Question: factor long highly structured polynomial

factor_problem.mw

I want to factor the following polynomial:

Teller := 2*i1^4*i2*i3+2*i1^4*i2*i4+2*i1^4*i2*i5+2*i1^4*i3*i4+2*i1^4*i3*i5+2*i1^4*i4*i5+4*i1^3*i2^2*i3+4*i1^3*i2^2*i4+4*i1^3*i2^2*i5+4*i1^3*i2*i3^2+6*i1^3*i2*i3*i4+6*i1^3*i2*i3*i5+4*i1^3*i2*i4^2+6*i1^3*i2*i4*i5+4*i1^3*i2*i5^2+4*i1^3*i3^2*i4+4*i1^3*i3^2*i5+4*i1^3*i3*i4^2+6*i1^3*i3*i4*i5+4*i1^3*i3*i5^2+4*i1^3*i4^2*i5+4*i1^3*i4*i5^2+2*i1^2*i2^3*i3+2*i1^2*i2^3*i4+2*i1^2*i2^3*i5+4*i1^2*i2^2*i3^2+6*i1^2*i2^2*i3*i4+6*i1^2*i2^2*i3*i5+4*i1^2*i2^2*i4^2+6*i1^2*i2^2*i4*i5+4*i1^2*i2^2*i5^2+2*i1^2*i2*i3^3+6*i1^2*i2*i3^2*i4+6*i1^2*i2*i3^2*i5+6*i1^2*i2*i3*i4^2+24*i1^2*i2*i3*i4*i5+6*i1^2*i2*i3*i5^2+2*i1^2*i2*i4^3+6*i1^2*i2*i4^2*i5+6*i1^2*i2*i4*i5^2+2*i1^2*i2*i5^3+2*i1^2*i3^3*i4+2*i1^2*i3^3*i5+4*i1^2*i3^2*i4^2+6*i1^2*i3^2*i4*i5+4*i1^2*i3^2*i5^2+2*i1^2*i3*i4^3+6*i1^2*i3*i4^2*i5+6*i1^2*i3*i4*i5^2+2*i1^2*i3*i5^3+2*i1^2*i4^3*i5+4*i1^2*i4^2*i5^2+2*i1^2*i4*i5^3+2*i1*i2^3*i3*i4+2*i1*i2^3*i3*i5+2*i1*i2^3*i4*i5+4*i1*i2^2*i3^2*i4+4*i1*i2^2*i3^2*i5+4*i1*i2^2*i3*i4^2+6*i1*i2^2*i3*i4*i5+4*i1*i2^2*i3*i5^2+4*i1*i2^2*i4^2*i5+4*i1*i2^2*i4*i5^2+2*i1*i2*i3^3*i4+2*i1*i2*i3^3*i5+4*i1*i2*i3^2*i4^2+6*i1*i2*i3^2*i4*i5+4*i1*i2*i3^2*i5^2+2*i1*i2*i3*i4^3+6*i1*i2*i3*i4^2*i5+6*i1*i2*i3*i4*i5^2+2*i1*i2*i3*i5^3+2*i1*i2*i4^3*i5+4*i1*i2*i4^2*i5^2+2*i1*i2*i4*i5^3+2*i1*i3^3*i4*i5+4*i1*i3^2*i4^2*i5+4*i1*i3^2*i4*i5^2+2*i1*i3*i4^3*i5+4*i1*i3*i4^2*i5^2+2*i1*i3*i4*i5^3+4*i1^3*i2*i3+4*i1^3*i2*i4+4*i1^3*i2*i5+4*i1^3*i3*i4+4*i1^3*i3*i5+4*i1^3*i4*i5+8*i1^2*i2^2*i3+8*i1^2*i2^2*i4+8*i1^2*i2^2*i5+8*i1^2*i2*i3^2+12*i1^2*i2*i3*i4+12*i1^2*i2*i3*i5+8*i1^2*i2*i4^2+12*i1^2*i2*i4*i5+8*i1^2*i2*i5^2+8*i1^2*i3^2*i4+8*i1^2*i3^2*i5+8*i1^2*i3*i4^2+12*i1^2*i3*i4*i5+8*