CF1455A Strange Functions

Let's define a function $ f(x) $ ( $ x $ is a positive integer) as follows: write all digits of the decimal representation of $ x $ backwards, then get rid of the leading zeroes. For example, $ f(321) = 123 $ , $ f(120) = 21 $ , $ f(1000000) = 1 $ , $ f(111) = 111 $ . Let's define another function $ g(x) = \dfrac{x}{f(f(x))} $ ( $ x $ is a positive integer as well). Your task is the following: for the given positive integer $ n $ , calculate the number of different values of $ g(x) $ among all numbers $ x $ such that $ 1 \le x \le n $ .

The first line contains one integer $ t $ ( $ 1 \le t \le 100 $ ) — the number of test cases. Each test case consists of one line containing one integer $ n $ ( $ 1 \le n < 10^{100} $ ). This integer is given without leading zeroes.

For each test case, print one integer — the number of different values of the function $ g(x) $ , if $ x $ can be any integer from $ [1, n] $ .

Explanations for the two first test cases of the example: 1. if $ n = 4 $ , then for every integer $ x $ such that $ 1 \le x \le n $ , $ \dfrac{x}{f(f(x))} = 1 $ ; 2. if $ n = 37 $ , then for some integers $ x $ such that $ 1 \le x \le n $ , $ \dfrac{x}{f(f(x))} = 1 $ (for example, if $ x = 23 $ , $ f(f(x)) = 23 $ , $ \dfrac{x}{f(f(x))} = 1 $ ); and for other values of $ x $ , $ \dfrac{x}{f(f(x))} = 10 $ (for example, if $ x = 30 $ , $ f(f(x)) = 3 $ , $ \dfrac{x}{f(f(x))} = 10 $ ). So, there are two different values of $ g(x) $ .