SSN 1

In Brazil, the equivalent to Social Security Number is usually called CPF. It is composed by 11 digits and the two lasts are function of the nine previous. In this way, if a person informs a CPF, by mistake or on purpose, it is possible to find out. Let us introduce some notation. Let a CPF be

a₁a₂a₃.a₄a₅a₆.a₇a₈a₉-b₁b₂

To get b₁, one can multiply a₁ by 1, a₂ by 2, a₃ by 3, so on, up to a₉ by 9 and sum these results. Then, b₁ is the remaining of this number when divided by 11, or 0 in case the remaining is 10.

Analogous, to get b₂, one can multiply a₁ by 9, a₂ by 8, a₃ by 7, so on, up to a₉ by 1 and sum these results. Then, b₂ is the remaining of this number when divided by 11, or 0 in case the remaining is 10.

Given a CPF number, you have to tell whether it is valid or not.