i1^2*i3*i5^2+8*i1^2*i4^2*i5+8*i1^2*i4*i5^2+4*i1*i2^3*i3+4*i1*i2^3*i4+4*i1*i2^3*i5+8*i1*i2^2*i3^2+12*i1*i2^2*i3*i4+12*i1*i2^2*i3*i5+8*i1*i2^2*i4^2+12*i1*i2^2*i4*i5+8*i1*i2^2*i5^2+4*i1*i2*i3^3+12*i1*i2*i3^2*i4+12*i1*i2*i3^2*i5+12*i1*i2*i3*i4^2+48*i1*i2*i3*i4*i5+12*i1*i2*i3*i5^2+4*i1*i2*i4^3+12*i1*i2*i4^2*i5+12*i1*i2*i4*i5^2+4*i1*i2*i5^3+4*i1*i3^3*i4+4*i1*i3^3*i5+8*i1*i3^2*i4^2+12*i1*i3^2*i4*i5+8*i1*i3^2*i5^2+4*i1*i3*i4^3+12*i1*i3*i4^2*i5+12*i1*i3*i4*i5^2+4*i1*i3*i5^3+4*i1*i4^3*i5+8*i1*i4^2*i5^2+4*i1*i4*i5^3+4*i2^3*i3*i4+4*i2^3*i3*i5+4*i2^3*i4*i5+8*i2^2*i3^2*i4+8*i2^2*i3^2*i5+8*i2^2*i3*i4^2+12*i2^2*i3*i4*i5+8*i2^2*i3*i5^2+8*i2^2*i4^2*i5+8*i2^2*i4*i5^2+4*i2*i3^3*i4+4*i2*i3^3*i5+8*i2*i3^2*i4^2+12*i2*i3^2*i4*i5+8*i2*i3^2*i5^2+4*i2*i3*i4^3+12*i2*i3*i4^2*i5+12*i2*i3*i4*i5^2+4*i2*i3*i5^3+4*i2*i4^3*i5+8*i2*i4^2*i5^2+4*i2*i4*i5^3+4*i3^3*i4*i5+8*i3^2*i4^2*i5+8*i3^2*i4*i5^2+4*i3*i4^3*i5+8*i3*i4^2*i5^2+4*i3*i4*i5^3+i1^4+3*i1^3*i2+3*i1^3*i3+3*i1^3*i4+3*i1^3*i5+3*i1^2*i2^2+6*i1^2*i2*i3+6*i1^2*i2*i4+6*i1^2*i2*i5+3*i1^2*i3^2+6*i1^2*i3*i4+6*i1^2*i3*i5+3*i1^2*i4^2+6*i1^2*i4*i5+3*i1^2*i5^2+i1*i2^3+3*i1*i2^2*i3+3*i1*i2^2*i4+3*i1*i2^2*i5+3*i1*i2*i3^2+10*i1*i2*i3*i4+10*i1*i2*i3*i5+3*i1*i2*i4^2+10*i1*i2*i4*i5+3*i1*i2*i5^2+i1*i3^3+3*i1*i3^2*i4+3*i1*i3^2*i5+3*i1*i3*i4^2+10*i1*i3*i4*i5+3*i1*i3*i5^2+i1*i4^3+3*i1*i4^2*i5+3*i1*i4*i5^2+i1*i5^3+4*i2^2*i3*i4+4*i2^2*i3*i5+4*i2^2*i4*i5+4*i2*i3^2*i4+4*i2*i3^2*i5+4*i2*i3*i4^2+4*i2*i3*i5^2+4*i2*i4^2*i5+4*i2*i4*i5^2+4*i3^2*i4*i5+4*i3*i4^2*i5+4*i3*i4*i5^2

What is the best strategy using Maple(latest version)? In a previous, less complicated example, the polynomial could be not be factored in a single expression, but I was succesfull to factor it in multiple factors.

kind regards,

Harry Garst