Implement the hill climbing algorithm in Python and use it to solve the following three peak finding problems on grid. For each problem, the initial point is (0,0).

grid1 = [[3, 7, 2, 8], [5, 2, 9, 1], [5, 3, 3, 1]]

grid2 = [[0, 0, 0, 1, 4], [0, 0, 2, 8, 10], [0, 0, 2, 4, 12], [0, 2, 4, 8, 16], [1, 4, 8, 16, 32]]

f = lambda x,y: -(1-x)**2 - 100*(y - x**2)**2 a,b,c,d,=-2,2,-1,3

grid3 = [[f(a + i*(b-a)/99, c + j*(d-c)/99) for j in range(100)] for i in range(100)]