Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. Suspects

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAs Sherlock Holmes was investigating a crime, he identified *n* suspects. He knows for sure that exactly one of them committed the crime. To find out which one did it, the detective lines up the suspects and numbered them from 1 to *n*. After that, he asked each one: "Which one committed the crime?". Suspect number *i* answered either "The crime was committed by suspect number *a*_{i}", or "Suspect number *a*_{i} didn't commit the crime". Also, the suspect could say so about himself (*a*_{i} = *i*).

Sherlock Holmes understood for sure that exactly *m* answers were the truth and all other answers were a lie. Now help him understand this: which suspect lied and which one told the truth?

Input

The first line contains two integers *n* and *m* (1 ≤ *n* ≤ 10^{5}, 0 ≤ *m* ≤ *n*) — the total number of suspects and the number of suspects who told the truth. Next *n* lines contain the suspects' answers. The *i*-th line contains either "+*a*_{i}" (without the quotes), if the suspect number *i* says that the crime was committed by suspect number *a*_{i}, or "-*a*_{i}" (without the quotes), if the suspect number *i* says that the suspect number *a*_{i} didn't commit the crime (*a*_{i} is an integer, 1 ≤ *a*_{i} ≤ *n*).

It is guaranteed that at least one suspect exists, such that if he committed the crime, then exactly *m* people told the truth.

Output

Print *n* lines. Line number *i* should contain "Truth" if suspect number *i* has told the truth for sure. Print "Lie" if the suspect number *i* lied for sure and print "Not defined" if he could lie and could tell the truth, too, depending on who committed the crime.

Examples

Input

1 1

+1

Output

Truth

Input

3 2

-1

-2

-3

Output

Not defined

Not defined

Not defined

Input

4 1

+2

-3

+4

-1

Output

Lie

Not defined

Lie

Not defined

Note

The first sample has the single person and he confesses to the crime, and Sherlock Holmes knows that one person is telling the truth. That means that this person is telling the truth.

In the second sample there are three suspects and each one denies his guilt. Sherlock Holmes knows that only two of them are telling the truth. Any one of them can be the criminal, so we don't know for any of them, whether this person is telling the truth or not.

In the third sample the second and the fourth suspect defend the first and the third one. But only one is telling the truth, thus, the first or the third one is the criminal. Both of them can be criminals, so the second and the fourth one can either be lying or telling the truth. The first and the third one are lying for sure as they are blaming the second and the fourth one.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/24/2019 01:18:17 (h2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|