2:

n = 8

The coins can form the following rows:
¤
¤ ¤
¤ ¤ ¤
¤ ¤

Because the 4th row is incomplete, we return 3.

Answer: {"fn_name": "arrangeCoins", "inputs": [[5]], "outputs": [2]}
user: Given a string s of zeros and ones, return the maximum score after splitting the string into two non-empty substrings (i.e. left substring and right substring).
The score after splitting a string is the number of zeros in the left substring plus the number of ones in the right substring.
 
Example 1:
Input: s = "011101"
Output: 5 
Explanation: 
All possible ways of splitting s into two non-empty substrings are:
left = "0" and right = "11101", score = 1 + 4 = 5 
left = "01" and right = "1101", score = 1 + 3 = 4 
left = "011" and right = "101", score = 1 + 2 = 3 
left = "0111" and right = "01", score = 1 + 1 = 2 
left = "01110" and right = "1", score = 2 + 1 = 3

Example 2:
Input: s = "00111"
Output: 5
Explanation: When left = "00" and right = "111", we get the maximum score = 2 + 3 = 5

Example 3:
Input: s = "1111"
Output: 3

 
Constraints:

2 <= s.length <= 500
The string s consists of characters '0' and '1' only.

Answer: {"fn_name": "maxScore", "inputs": [["\"011101\""]], "outputs": [5]}
user: Given a non-empty string s, you may delete at most one character.  Judge whether you can make it a palindrome.


Example 1:

Input: "aba"
Output: True



Example 2:

Input: "abca"
Output: True
Explanation: You could delete the character 'c'.



Note:

The string will only contain lowercase characters a-z.
The maximum length of the string is 50000.

Answer: {"fn_name": "validPalindrome", "inputs": [["\"aba\""]], "outputs": [true]}
user: Given an array of integers arr, a lucky integer is an integer which has a frequency in the array equal to its value.
Return a lucky integer in the array. If there are multiple lucky integers return the largest of them. If there is no lucky integer return -1.
 
Example 1:
Input: arr = [2,2,3,4]
Output: 2
Explanation: The only lucky number in the array is 2 because frequency[2] == 2.

Example 2:
Input: arr = [1,2,2,3,3,3]
Output: 3
Explanation: 1, 2 and 3 are all lucky numbers, return the largest of them.

Example 3:
Input: arr = [2,2,2,3,3]
Output: -1
Explanation: There are no lucky numbers in the array.

Example 4:
Input: arr = [5]
Output: -1

Example 5:
Input: arr = [7,7,7,7,7,7,7]
Output: 7

 
Constraints:

1 <= arr.length <= 500
1 <= arr[i] <= 500

Answer: {"fn_name": "findLucky", "inputs": [[[2, 2, 3, 4]]], "outputs": [2]}
user: A bus has n stops numbered from 0 to n - 1 that form a circle. We know the distance between all pairs of neighboring stops where distance[i] is the distance between the stops number i and (i + 1) % n.
The bus goes along both directions i.e. clockwise and counterclockwise.
Return the shortest distance between the given start and destination stops.
 
Example 1:

Input: distance = [1,2,3,4], start = 0, destination = 1
Output: 1
Explanation: Distance between 0 and 1 is 1 or 9, minimum is 1.
 
Example 2:

Input: distance = [1,2,3,4], start = 0, destination = 2
Output: 3
Explanation: Distance between 0 and 2 is 3 or 7, minimum is 3.

 
Example 3:

Input: distance = [1,2,3,4], start = 0, destination = 3
Output: 4
Explanation: Distance between 0 and 3 is 6 or 4, minimum is 4.

 
Constraints:

1 <= n <= 10^4
distance.length == n
0 <= start, destination < n
0 <= distance[i] <= 10^4

Answer: {"fn_name": "distanceBetweenBusStops", "inputs": [[[1, 2, 3, 4], 0, 1]], "outputs": [1]}
user: Given an integer n. Each number from 1 to n is grouped according to the sum of its digits. 
Return how many groups have the largest size.
 
Example 1:
Input: n = 13
Output: 4
Explanation: There are 9 groups in total, they are grouped according sum of its digits of numbers from 1 to 13:
[1,10], [2,11], [3,12], [4,13], [5], [6], [7], [8], [9]. There are 4 groups with largest size.

Example 2:
Input: n = 2
Output: 2
Explanation: There are 2 groups [1], [2] of size 1.

