-w2*(-y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))    +z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))    + (z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4))    -y2*(w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))    -z3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +    (z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5)) +z1*(w2*(-y4*(z5^2+y5^2+x5^2+w5^2)    -y3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +y5*(z4^2+y4^2+x4^2+w4^2)    + (y4-y5)*(z3^2+y3^2+x3^2+w3^2)) -w3*(y5*(z4^2+y4^2+x4^2+w4^2)    -y4*(z5^2+y5^2+x5^2+w5^2)) -y2*(-w4*(z5^2+y5^2+x5^2+w5^2)    -w3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2)    +w5*(z4^2+y4^2+x4^2+w4^2) + (w4-w5)*(z3^2+y3^2+x3^2+w3^2))    +y3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) -    (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2) + (-w4*y5-w3*(y4-y5) +w5*y4+    (w4-w5)*y3)*(z2^2+y2^2+x2^2+w2^2)) +z2*(w3*(y5*(z4^2+y4^2+x4^2+w4^2)    -y4*(z5^2+y5^2+x5^2+w5^2)) -y3*(w5*(z4^2+y4^2+x4^2+w4^2)    -w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2))    + (z1^2+y1^2+x1^2+w1^2)*(w2*(y4*z5+y3*(z4-z5) -y5*z4-    (y4-y5)*z3) -w3*(y4*z5-y5*z4) +y2*(-w4*z5-w3*(z4-z5)    +w5*z4+ (w4-w5)*z3) -y3*(w5*z4-w4*z5) + (w5*y4-w4*y5)*z3-    (-w4*y5-w3*(y4-y5) +w5*y4+ (w4-w5)*y3)*z2) +    (z2^2+y2^2+x2^2+w2^2)*(w3*(y4*z5-y5*z4) +y3*(w5*z4-w4*z5) -    (w5*y4-w4*y5)*z3)) +y0*(-w1*(-x2*(-z4*(z5^2+y5^2+x5^2+w5^2)    -z3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +    (z4^2+y4^2+x4^2+w4^2)*z5+ (z3^2+y3^2+x3^2+w3^2)*(z4-z5))    +x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))    +z2*(-x4*(z5^2+y5^2+x5^2+w5^2)    -x3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2)    +x5*(z4^2+y4^2+x4^2+w4^2) + (x4-x5)*(z3^2+y3^2+x3^2+w3^2))    -z3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) +    (z2^2+y2^2+x2^2+w2^2)*(x4*z5+x3*(z4-z5) -x5*z4- (x4-x5)*z3) -    (z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4)) -x1*(w2*(-z4*(z5^2+y5^2+x5^2+w5^2)    -z3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +    (z4^2+y4^2+x4^2+w4^2)*z5+ (z3^2+y3^2+x3^2+w3^2)*(z4-z5))    -w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))    -z2*(-w4*(z5^2+y5^2+x5^2+w5^2)    -w3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +w5*(z4^2+y4^2+x4^2+w4^2)    + (w4-w5)*(z3^2+y3^2+x3^2+w3^2)) +z3*(w5*(z4^2+y4^2+x4^2+w4^2)    -w4*(z5^2+y5^2+x5^2+w5^2)) + (z2^2+y2^2+x2^2+w2^2)*(-w4*z5-w3*(z4-z5)    +w5*z4+ (w4-w5)*z3) - (z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5))    -w2*(-x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))    +z3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2))    + (z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4))    -x2*(w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))    -z3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +    (z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5)) +z1*(w2*(-x4*(z5^2+y5^2+x5^2+w5^2)    -x3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +x5*(z4^2+y4^2+x4^2+w4^2)    + (x4-x5)*(z3^2+y3^2+x3^2+w3^2)) -w3*(x5*(z4^2+y4^2+x4^2+w4^2)    -x4*(z5^2+y5^2+x5^2+w5^2)) -x2*(-w4*(z5^2+y5^2+x5^2+w5^2)    -w3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2)    +w5*(z4^2+y4^2+x4^2+w4^2) + (w4-w5)*(z3^2+y3^2+x3^2+w3^2))    +x3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) -    (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2) + (-w4*x5-w3*(x4-x5) +w5*x4+    (w4-w5)*x3)*(z2^2+y2^2+x2^2+w2^2)) +z2*(w3*(x5*(z4^2+y4^2+x4^2+w4^2)    -x4*(z5^2+y5^2+x5^2+w5^2)) -x3*(w5*(z4^2+y4^2+x4^2+w4^2)    -w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2)) +    (z1^2+y1^2+x1^2+w1^2)*(w2*(x4*z5+x3*(z4-z5) -x5*z4- (x4-x5)*z3)    -w3*(x4*z5-x5*z4) +x2*(-w4*z5-w3*(z4-z5) +w5*z4+ (w4-w5)*z3)    -x3*(w5*z4-w4*z5) + (w5*x4-w4*x5)*z3- (-w4*x5-w3*(x4-x5) +w5*x4+    (w4-w5)*x3)*z2) + (z2^2+y2^2+x2^2+w2^2)*(w3*(x4*z5-x5*z4)    +x3*(w5*z4-w4*z5) - (w5*x4-w4*x5)*z3))    -w1*(-x2*(-y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))    +z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))    + (z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4))    +y2*(-x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))    +z3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) +    (z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4)) -z2*(-x3*(y5*(z4^2+y4^2+x4^2+w4^2)    -y4*(z5^2+y5^2+x5^2+w5^2)) +y3*(x5*(z4^2+y4^2+x4^2+w4^2)    -x4*(z5^2+y5^2+x5^2+w5^2)) + (x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2))    + (z2^2+y2^2+x2^2+w2^2)*(x3*(y4*z5-y5*z4)    -y3*(x4*z5-x5*z4) + (x4*y5-x5*y4)*z3))    +x1*(-w2*(-y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))    +z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))    + (z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4))    -y2*(w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))    -z3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +    (z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5)) +z2*(w3*(y5*(z4^2+y4^2+x4^2+w4^2)    -y4*(z5^2+y5^2+x5^2+w5^2)) -y3*(w5*(z4^2+y4^2+x4^2+w4^2)    -w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2))    + (z2^2+y2^2+x2^2+w2^2)*(w3*(y4*z5-y5*z4)    +y3*(w5*z4-w4*z5) - (w5*y4-w4*y5)*z3))    -y1*(-w2*(-x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))    +z3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2))    + (z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4))    -x2*(w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))    -z3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +    (z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5)) +z2*(w3*(x5*(z4^2+y4^2+x4^2+w4^2)    -x4*(z5^2+y5^2+x5^2+w5^2)) -x3*(w5*(z4^2+y4^2+x4^2+w4^2)    -w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2))    + (z2^2+y2^2+x2^2+w2^2)*(w3*(x4*z5-x5*z4) +x3*(w5*z4-w4*z5)    - (w5*x4-w4*x5)*z3)) -z0*(-w1*(-x2*(-y4*(z5^2+y5^2+x5^2+w5^2)    -y3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +y5*(z4^2+y4^2+x4^2+w4^2)    + (y4-y5)*(z3^2+y3^2+x3^2+w3^2)) +x3*(y5*(z4^2+y4^2+x4^2+w4^2)    -y4*(z5^2+y5^2+x5^2+w5^2)) +y2*(-x4*(z5^2+y5^2+x5^2+w5^2)    -x3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2)    +x5*(z4^2+y4^2+x4^2+w4^2) + (x4-x5)*(z3^2+y3^2+x3^2+w3^2))    -y3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) -    (x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2) + (x4*y5+x3*(y4-y5) -x5*y4-    (x4-x5)*y3)*(z2^2+y2^2+x2^2+w2^2)) -x1*(w2*(-y4*(z5^2+y5^2+x5^2+w5^2)    -y3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +y5*(z4^2+y4^2+x4^2+w4^2)    + (y4-y5)*(z3^2+y3^2+x3^2+w3^2)) -w3*(y5*(z4^2+y4^2+x4^2+w4^2)    -y4*(z5^2+y5^2+x5^2+w5^2)) -y2*(-w4*(z5^2+y5^2+x5^2+w5^2)    -w3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2)    +w5*(z4^2+y4^2+x4^2+w4^2) + (w4-w5)*(z3^2+y3^2+x3^2+w3^2))    +y3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) -    (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2) + (-w4*y5-w3*(y4-y5) +w5*y4+    (w4-w5)*y3)*(z2^2+y2^2+x2^2+w2^2)) -w2*(-x3*(y5*(z4^2+y4^2+x4^2+w4^2)    -y4*(z5^2+y5^2+x5^2+w5^2)) +y3*(x5*(z4^2+y4^2+x4^2+w4^2)    -x4*(z5^2+y5^2+x5^2+w5^2)) + (x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2))    -x2*(w3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))    -y3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +    (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2)) +y1*(w2*(-x4*(z5^2+y5^2+x5^2+w5^2)    -x3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +x5*(z4^2+y4^2+x4^2+w4^2)    + (x4-x5)*(z3^2+y3^2+x3^2+w3^2)) -w3*(x5*(z4^2+y4^2+x4^2+w4^2)    -x4*(z5^2+y5^2+x5^2+w5^2)) -x2*(-w4*(z5^2+y5^2+x5^2+w5^2)    -w3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +w5*(z4^2+y4^2+x4^2+w4^2)    + (w4-w5)*(z3^2+y3^2+x3^2+w3^2)) +x3*(w5*(z4^2+y4^2+x4^2+w4^2)    -w4*(z5^2+y5^2+x5^2+w5^2)) - (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2)    + (-w4*x5-w3*(x4-x5) +w5*x4+ (w4-w5)*x3)*(z2^2+y2^2+x2^2+w2^2))    +y2*(w3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2))    -x3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +    (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2)) + (w3*(x4*y5-x5*y4) +x3*(w5*y4-w4*y5)    - (w5*x4-w4*x5)*y3)*(z2^2+y2^2+x2^2+w2^2) + (w2*(x4*y5+x3*(y4-y5)    -x5*y4- (x4-x5)*y3) -w3*(x4*y5-x5*y4) +x2*(-w4*y5-w3*(y4-y5)    +w5*y4+ (w4-w5)*y3) -x3*(w5*y4-w4*y5) + (w5*x4-w4*x5)*y3-    (-w4*x5-w3*(x4-x5) +w5*x4+ (w4-w5)*x3)*y2)*(z1^2+y1^2+x1^2+w1^2))    +z1*(-w2*(-x3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))    +y3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) +    (x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2)) -x2*(w3*(y5*(z4^2+y4^2+x4^2+w4^2)    -y4*(z5^2+y5^2+x5^2+w5^2)) -y3*(w5*(z4^2+y4^2+x4^2+w4^2)    -w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2))    +y2*(w3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2))    -x3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +    (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2)) + (w3*(x4*y5-x5*y4)    +x3*(w5*y4-w4*y5) - (w5*x4-w4*x5)*y3)*(z2^2+y2^2+x2^2+w2^2)) +    (z0^2+y0^2+x0^2+w0^2)*(-w1*(x2*(y4*z5+y3*(z4-z5) -y5*z4- (y4-y5)*z3)    -x3*(y4*z5-y5*z4) -y2*(x4*z5+x3*(z4-z5) -x5*z4- (x4-x5)*z3)    +y3*(x4*z5-x5*z4) - (x4*y5-x5*y4)*z3+ (x4*y5+x3*(y4-y5) -x5*y4-    (x4-x5)*y3)*z2) +x1*(w2*(y4*z5+y3*(z4-z5) -y5*z4- (y4-y5)*z3)    -w3*(y4*z5-y5*z4) +y2*(-w4*z5-w3*(z4-z5) +w5*z4+ (w4-w5)*z3)    -y3*(w5*z4-w4*z5) + (w5*y4-w4*y5)*z3- (-w4*y5-w3*(y4-y5) +w5*y4+    (w4-w5)*y3)*z2) -w2*(x3*(y4*z5-y5*z4) -y3*(x4*z5-x5*z4) +    (x4*y5-x5*y4)*z3) +x2*(w3*(y4*z5-y5*z4) +y3*(w5*z4-w4*z5) -    (w5*y4-w4*y5)*z3) -y1*(w2*(x4*z5+x3*(z4-z5) -x5*z4- (x4-x5)*z3)    -w3*(x4*z5-x5*z4) +x2*(-w4*z5-w3*(z4-z5) +w5*z4+ (w4-w5)*z3)    -x3*(w5*z4-w4*z5) + (w5*x4-w4*x5)*z3- (-w4*x5-w3*(x4-x5) +w5*x4+    (w4-w5)*x3)*z2) -y2*(w3*(x4*z5-x5*z4) +x3*(w5*z4-w4*z5) -    (w5*x4-w4*x5)*z3) + (w3*(x4*y5-x5*y4) +x3*(w5*y4-w4*y5) -    (w5*x4-w4*x5)*y3)*z2+ (w2*(x4*y5+x3*(y4-y5) -x5*y4- (x4-x5)*y3)    -w3*(x4*y5-x5*y4) +x2*(-w4*y5-w3*(y4-y5) +w5*y4+ (w4-w5)*y3)    -x3*(w5*y4-w4*y5) + (w5*x4-w4*x5)*y3- (-w4*x5-w3*(x4-x5) +w5*x4+    (w4-w5)*x3)*y2)*z1) - (z1^2+y1^2+x1^2+w1^2)*(-w2*(x3*(y4*z5-y5*z4)    -y3*(x4*z5-x5*z4) + (x4*y5-x5*y4)*z3) +x2*(w3*(y4*z5-y5*z4)    +y3*(w5*z4-w4*z5) - (w5*y4-w4*y5)*z3) -y2*(w3*(x4*z5-x5*z4)    +x3*(w5*z4-w4*z5) - (w5*x4-w4*x5)*z3) + (w3*(x4*y5-x5*y4)    +x3*(w5*y4-w4*y5) - (w5*x4-w4*x5)*y3)*z2)) == 0) {    print "are in the surface of a 4D sphere";} else {    print "are NOT on a 4D sphere surface";}