Sqrt Bo

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 131072/131072 K (Java/Others)

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

Hint

wange2014

Source

2016 Multi-University Training Contest 3

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