Divisors

We are interested in the divisors of a given natural number $n$. Let $D(n)$ denote the set of all divisors of $n$. We are given an expression built from constants taken from $D(n)$, variables that may take any value in $D(n)$, and two binary functions that compute the greatest common divisor and the least common multiple.

For a given expression, decide whether its value is the same for every possible assignment of values to the variables, that is, whether the expression denotes a constant function.

The first line contains an integer $t$ ($1 \le t \le 1000$), the number of test cases. Each of the next $t$ lines describes one test case.

Each description starts with an integer $n$ ($1 \le n \le 10^{18}$), followed by the description of the expression. An expression is a constant, a variable, or a function application.

• Each number is a constant and is a positive divisor of $n$.
• A variable is a sequence of at most $5$ lowercase English letters; identical sequences denote the same variable.
• The names NWD and NWW denote the functions computing the greatest common divisor and the least common multiple, respectively. A function name is followed by a single space and then the space-separated descriptions of its two arguments, each of which is itself an expression (so the description is recursive).

The total size of the input does not exceed $2$ MB.

Print $t$ lines, one answer per test case. For each test case print TAK (Polish for yes) if the expression denotes a constant function regardless of the variable values, and NIE (Polish for no) otherwise.