def divided_differences(xi, yi, dyi):
    n = len(xi) * 2
    m = 5
    matrix = [[ 0 for x in range(50)] for y in range(50)]
    for i in range(0, n):
        matrix[i][0] = yi[int(i/2)] #diferencas de ordem 0

    for i in range(1, m): #diferenças de ordem m
        for j in range(0, n - i):
            a = (xi[int((j+i)/2)] - xi[int(j/2)])
            if(a == 0):
                matrix[j][i] = dyi[int(j/2)]
            else:
                matrix[j][i] = (matrix[j + 1][i - 1] - matrix[j][i - 1]) / a
    return matrix[0][4]