





'''simple docstring'''






from __future__ import annotations






def      __A						(							a_						:  list[list[int]]	):







		for i in range(1      ,len(matrix[0]	)	):
				matrix[0][i] += matrix[0][i - 1]

		# preprocessing the first column
		for i in range(1      ,len(lowerCAmelCase__	)	):
				matrix[i][0] += matrix[i - 1][0]

		# updating the path cost for current position
		for i in range(1      ,len(lowerCAmelCase__	)	):
				for j in range(1      ,len(matrix[0]	)	):
						matrix[i][j] += min(matrix[i - 1][j]      ,matrix[i][j - 1]	)

		return matrix[-1][-1]


if __name__ == "__main__":
			import doctest

			doctest.testmod()










'''simple docstring'''






from __future__ import annotations






def      __A						(							a_						:  float      ,a_						:  float      ,a_						:  float      ,):
		if (stress, tangential_force, area).count(0	) != 1:
				raise ValueError("You cannot supply more or less than 2 values"	)
		elif stress < 0:
				raise ValueError("Stress cannot be negative"	)
		elif tangential_force < 0:
				raise ValueError("Tangential Force cannot be negative"	)
		elif area < 0:
				raise ValueError("Area cannot be negative"	)
		elif stress == 0:
				return (
				    "stress",
				    tangential_force / area,
				)
		elif tangential_force == 0:
				return (
				    "tangential_force",
				    stress * area,
				)
		else:
				return (
				    "area",
				    tangential_force / stress,
				)


if __name__ == "__main__":
					import doctest

					doctest.testmod()



