Cantor Set

Interview

Time limit1sMemory limit128 MB

Summary

Given a decimal x between 0 and 1 that ends within 6 fractional digits, decide whether x lies in the Cantor set, that is, whether some ternary expansion of x avoids the digit 1.

Level: Medium5 of 10
Topics: Math, Number theory, Implementation, Combinatorics
Solved: No attempts yet

Problem

The ternary expansion of a number is that number written in base 3. A number can have more than one ternary expansion. A ternary expansion is indicated with a subscript 3. For example, $1 = 1_3 = 0.222\ldots_3$ , and $0.875 = 0.212121\ldots_3$ .

The Cantor set is defined as the real numbers between 0 and 1 inclusive that have a ternary expansion that does not contain a 1. If a number has more than one ternary expansion, it is enough for a single one to not contain a 1.

For example, $0 = 0.000\ldots_3$ and $1 = 0.222\ldots_3$ , so they are in the Cantor set. But $0.875 = 0.212121\ldots_3$ and this is its only ternary expansion, so it is not in the Cantor set.

Your task is to determine whether a given number is in the Cantor set.

Input

The input consists of several test cases.

Each test case consists of a single line containing a number $x$ written in decimal notation, with $0 \le x \le 1$ , and having at most 6 digits after the decimal point.

The last line of input is END. This is not a test case.

Output

For each test case, output MEMBER if $x$ is in the Cantor set, and NON-MEMBER if $x$ is not in the Cantor set.

Examples1

Example 1
Input
```
0
1
0.875
END
```
Expected output
```
MEMBER
MEMBER
NON-MEMBER
```