FA

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

Medium4MathImplementationSimulationHash mapNo attempts yetTime limit1sMemory limit128 MB

Description

Examples4

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.