Narcissistic Number Check

Problem Description

A "narcissistic number" (also called an Armstrong number) is an $N$-digit number whose $N$-th powers of its decimal digits sum to the number itself. For example, $153$ is a $3$-digit number, and the sum of the cubes of its digits is $1^3+5^3+3^3=153$, so $153$ is narcissistic; $1634$ is a $4$-digit number, and the sum of the fourth powers of its digits is $1^4+6^4+3^4+4^4=1634$, so $1634$ is narcissistic. Now, given several positive integers, determine whether each of them is a narcissistic number.

Input Format

The first line of input is a positive integer $M$, the number of integers to be judged. It is guaranteed that $1 \le M \le 100$.

The following $M$ lines each contain one integer to be judged. These integers are all less than $10^8$.

Output Format

Output $M$ lines. For each corresponding integer, if it is a narcissistic number output the uppercase letter T, otherwise output the uppercase letter F.

Hint: you do not need to wait for all input to finish before outputting; you may judge and output each number as it is read, then read the next.

Sample Input 1

3
152
111
153

Sample Output 1

F
F
T

Sample Input 2

5
8208
548834
88593477
12345
5432

Sample Output 2

T
T
T
F
F

Sample Explanation

In the first sample, three numbers are input: $152$, $111$ and $153$. For $152$, it is a $3$-digit number, and $1^3+5^3+2^3=1+125+8=134$, which is not equal to $152$, so output F. For $111$, $1^3+1^3+1^3=3$, not equal to $111$, output F. For $153$, $1^3+5^3+3^3=1+125+27=153$, equal to itself, so output T.

Constraints

$1 \le M \le 100$

Each integer to be judged is less than $10^8$.