Example 3:
Input: n = 15
Output: 6

Example 4:
Input: n = 24
Output: 5

 
Constraints:

1 <= n <= 10^4

Answer: {"fn_name": "countLargestGroup", "inputs": [[13]], "outputs": [4]}
user: Given an array containing n distinct numbers taken from 0, 1, 2, ..., n, find the one that is missing from the array.

Example 1:


Input: [3,0,1]
Output: 2


Example 2:


Input: [9,6,4,2,3,5,7,0,1]
Output: 8


Note:
Your algorithm should run in linear runtime complexity. Could you implement it using only constant extra space complexity?

Answer: {"fn_name": "missingNumber", "inputs": [[[3, 0, 1]]], "outputs": [2]}
user: Given an array A of positive lengths, return the largest perimeter of a triangle with non-zero area, formed from 3 of these lengths.
If it is impossible to form any triangle of non-zero area, return 0.
 



Example 1:
Input: [2,1,2]
Output: 5


Example 2:
Input: [1,2,1]
Output: 0


Example 3:
Input: [3,2,3,4]
Output: 10


Example 4:
Input: [3,6,2,3]
Output: 8

 
Note:

3 <= A.length <= 10000
1 <= A[i] <= 10^6

Answer: {"fn_name": "largestPerimeter", "inputs": [[[1, 2, 2]]], "outputs": [5]}
user: Given an integer (signed 32 bits), write a function to check whether it is a power of 4.

Example:
Given num = 16, return true.
Given num = 5, return false.


Follow up: Could you solve it without loops/recursion?

Credits:Special thanks to @yukuairoy  for adding this problem and creating all test cases.

Answer: {"fn_name": "isPowerOfFour", "inputs": [[16]], "outputs": [true]}
user: An array is monotonic if it is either monotone increasing or monotone decreasing.
An array A is monotone increasing if for all i <= j, A[i] <= A[j].  An array A is monotone decreasing if for all i <= j, A[i] >= A[j].
Return true if and only if the given array A is monotonic.
 



Example 1:
Input: [1,2,2,3]
Output: true


Example 2:
Input: [6,5,4,4]
Output: true


Example 3:
Input: [1,3,2]
Output: false


Example 4:
Input: [1,2,4,5]
Output: true


Example 5:
Input: [1,1,1]
Output: true

 
Note:

1 <= A.length <= 50000
-100000 <= A[i] <= 100000

Answer: {"fn_name": "isMonotonic", "inputs": [[[1, 2, 2, 3]]], "outputs": [true]}
user: Given a string S, return the "reversed" string where all characters that are not a letter stay in the same place, and all letters reverse their positions.
 









Example 1:
Input: "ab-cd"
Output: "dc-ba"


Example 2:
Input: "a-bC-dEf-ghIj"
Output: "j-Ih-gfE-dCba"


Example 3:
Input: "Test1ng-Leet=code-Q!"
Output: "Qedo1ct-eeLg=ntse-T!"

 

Note:

S.length <= 100
33 <= S[i].ASCIIcode <= 122 
S doesn't contain \ or "

Answer: {"fn_name": "reverseOnlyLetters", "inputs": [["\"ab-cd\""]], "outputs": ["\"dc-ba\""]}
user: On a N * N grid, we place some 1 * 1 * 1 cubes that are axis-aligned with the x, y, and z axes.
Each value v = grid[i][j] represents a tower of v cubes placed on top of grid cell (i, j).
Now we view the projection of these cubes onto the xy, yz, and zx planes.
A projection is like a shadow, that maps our 3 dimensional figure to a 2 dimensional plane. 
Here, we are viewing the "shadow" when looking at the cubes from the top, the front, and the side.
Return the total area of all three projections.
 







































Example 1:
Input: [[2]]
Output: 5


Example 2:
Input: [[1,2],[3,4]]
Output: 17
Explanation: 
Here are the three projections ("shadows") of the shape made with each axis-aligned plane.



