Sqrt Bo

Problem Description

Let's define the function $f(n)=\lfloor \sqrt{n}\rfloor$. Bo wanted to know the minimum number $y$ which satisfies $f^y(n)=1$. note:$f^1(n)=f(n),f^y(n)=f(f^{y-1}(n))$ It is a pity that Bo can only use 1 unit of time to calculate this function each time. And Bo is impatient, he cannot stand waiting for longer than 5 units of time. So Bo wants to know if he can solve this problem in 5 units of time.

Input

This problem has multi test cases(no more than $120$). Each test case contains a non-negative integer $n(n<10^{100})$.

Output

For each test case print a integer - the answer $y$ or a string "TAT" - Bo can't solve this problem.

Sample Input

233
233333333333333333333333333333333333333333333333333333333

Sample Output

3
TAT

Author

绍兴一中

Source

2016 Multi-University Training Contest 3