A. MIT Time
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Busy Beaver arrived to his MIT class late! However, thanks to "MIT time", all classes actually start $$$5$$$ minutes later than the posted time.

Busy Beaver wants to make a generalization of this system. Namely, if someone arrives $$$N$$$ minutes late to an event, then:

  • if $$$N \le 5$$$, they arrived on "MIT time";
  • if $$$5 \lt N \le 25$$$, they arrived on "MIT$$$^2$$$ time";
  • if $$$25 \lt N \le 125$$$, they arrived on "MIT$$$^3$$$ time";
  • and so on. Formally, if $$$k \ge 2$$$, then "MIT$$$^k$$$ time" is when $$$5^{k-1} \lt N \le 5^k$$$.
Given $$$N$$$, determine on which of "MIT time", "MIT$$$^2$$$ time", etc. this person arrived at.
Input

The first line contains a single integer $$$T$$$ $$$(1 \leq T \leq 10^5)$$$ — the number of test cases.

The only line of each test case contains a single integer $$$N$$$ ($$$1 \le N \le 10^9$$$) — the number of minutes late to an event the person is.

Output

For each test case, output a single line that consists of either "MIT time" or "MIT^$$$k$$$ time" for some integer $$$k \geq 2$$$, corresponding to the time this person arrives at.

Example
Input
5
4
5
13
126
1
Output
MIT time
MIT time
MIT^2 time
MIT^4 time
MIT time
Note

In the first test case, $$$N = 4$$$, which is at most $$$5$$$, so this is MIT time.

In the second test case, $$$N = 5$$$, which is equal to $$$5$$$, so this is also MIT time.

In the third test case, $$$N = 13$$$, which is not more than $$$25$$$ but more than $$$5$$$, so this is MIT$$$^2$$$ time.

The fourth test case, $$$N = 126$$$, which is not more than $$$5^4=625$$$ but more than $$$5^3 = 125$$$, so this is MIT$$$^4$$$ time.