



'''simple docstring'''



import decimal


def 							__UpperCAmelCase				(				)		->						int:
				snake_case__      :   str      =    0
				snake_case__      :   List[str]      =    decimal.Context(prec=105			)
				for i in range(2   ,				100			):
								snake_case__      :   Optional[int]      =    decimal.Decimal(UpperCamelCase__			)
								snake_case__      :   List[str]      =    number.sqrt(UpperCamelCase__			)
								if len(str(UpperCamelCase__			)			) > 1:
												answer += int(str(UpperCamelCase__			)[0]			)
												snake_case__      :   Optional[Any]      =    str(UpperCamelCase__			)[2:101]
												answer += sum(int(UpperCamelCase__			) for x in sqrt_number_str			)
				return answer


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				print(F"{solution() = }")






"""simple docstring"""

from __future__ import annotations

from queue import Queue
def 						UpperCAmelCase   (						a_,		a_     ):





		'''simple docstring'''


		a ^= b
		b ^= a
		a ^= b
		return a, b
def 						UpperCAmelCase   (						a_,		a_     ):





		'''simple docstring'''


		lowerCamelCase	:     int            =       1
		while (1 << j) < max_node:
				for i in range(1,		max_node + 1     ):
						lowerCamelCase	:     Tuple            =       parent[j - 1][parent[j - 1][i]]
				j += 1
		return parent
def 						UpperCAmelCase   (						a_,		a_,		a_,		a_     ):





		'''simple docstring'''


		if level[u] < level[v]:
				lowerCamelCase      ,       lowerCamelCase	:     List[Any]            =       swap(a_,		a_     )
		# making depth of u same as depth of v
		for i in range(18,		-1,		-1     ):
				if level[u] - (1 << i) >= level[v]:
						lowerCamelCase	:     int            =       parent[i][u]
    # at the same depth if u==v that mean lca is found
		if u == v:
				return u
		# moving both nodes upwards till lca in found
		for i in range(18,		-1,		-1     ):
				if parent[i][u] not in [0, parent[i][v]]:
						lowerCamelCase      ,       lowerCamelCase	:     str            =       parent[i][u], parent[i][v]
    # returning longest common ancestor of u,v
		return parent[0][u]
def 						UpperCAmelCase   (						a_,		a_,		a_,		a_,		a_ = 1,		):





		'''simple docstring'''


		lowerCamelCase	:     Any            =       0
		lowerCamelCase	:     Queue[int]            =       Queue(maxsize=a_     )
		q.put(a_     )
		while q.qsize() != 0:
				lowerCamelCase	:     Tuple            =       q.get()
				for v in graph[u]:
						if level[v] == -1:
								lowerCamelCase	:     Optional[Any]            =       level[u] + 1
								q.put(a_     )
								lowerCamelCase	:     str            =       u
		return level, parent
def 						UpperCAmelCase   (						):





		'''simple docstring'''


		lowerCamelCase	:     Any            =       13
		# initializing with 0
		lowerCamelCase	:     Dict            =       [[0 for _ in range(max_node + 10     )] for _ in range(20     )]
		# initializing with -1 which means every node is unvisited
		lowerCamelCase	:     List[Any]            =       [-1 for _ in range(max_node + 10     )]
		lowerCamelCase	:     dict[int, list[int]]            =       {
		    1: [2, 3, 4],
		    2: [5],
		    3: [6, 7],
		    4: [8],
		    5: [9, 10],
		    6: [11],
		    7: [],
		    8: [12, 13],
		    9: [],
		    10: [],
		    11: [],
		    12: [],
		    13: [],
		}
		lowerCamelCase      ,       lowerCamelCase	:     Dict            =       breadth_first_search(a_,		a_,		a_,		a_,		1     )
		lowerCamelCase	:     List[Any]            =       create_sparse(a_,		a_     )
		print('LCA of node 1 and 3 is: ',		lowest_common_ancestor(1,		3,		a_,		a_     )     )
		print('LCA of node 5 and 6 is: ',		lowest_common_ancestor(5,		6,		a_,		a_     )     )
		print('LCA of node 7 and 11 is: ',		lowest_common_ancestor(7,		11,		a_,		a_     )     )
		print('LCA of node 6 and 7 is: ',		lowest_common_ancestor(6,		7,		a_,		a_     )     )
		print('LCA of node 4 and 12 is: ',		lowest_common_ancestor(4,		12,		a_,		a_     )     )
		print('LCA of node 8 and 8 is: ',		lowest_common_ancestor(8,		8,		a_,		a_     )     )


if __name__ == "__main__":
					main()