Example 3:
Input: [[1,0],[0,2]]
Output: 8


Example 4:
Input: [[1,1,1],[1,0,1],[1,1,1]]
Output: 14


Example 5:
Input: [[2,2,2],[2,1,2],[2,2,2]]
Output: 21

 



Note:

1 <= grid.length = grid[0].length <= 50
0 <= grid[i][j] <= 50

Answer: {"fn_name": "projectionArea", "inputs": [[[[2], [], []]]], "outputs": [5]}
user: On an 8 x 8 chessboard, there is one white rook.  There also may be empty squares, white bishops, and black pawns.  These are given as characters 'R', '.', 'B', and 'p' respectively. Uppercase characters represent white pieces, and lowercase characters represent black pieces.
The rook moves as in the rules of Chess: it chooses one of four cardinal directions (north, east, west, and south), then moves in that direction until it chooses to stop, reaches the edge of the board, or captures an opposite colored pawn by moving to the same square it occupies.  Also, rooks cannot move into the same square as other friendly bishops.
Return the number of pawns the rook can capture in one move.
 
Example 1:

Input: [[".",".",".",".",".",".",".","."],[".",".",".","p",".",".",".","."],[".",".",".","R",".",".",".","p"],[".",".",".",".",".",".",".","."],[".",".",".",".",".",".",".","."],[".",".",".","p",".",".",".","."],[".",".",".",".",".",".",".","."],[".",".",".",".",".",".",".","."]]
Output: 3
Explanation: 
In this example the rook is able to capture all the pawns.

Example 2:

Input: [[".",".",".",".",".",".",".","."],[".","p","p","p","p","p",".","."],[".","p","p","B","p","p",".","."],[".","p","B","R","B","p",".","."],[".","p","p","B","p","p",".","."],[".","p","p","p","p","p",".","."],[".",".",".",".",".",".",".","."],[".",".",".",".",".",".",".","."]]
Output: 0
Explanation: 
Bishops are blocking the rook to capture any pawn.

Example 3:

Input: [[".",".",".",".",".",".",".","."],[".",".",".","p",".",".",".","."],[".",".",".","p",".",".",".","."],["p","p",".","R",".","p","B","."],[".",".",".",".",".",".",".","."],[".",".",".","B",".",".",".","."],[".",".",".","p",".",".",".","."],[".",".",".",".",".",".",".","."]]
Output: 3
Explanation: 
The rook can capture the pawns at positions b5, d6 and f5.

 
Note:

board.length == board[i].length == 8
board[i][j] is either 'R', '.', 'B', or 'p'
There is exactly one cell with board[i][j] == 'R'

Answer: {"fn_name": "numRookCaptures", "inputs": [[[["\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\".\""], ["\".\"", "\".\"", "\".\"", "\"p\"", "\".\"", "\".\"", "\".\"", "\".\""], ["\".\"", "\".\"", "\".\"", "\"R\"", "\".\"\n", "\".\"", "\".\"", "\"p\""], ["\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\".\""], ["\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\".\""], ["\".\"", "\".\"\n", "\".\"", "\"p\"", "\".\"", "\".\"", "\".\"", "\".\""], ["\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\".\""], ["\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\".\"", "\"\n.\""], [], []]]], "outputs": [0]}
user: Given an array of integers nums.
A pair (i,j) is called good if nums[i] == nums[j] and i < j.
Return the number of good pairs.
 
Example 1:
Input: nums = [1,2,3,1,1,3]
Output: 4
Explanation: There are 4 good pairs (0,3), (0,4), (3,4), (2,5) 0-indexed.

Example 2:
Input: nums = [1,1,1,1]
Output: 6
Explanation: Each pair in the array are good.

Example 3:
Input: nums = [1,2,3]
Output: 0

 
Constraints:

1 <= nums.length <= 100
1 <= nums[i] <= 100

Answer: {"fn_name": "numIdenticalPairs", "inputs": [[[1, 2, 3, 1, 1, 3]]], "outputs": [4]}
user: Given a m * n matrix grid which is sorted in non-increasing order both row-wise and column-wise. 
Return the number of negative numbers in grid.
 
Example 1:
Input: grid = [[4,3,2,-1],[3,2,1,-1],[1,1,-1,-2],[-1,-1,-2,-3]]
Output: 8
Explanation: There are 8 negatives number in the matrix.

Example 2:
Input: grid = [[3,2],[1,0]]
Output: 0

Example 3:
Input: grid = [[1,-1],[-1,-1]]
Output: 3

Example 4:
Input: grid = [[-1]]
Output: 1

 
Constraints:

m == grid.length
n == grid[i].length
1 <= m, n <= 100
-100 <= grid[i][j] <= 100

Answer: {"fn_name": "countNegatives", "inputs": [[[[4, 3, 2, -1], [3, 2, 1, -1], [1, 1, -1, -2], [-1, -1, -2, -3], [], []]]], "outputs": [8]}
user: Write a program to check whether a given number is an ugly number.

