Minimum 11 Multiples

The polynomial f(x)=ax6+bx5+cx4+dx3+ex2+fx1+g f(x) = ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx^1 + g has non-zero integral coefficients, and f(n)f(n) is a multiple of 1111 whenever nn is an integer. What is the minimum number of coefficients: a,b,c,d,e,f,ga, b, c, d, e, f, g, that must be a multiple of 1111?

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