Fibonacci String

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For a string $S$ let the unique set of characters that occur in it one or more times be $C$. Consider a permutation of the elements of $C$ as $(c_1, c_2, c_3 ... )$. Let $f(c)$ be the number of times $c$ occurs in $S$. If any such permutation of the elements of $C$ satisfies $f(c_i) = f(c_{i1}) + f(c_{i2})$ for all $i \ge 3$, the string is said to be a **dynamic string**. Mr Bancroft is given the task to check if the string is dynamic, but he is busy playing with sandpaper. Would you help him in such a state? Note that if the number of distinct characters in the string is less than 3, i.e. if $C < 3$, then the string is always dynamic. ###Input:  First line will contain $T$, number of testcases. Then the testcases follow.  Each testcase contains of a single line of input, a string $S$. ###Output: For each testcase, output in a single line "**Dynamic**" if the given string is dynamic, otherwise print "**Not**". (Note that the judge is case sensitive) ###Constraints  $1 \leq T \leq 10$  $1 \leq S \leq 10^5$  $S$ contains only lower case alphabets: $a$, $b$, ..., $z$ ###Sample Input: 3 aaaabccc aabbcc ppppmmnnoooopp ###Sample Output: Dynamic Not Dynamic ###Explanation:  **Testase 1:** For the given string, $C = \{a, b, c\}$ and $f(a)=4, f(b)=1, f(c)=3$. $f(a) = f(c) + f(b)$ so the permutation $(b, c, a)$ satisfies the requirement.  **Testcase 2:** Here too $C = \{a, b, c\}$ but no permutation satisfies the requirement of a dynamic string.  **Testcase 3:** Here $C = \{m, n, o, p\}$ and $(m, n, o, p)$ is a permutation that makes it a dynamic string.Author:  avijit_agarwal 
Editorial  https://discuss.codechef.com/problems/CLFIBD 
Tags  avijit_agarwal, cakewalk, cole2018, string 
Date Added:  31032018 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.5, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, CLOJ, COB, FS 
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