Ugly numbers are positive numbers whose prime factors only include 2, 3, 5.

Example 1:


Input: 6
Output: true
Explanation: 6 = 2 × 3

Example 2:


Input: 8
Output: true
Explanation: 8 = 2 × 2 × 2


Example 3:


Input: 14
Output: false 
Explanation: 14 is not ugly since it includes another prime factor 7.


Note:


       1 is typically treated as an ugly number.
       Input is within the 32-bit signed integer range: [−231,  231 − 1].

Answer: {"fn_name": "isUgly", "inputs": [[6]], "outputs": [true]}
user: You are given a string text of words that are placed among some number of spaces. Each word consists of one or more lowercase English letters and are separated by at least one space. It's guaranteed that text contains at least one word.
Rearrange the spaces so that there is an equal number of spaces between every pair of adjacent words and that number is maximized. If you cannot redistribute all the spaces equally, place the extra spaces at the end, meaning the returned string should be the same length as text.
Return the string after rearranging the spaces.
 
Example 1:
Input: text = "  this   is  a sentence "
Output: "this   is   a   sentence"
Explanation: There are a total of 9 spaces and 4 words. We can evenly divide the 9 spaces between the words: 9 / (4-1) = 3 spaces.

Example 2:
Input: text = " practice   makes   perfect"
Output: "practice   makes   perfect "
Explanation: There are a total of 7 spaces and 3 words. 7 / (3-1) = 3 spaces plus 1 extra space. We place this extra space at the end of the string.

Example 3:
Input: text = "hello   world"
Output: "hello   world"

Example 4:
Input: text = "  walks  udp package   into  bar a"
Output: "walks  udp  package  into  bar  a "

Example 5:
Input: text = "a"
Output: "a"

 
Constraints:

1 <= text.length <= 100
text consists of lowercase English letters and ' '.
text contains at least one word.

Answer: {"fn_name": "reorderSpaces", "inputs": [["\"  this   is  a sentence \""]], "outputs": ["\" this is a sentence \"    "]}
user: At a lemonade stand, each lemonade costs $5. 
Customers are standing in a queue to buy from you, and order one at a time (in the order specified by bills).
Each customer will only buy one lemonade and pay with either a $5, $10, or $20 bill.  You must provide the correct change to each customer, so that the net transaction is that the customer pays $5.
Note that you don't have any change in hand at first.
Return true if and only if you can provide every customer with correct change.
 

Example 1:
Input: [5,5,5,10,20]
Output: true
Explanation: 
From the first 3 customers, we collect three $5 bills in order.
From the fourth customer, we collect a $10 bill and give back a $5.
From the fifth customer, we give a $10 bill and a $5 bill.
Since all customers got correct change, we output true.


Example 2:
Input: [5,5,10]
Output: true


Example 3:
Input: [10,10]
Output: false


Example 4:
Input: [5,5,10,10,20]
Output: false
Explanation: 
From the first two customers in order, we collect two $5 bills.
For the next two customers in order, we collect a $10 bill and give back a $5 bill.
For the last customer, we can't give change of $15 back because we only have two $10 bills.
Since not every customer received correct change, the answer is false.

 
Note:

0 <= bills.length <= 10000
bills[i] will be either 5, 10, or 20.

Answer: {"fn_name": "lemonadeChange", "inputs": [[[5, 5, 5, 10, 20]]], "outputs": [true]}
user: Given a string containing just the characters '(', ')', '{', '}', '[' and ']', determine if the input string is valid.

An input string is valid if:


       Open brackets must be closed by the same type of brackets.
       Open brackets must be closed in the correct order.


Note that an empty string is also considered valid.

Example 1:


Input: "()"
Output: true


Example 2:


Input: "()[]{}"
Output: true


Example 3:


Input: "(]"
Output: false


Example 4:


Input: "([)]"
Output: false


Example 5:


Input: "{[]}"
Output: true

Answer: {"fn_name": "isValid", "inputs": [["\"()\""]], "outputs": [false]}
user: Given an integer array sorted in non-decreasing order, there is exactly one integer in the array that occurs more than 25% of the time.
Return that integer.
 
