def 			__UpperCamelCase     (    A			,				A = False				):
     if n == 2:
          return True
     if not n % 2 or n < 2:
          return False
     if n > 5 and n % 10 not in (1, 3, 7, 9):  # can quickly check last digit
          return False
     if n > 3317044064679887385961981 and not allow_probable:
          raise ValueError(
              '''Warning: upper bound of deterministic test is exceeded. '''
              '''Pass allow_probable=True to allow probabilistic test. '''
              '''A return value of True indicates a probable prime.'''				)
     # array bounds provided by analysis
     UpperCamelCase__					    =   [
         2047,
         1373653,
         25326001,
         3215031751,
         2152302898747,
         3474749660383,
         341550071728321,
         1,
         3825123056546413051,
         1,
         1,
         318665857834031151167461,
         3317044064679887385961981,
     ]

     UpperCamelCase__					    =   [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
     for idx, _p in enumerate(__snake_case			,				1				):
          if n < _p:
               # then we have our last prime to check
               UpperCamelCase__					    =   primes[:idx]
               break
     UpperCamelCase__    ,							UpperCamelCase__					    =   n - 1, 0
     # break up n -1 into a power of 2 (s) and
     # remaining odd component
     # essentially, solve for d * 2 ** s == n - 1
     while d % 2 == 0:
          d //= 2
          s += 1
     for prime in plist:
          UpperCamelCase__					    =   False
          for r in range(__snake_case				):
               UpperCamelCase__					    =   pow(__snake_case			,				d * 2**r			,				__snake_case				)
               # see article for analysis explanation for m
               if (r == 0 and m == 1) or ((m + 1) % n == 0):
                    UpperCamelCase__					    =   True
                    # this loop will not determine compositeness
                    break
          if pr:
               continue
          # if pr is False, then the above loop never evaluated to true,
          # and the n MUST be composite
          return False
     return True







def 			__UpperCamelCase     (    ):
     assert not miller_rabin(561				)
     assert miller_rabin(563				)
     # 2047

     assert not miller_rabin(838201				)
     assert miller_rabin(838207				)
     # 1_373_653

     assert not miller_rabin(17316001				)
     assert miller_rabin(17316017				)
     # 25_326_001

     assert not miller_rabin(3078386641				)
     assert miller_rabin(3078386653				)
     # 3_215_031_751

     assert not miller_rabin(1713045574801				)
     assert miller_rabin(1713045574819				)
     # 2_152_302_898_747

     assert not miller_rabin(2779799728307				)
     assert miller_rabin(2779799728327				)
     # 3_474_749_660_383

     assert not miller_rabin(113850023909441				)
     assert miller_rabin(113850023909527				)
     # 341_550_071_728_321

     assert not miller_rabin(1275041018848804351				)
     assert miller_rabin(1275041018848804391				)
     # 3_825_123_056_546_413_051

     assert not miller_rabin(79666464458507787791867				)
     assert miller_rabin(79666464458507787791951				)
     # 318_665_857_834_031_151_167_461

     assert not miller_rabin(552840677446647897660333				)
     assert miller_rabin(552840677446647897660359				)
     # 3_317_044_064_679_887_385_961_981
     # upper limit for probabilistic test


if __name__ == "__main__":
     test_miller_rabin()











import os

# Precomputes a list of the 100 first triangular numbers
lowerCamelCase      :       str    =						[int(0.5 * n * (n + 1)) for n in range(1, 101)]





def    __lowerCAmelCase   (    ):
     __lowerCAmelCase             =       os.path.dirname(os.path.realpath(__snake_case							)							)
     __lowerCAmelCase             =       os.path.join(__snake_case       ,			"words.txt"							)

     __lowerCAmelCase             =       ""
     with open(__snake_case							) as f:
          __lowerCAmelCase             =       f.readline()

     __lowerCAmelCase             =       [word.strip("\""							) for word in words.strip("\r\n"							).split(","							)]
     __lowerCAmelCase             =       [
         word
         for word in [sum(ord(__snake_case							) - 64 for x in word							) for word in words]
         if word in TRIANGULAR_NUMBERS
     ]
     return len(__snake_case							)


if __name__ == "__main__":
 print(solution())






