Rohan needs your help to solve the following problem.

For $2$ integers $X$ and $Y$:

• $f(X,Y) = max(NumOfDigits(X), NumOfDigits(Y))$where the function $NumOfDigits(x)$ represents the number of digits present in the decimal notation of $x$.

Rohan has been given an integer $N$. He has to find the minimum value of $f(X, Y)$ as $(X, Y)$ ranges over all pairs of positive integers such that $N = X * Y$.

Constraints

$1 \le N \le 10^{10}$
$1 \le T \le 10^2$

Input Format

The first line of the input contains an integer $T$ denoting the number of test cases. The description of $T$ test cases is as follows. The first line of each test case contains the number $N$.

Output Format

Find the minimum value of $f(X, Y)$ as $(X, Y)$ ranges over all pairs of positive integers such that $N = X * Y$.