Example 1:
Input: arr = [1,2,2,6,6,6,6,7,10]
Output: 6

 
Constraints:

1 <= arr.length <= 10^4
0 <= arr[i] <= 10^5

Answer: {"fn_name": "findSpecialInteger", "inputs": [[[1, 2, 2, 6, 6, 6, 6, 7, 10]]], "outputs": [6]}
user: Return the number of permutations of 1 to n so that prime numbers are at prime indices (1-indexed.)
(Recall that an integer is prime if and only if it is greater than 1, and cannot be written as a product of two positive integers both smaller than it.)
Since the answer may be large, return the answer modulo 10^9 + 7.
 
Example 1:
Input: n = 5
Output: 12
Explanation: For example [1,2,5,4,3] is a valid permutation, but [5,2,3,4,1] is not because the prime number 5 is at index 1.

Example 2:
Input: n = 100
Output: 682289015

 
Constraints:

1 <= n <= 100

Answer: {"fn_name": "numPrimeArrangements", "inputs": [[5]], "outputs": [12]}
user: Given a list of strings words representing an English Dictionary, find the longest word in words that can be built one character at a time by other words in words.  If there is more than one possible answer, return the longest word with the smallest lexicographical order.  If there is no answer, return the empty string.

Example 1:

Input: 
words = ["w","wo","wor","worl", "world"]
Output: "world"
Explanation: 
The word "world" can be built one character at a time by "w", "wo", "wor", and "worl".



Example 2:

Input: 
words = ["a", "banana", "app", "appl", "ap", "apply", "apple"]
Output: "apple"
Explanation: 
Both "apply" and "apple" can be built from other words in the dictionary. However, "apple" is lexicographically smaller than "apply".



Note:
All the strings in the input will only contain lowercase letters.
The length of words will be in the range [1, 1000].
The length of words[i] will be in the range [1, 30].

Answer: {"fn_name": "longestWord", "inputs": [[["\"w\"", "\"wo\"", "\"wor\"", "\"worl\"", "\"world\""]]], "outputs": [""]}
user: =====Function Descriptions=====
.remove(x)

This operation removes element x from the set.
If element x does not exist, it raises a KeyError.
The .remove(x) operation returns None.

Example

>>> s = set([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> s.remove(5)
>>> print s
set([1, 2, 3, 4, 6, 7, 8, 9])
>>> print s.remove(4)
None
>>> print s
set([1, 2, 3, 6, 7, 8, 9])
>>> s.remove(0)
KeyError: 0

.discard(x)

This operation also removes element x from the set.
If element x does not exist, it does not raise a KeyError.
The .discard(x) operation returns None.

Example

>>> s = set([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> s.discard(5)
>>> print s
set([1, 2, 3, 4, 6, 7, 8, 9])
>>> print s.discard(4)
None
>>> print s
set([1, 2, 3, 6, 7, 8, 9])
>>> s.discard(0)
>>> print s
set([1, 2, 3, 6, 7, 8, 9])

.pop()

This operation removes and return an arbitrary element from the set.
If there are no elements to remove, it raises a KeyError.

Example

>>> s = set([1])
>>> print s.pop()
1
>>> print s
set([])
>>> print s.pop()
KeyError: pop from an empty set

=====Problem Statement=====
You have a non-empty set s, and you have to execute N commands given in N lines.
The commands will be pop, remove and discard. 

=====Input Format=====
The first line contains integer n, the number of elements in the set s.
The second line contains n space separated elements of set s. All of the elements are non-negative integers, less than or equal to 9.
The third line contains integer N, the number of commands.
The next N lines contains either pop, remove and/or discard commands followed by their associated value.

=====Constraints=====
0 < n < 20
0 < N < 20

=====Output Format====
Print the sum of the elements of set s on a single line.
user: =====Function Descriptions=====
group()

A group() expression returns one or more subgroups of the match.
Code

>>> import re
>>> m = re.match(r'(\w+)@(\w+)\.(\w+)','username@hackerrank.com')
>>> m.group(0)       # The entire match 
'username@hackerrank.com'
>>> m.group(1)       # The first parenthesized subgroup.
'username'
>>> m.group(2)       # The second parenthesized subgroup.
'hackerrank'
>>> m.group(3)       # The third parenthesized subgroup.
'com'
>>> m.group(1,2,3)   # Multiple arguments give us a tuple.
('username', 'hackerrank', 'com')

groups()

A groups() expression returns a tuple containing all the subgroups of the match.
Code

>>> import re
>>> m = re.match(r'(\w+)@(\w+)\.(\w+)','username@hackerrank.com')
>>> m.groups()
('username', 'hackerrank', 'com')

groupdict()

A groupdict() expression returns a dictionary containing all the named subgroups of the match, keyed by the subgroup name.
Code

>>> m = re.match(r'(?P<user>\w+)@(?P<website>\w+)\.(?P<extension>\w+)','myname@hackerrank.com')
>>> m.groupdict()
{'website': 'hackerrank', 'user': 'myname', 'extension': 'com'}

=====Problem Statement=====
You are given a string S.
Your task is to find the first occurrence of an alphanumeric character in (read from left to right) that has consecutive repetitions. 

