FA

Time limit1sMemory limit128 MB

Summary

Starting from a huge integer x, repeatedly replace it with (first digit) times (digit count) and report whether the sequence eventually cycles forever.

Level: Medium4 of 10
Topics: Math, Implementation, Simulation, Hash map
Solved: No attempts yet

Problem

The function $F(x)$ returns the first digit of $x$ multiplied by the number of digits of $x$ .

For example, if $x = 932$ , the first digit is $9$ and the number of digits is $3$ , so $F(932) = 9 \times 3 = 27$ .

Apply $F$ to the given $x$ , then apply $F$ to the result, and keep repeating. If the same number keeps coming out from some point on, $x$ is called an FA number.

Decide whether $x$ is an FA number.

Input

The first line contains an integer $x$ ( $0 \le x \le 10^{100}$ ).

Output

Print FA if $x$ is an FA number, and NFA otherwise.

Examples4

Example 1
Input
```
932
```
Expected output
```
FA
```
Example 2
Input
```
0
```
Expected output
```
FA
```
Example 3
Input
```
7
```
Expected output
```
FA
```
Example 4
Input
```
10
```
Expected output
```
FA
```