
'''simple docstring'''
lowerCAmelCase					:    List[Any]           = range(2, 20 + 1)
lowerCAmelCase					:    Union[str, Any]           = [10**k for k in range(ks[-1] + 1)]
lowerCAmelCase					:    dict[int, dict[int, list[list[int]]]]           = {}







def 		A_(     A						:		Any		,     A						:		Dict		,     A						:		str		,     A						:		str):
							UpperCamelCase   			=     sum(a_i[j] for j in range(A		,     len(A)))
							UpperCamelCase   			=     sum(a_i[j] * base[j] for j in range(min(len(A)		,     A)))

							UpperCamelCase			,	UpperCamelCase   			=     0, 0
							UpperCamelCase   			=     n - i

							UpperCamelCase   			=     memo.get(A)

							if sub_memo is not None:
														UpperCamelCase   			=     sub_memo.get(A)

														if jumps is not None and len(A) > 0:
																					# find and make the largest jump without going over
																					UpperCamelCase   			=     -1
																					for _k in range(len(A) - 1		,     -1		,     -1):
																												if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
																																			UpperCamelCase   			=     _k
																																			break

																					if max_jump >= 0:
																												UpperCamelCase			,	UpperCamelCase			,	UpperCamelCase   			=     jumps[max_jump]
																												# since the difference between jumps is cached, add c
																												UpperCamelCase   			=     diff + c
																												for j in range(min(A		,     len(A))):
																																			UpperCamelCase			,	UpperCamelCase   			=     divmod(A		,     10)
																												if new_c > 0:
																																			add(A		,     A		,     A)

														else:
																					UpperCamelCase   			=     []
							else:
														UpperCamelCase   			=     {c: []}
														UpperCamelCase   			=     sub_memo

							if dn >= max_dn or c + diff >= base[k]:
														return diff, dn

							if k > ks[0]:
														while True:
																					# keep doing smaller jumps
																					UpperCamelCase			,	UpperCamelCase   			=     next_term(A		,     k - 1		,     i + dn		,     A)
																					diff += _diff
																					dn += terms_jumped

																					if dn >= max_dn or c + diff >= base[k]:
																												break
							else:
														# would be too small a jump, just compute sequential terms instead
														UpperCamelCase			,	UpperCamelCase   			=     compute(A		,     A		,     i + dn		,     A)
														diff += _diff
														dn += terms_jumped

							UpperCamelCase   			=     sub_memo[c]

							# keep jumps sorted by # of terms skipped
							UpperCamelCase   			=     0
							while j < len(A):
														if jumps[j][1] > dn:
																					break
														j += 1

							# cache the jump for this value digitsum(b) and c
							sub_memo[c].insert(A		,     (diff, dn, k))
							return (diff, dn)







def 		A_(     A						:		int		,     A						:		Optional[int]		,     A						:		str		,     A						:		List[str]):
							if i >= n:
														return 0, i
							if k > len(A):
														a_i.extend([0 for _ in range(k - len(A))])

							# note: a_i -> b * 10^k + c
							# ds_b -> digitsum(b)
							# ds_c -> digitsum(c)
							UpperCamelCase   			=     i
							UpperCamelCase			,	UpperCamelCase			,	UpperCamelCase   			=     0, 0, 0
							for j in range(len(A)):
														if j >= k:
																					ds_b += a_i[j]
														else:
																					ds_c += a_i[j]

							while i < n:
														i += 1
														UpperCamelCase   			=     ds_c + ds_b
														diff += addend
														UpperCamelCase   			=     0
														for j in range(A):
																					UpperCamelCase   			=     a_i[j] + addend
																					UpperCamelCase			,	UpperCamelCase   			=     divmod(A		,     10)

																					ds_c += a_i[j]

														if addend > 0:
																					break

							if addend > 0:
														add(A		,     A		,     A)
							return diff, i - start_i







def 		A_(     A						:		str		,     A						:		Dict		,     A						:		Tuple):
							for j in range(A		,     len(A)):
														UpperCamelCase   			=     digits[j] + addend
														if s >= 10:
																					UpperCamelCase			,	UpperCamelCase   			=     divmod(A		,     10)
																					UpperCamelCase   			=     addend // 10 + quotient
														else:
																					UpperCamelCase   			=     s
																					UpperCamelCase   			=     addend // 10

														if addend == 0:
																					break

							while addend > 0:
														UpperCamelCase			,	UpperCamelCase   			=     divmod(A		,     10)
														digits.append(A)







def 		A_(     A						:		int = 10**15):
							UpperCamelCase   			=     [1]
							UpperCamelCase   			=     1
							UpperCamelCase   			=     0
							while True:
														UpperCamelCase			,	UpperCamelCase   			=     next_term(A		,     20		,     i + dn		,     A)
														dn += terms_jumped
														if dn == n - i:
																					break

							UpperCamelCase   			=     0
							for j in range(len(A)):
														a_n += digits[j] * 10**j
							return a_n


if __name__ == "__main__":
						print(f"""{solution() = }""")







from random import randint
from tempfile import TemporaryFile

import numpy as np



def   __UpperCAmelCase					(      __a :     Optional[Any]						,__a :     int						,__a :     Any      )     ->	int:

					"""simple docstring"""

					_a      :       int   =						0
					if start < end:
										_a      :       Tuple   =						randint(__a						,__a      )
										_a      :       Tuple   =						a[end]
										_a      :       List[str]   =						a[pivot]
										_a      :       Any   =						temp

										_a ,   _a      :       Optional[int]   =						_in_place_partition(__a						,__a						,__a      )
										count += _in_place_quick_sort(__a						,__a						,p - 1      )
										count += _in_place_quick_sort(__a						,p + 1						,__a      )
					return count



def   __UpperCAmelCase					(      __a :     List[Any]						,__a :     Tuple						,__a :     Dict      )     ->	Dict:

					"""simple docstring"""

					_a      :       Dict   =						0
					_a      :       Tuple   =						randint(__a						,__a      )
					_a      :       List[Any]   =						a[end]
					_a      :       str   =						a[pivot]
					_a      :       str   =						temp
					_a      :       Dict   =						start - 1
					for index in range(__a						,__a      ):
										count += 1
										if a[index] < a[end]:  # check if current val is less than pivot value
															_a      :       int   =						new_pivot_index + 1
															_a      :       Any   =						a[new_pivot_index]
															_a      :       Optional[int]   =						a[index]
															_a      :       str   =						temp

					_a      :       Union[str, Any]   =						a[new_pivot_index + 1]
					_a      :       Tuple   =						a[end]
					_a      :       Any   =						temp
					return new_pivot_index + 1, count


a__												=						TemporaryFile()
a__												=						100  # 1000 elements are to be sorted


a__						,     a__												=						0, 1  # mean and standard deviation
a__												=						np.random.normal(mu, sigma, p)
np.save(outfile, X)
print('''The array is''')
print(X)


outfile.seek(0)  # using the same array
a__												=						np.load(outfile)
a__												=						len(M) - 1
a__												=						_in_place_quick_sort(M, 0, r)

print(
    '''No of Comparisons for 100 elements selected from a standard normal distribution'''
    '''is :'''
)







print(z)