=====Input Format=====
A single line of input containing the string S.

=====Constraints=====
0<len(S)<100

=====Output Format=====
Print the first occurrence of the repeating character. If there are no repeating characters, print -1.
user: =====Function Descriptions=====
itertools.product()

This tool computes the cartesian product of input iterables.
It is equivalent to nested for-loops.
For example, product(A, B) returns the same as ((x,y) for x in A for y in B).

Sample Code

>>> from itertools import product
>>>
>>> print list(product([1,2,3],repeat = 2))
[(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)]
>>>
>>> print list(product([1,2,3],[3,4]))
[(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)]
>>>
>>> A = [[1,2,3],[3,4,5]]
>>> print list(product(*A))
[(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 3), (3, 4), (3, 5)]
>>>
>>> B = [[1,2,3],[3,4,5],[7,8]]
>>> print list(product(*B))
[(1, 3, 7), (1, 3, 8), (1, 4, 7), (1, 4, 8), (1, 5, 7), (1, 5, 8), (2, 3, 7), (2, 3, 8), (2, 4, 7), (2, 4, 8), (2, 5, 7), (2, 5, 8), (3, 3, 7), (3, 3, 8), (3, 4, 7), (3, 4, 8), (3, 5, 7), (3, 5, 8)]

=====Problem Statement=====
You are given a two lists A and B. Your task is to compute their cartesian product AXB.
Example
A = [1, 2]
B = [3, 4]

AxB = [(1, 3), (1, 4), (2, 3), (2, 4)]
Note: A and B are sorted lists, and the cartesian product's tuples should be output in sorted order.

=====Input Format=====
The first line contains the space separated elements of list A.
The second line contains the space separated elements of list B.
Both lists have no duplicate integer elements.

=====Constraints=====
0<A<30
0<B<30

=====Output Format=====
Output the space separated tuples of the cartesian product.
user: =====Problem Statement=====
You are given an integer, N. Your task is to print an alphabet rangoli of size N. (Rangoli is a form of Indian folk art based on creation of patterns.)

Different sizes of alphabet rangoli are shown below:

#size 3

----c----
--c-b-c--
c-b-a-b-c
--c-b-c--
----c----

#size 5

--------e--------
------e-d-e------
----e-d-c-d-e----
--e-d-c-b-c-d-e--
e-d-c-b-a-b-c-d-e
--e-d-c-b-c-d-e--
----e-d-c-d-e----
------e-d-e------
--------e--------

#size 10

------------------j------------------
----------------j-i-j----------------
--------------j-i-h-i-j--------------
------------j-i-h-g-h-i-j------------
----------j-i-h-g-f-g-h-i-j----------
--------j-i-h-g-f-e-f-g-h-i-j--------
------j-i-h-g-f-e-d-e-f-g-h-i-j------
----j-i-h-g-f-e-d-c-d-e-f-g-h-i-j----
--j-i-h-g-f-e-d-c-b-c-d-e-f-g-h-i-j--
j-i-h-g-f-e-d-c-b-a-b-c-d-e-f-g-h-i-j
--j-i-h-g-f-e-d-c-b-c-d-e-f-g-h-i-j--
----j-i-h-g-f-e-d-c-d-e-f-g-h-i-j----
------j-i-h-g-f-e-d-e-f-g-h-i-j------
--------j-i-h-g-f-e-f-g-h-i-j--------
----------j-i-h-g-f-g-h-i-j----------
------------j-i-h-g-h-i-j------------
--------------j-i-h-i-j--------------
----------------j-i-j----------------
------------------j------------------

The center of the rangoli has the first alphabet letter a, and the boundary has the Nth alphabet letter (in alphabetical order).

=====Input Format=====
Only one line of input containing N, the size of the rangoli.

=====Constraints=====
0 < N < 27

=====Output Format=====
Print the alphabet rangoli in the format explained above.