Kakezan

Taro is an elementary school student who has just learned multiplication. Somehow he has taken a liking to it, and whenever he sees a number he wants to multiply. Lately he seems to enjoy applying the following procedure to nonnegative integers.

• Step 1. If a nonnegative integer $n$ has one digit in decimal, the procedure ends. Otherwise, go to step 2.
• Step 2. When a integer $n \ge 10$ is written in decimal, it can be split into two numbers by cutting between any two digits (for example, $2012 \to 20, 12$). Among all such cuts, take the two resulting numbers, multiply them, and use the largest product as the next $n$, then return to step 1. See "Notes on step 2" below for details.

Taro likes this procedure, but for large numbers he cannot predict how many times step 2 must be repeated, and he thinks it might even have to be repeated infinitely many times. So he asked you, his older brother in university, how many times step 2 must be performed for a nonnegative integer $n$.

Your task is, given $Q$ nonnegative integers N1..NQ, to determine for each integer how many times step 2 is performed before the procedure ends. If infinitely many repetitions are needed, output -1.

When splitting, cases where the result has a leading zero must also be considered. For example, when $n=1024$, computing $1*024$, $10*24$, and $102*4$ gives 24, 240, and 408 respectively, so 408 is chosen and becomes the next $n$.

Q
N1
N2
...
NQ

• Q is the number of nonnegative integers given.
• Ni is the i-th nonnegative integer Taro is curious about.

Output Q integers separated by newlines.

R1
R2
..
RQ

• Ri is the number of times step 2 is executed for Ni before the procedure ends.
• If step 2 must be executed infinitely many times for Ni, Ri is -1.

• 1≤Q≤100
• 0≤Ni≤106