Homework

In informatics class today, Petya learned about numeral systems with different bases. A base-$k$ numeral system uses digits with weights from 0 to $k-1$; the first 10 digits are written with ordinary digits, and beyond that Latin letters and other symbols are also used.

Now Petya is trying to solve the following homework. Numbers $x$, $y$, and $z$ written with decimal digits are given. Find every base $k$ such that all digits used in the numbers exist in this numeral system and, when $x$, $y$, and $z$ are treated as numbers written in base $k$, the product of $x$ and $y$ equals $z$.

Petya started solving this problem and discovered that under some conditions infinitely many different values of $k$ work. He decided to first determine whether this case occurs. Help him find out.

The first line contains the number $t$, the number of tests in the input ($1 \le t \le 1000$).

Then follow $t$ test descriptions. Each test is described by three lines containing the numbers $x$, $y$, and $z$, respectively. Each of these numbers is positive, consists only of decimal digits, and has no leading zeros. The length of each of $x$ and $y$ does not exceed 100, and the length of $z$ does not exceed 200.

For each test, output its answer on a separate line: Infinity if there are infinitely many values of $k$ such that treating the input numbers as written in base $k$ makes the product of $x$ and $y$ equal $z$, or Finite if there are finitely many such $k$.