





import sys

__A							:			Union[str, Any]         =			(
    "73167176531330624919225119674426574742355349194934"
    "96983520312774506326239578318016984801869478851843"
    "85861560789112949495459501737958331952853208805511"
    "12540698747158523863050715693290963295227443043557"
    "66896648950445244523161731856403098711121722383113"
    "62229893423380308135336276614282806444486645238749"
    "30358907296290491560440772390713810515859307960866"
    "70172427121883998797908792274921901699720888093776"
    "65727333001053367881220235421809751254540594752243"
    "52584907711670556013604839586446706324415722155397"
    "53697817977846174064955149290862569321978468622482"
    "83972241375657056057490261407972968652414535100474"
    "82166370484403199890008895243450658541227588666881"
    "16427171479924442928230863465674813919123162824586"
    "17866458359124566529476545682848912883142607690042"
    "24219022671055626321111109370544217506941658960408"
    "07198403850962455444362981230987879927244284909188"
    "84580156166097919133875499200524063689912560717606"
    "05886116467109405077541002256983155200055935729725"
    "71636269561882670428252483600823257530420752963450"
)





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> int:




    """simple docstring"""




    _A     =							1
    for digit in s:
        product *= int(_SCREAMING_SNAKE_CASE				)
    return product





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE = N				)							-> int:




    """simple docstring"""




    _A     =							-sys.maxsize - 1
    _A     =							n[:13]
    _A     =							13
    while cur_index < len(_SCREAMING_SNAKE_CASE				) - 13:
        if int(n[cur_index]				) >= int(substr[0]				):
            _A     =							substr[1:] + n[cur_index]
            cur_index += 1
        else:
            _A     =							max(_SCREAMING_SNAKE_CASE							,     str_eval(_SCREAMING_SNAKE_CASE				)				)
            _A     =							n[cur_index : cur_index + 13]
            cur_index += 13
    return largest_product


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












from collections import defaultdict
from math import ceil, sqrt





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE = 1_000_000							,     _SCREAMING_SNAKE_CASE = 10				)							-> int:




    """simple docstring"""




    _A     =							defaultdict(_SCREAMING_SNAKE_CASE				)

    for outer_width in range(3							,     (t_limit // 4) + 2				):
        if outer_width * outer_width > t_limit:
            _A     =							max(
                ceil(sqrt(outer_width * outer_width - t_limit				)				)							,     1				)
        else:
            _A     =							1

        hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

        for hole_width in range(_SCREAMING_SNAKE_CASE							,     outer_width - 1							,     2				):
            count[outer_width * outer_width - hole_width * hole_width] += 1

    return sum(1 for n in count.values() if 1 <= n <= 10				)


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





