Andi is a young and prominent detective in the police force. His ability to track down criminals, uncover the truth, and solve cases never ceases to amaze all of his colleagues. One day, he is faced with a suspicious eyewitness testimony when working on a certain case. In usual cases, Andi simply ignores such unreliable testimony; however, in this case, the eyewitness testimony is too important to be ignored. To resolve this situation, Andi has to rely on technology, i.e. using a lie detector.
Andi proceeds to use a lie detector to detect whether the eyewitness testimony is true. However, Andi notices that the lie detector he used might have been tampered, thus, he employs a second lie detector to detect whether the first lie detector's result is correct. This situation happens repeatedly such that Andi ends up employing $N$ lie detectors in total. The $i^(t h)$ lie detector reports the truth of the $(i -1)^(t h)$ lie detector for $i = 2.. N$, and the $1^(s t)$ lie detector reports the truth of the eyewitness testimony.
In the end, Andi knows that the last ($N^(t h)$) lie detector has not been tampered and always report the truth correctly. Now, he needs to determine whether the eyewitness testimony is true given the result of all lie detectors.
For example, let $N = 4$ and the lie detectors result are $(texttt(L I E), texttt(L I E), texttt(T R U T H), texttt(T R U T H))$.
Therefore, the eyewitness testimony in this example is true.
Input begins with a line containing an integer $N$ ($2 <= N <= 100000$). The next $N$ lines, each contains a string $S_i$ (either _TRUTH_ or _LIE_) representing the output of the $i^(t h)$ lie detector for $i = 1.. N$ respectively.
Output contains a string _TRUTH_ or _LIE_ in a line whether the eyewitness testimony is true or false.
_Explanation for the sample input/output #1_
This sample is illustrated in the problem description above.
## Input
Input begins with a line containing an integer $N$ ($2 <= N <= 100000$). The next $N$ lines, each contains a string $S_i$ (either _TRUTH_ or _LIE_) representing the output of the $i^(t h)$ lie detector for $i = 1.. N$ respectively.
## Output
Output contains a string _TRUTH_ or _LIE_ in a line whether the eyewitness testimony is true or false.
[samples]
## Note
_Explanation for the sample input/output #1_This sample is illustrated in the problem description above.
**Definitions**
Let $ T \in \mathbb{Z}^+ $ be the number of test cases.
For each test case:
- Let $ n \in \mathbb{Z}^+ $ be the number of moves.
- Let $ R, r \in \mathbb{R}^+ $ be the radii of the table and robot, respectively, with $ r < R $.
- Let $ \vec{d}_i = (dx_i, dy_i) \in \mathbb{Z}^2 $ for $ i \in \{1, \dots, n\} $ be the displacement vectors of the moves, with $ |dx_i| + |dy_i| > 0 $.
- Let $ \vec{p}_0 = (S_x, S_y) \in \mathbb{R}^2 $ be the starting position (center of the robot).
- Let $ \vec{p}_k = \vec{p}_0 + \sum_{j=1}^k \vec{d}_j $ be the position of the robot's center after $ k $ moves, for $ k \in \{0, \dots, n\} $.
**Constraints**
For all $ k \in \{0, 1, \dots, n\} $:
$$
\|\vec{p}_k\| \le R - r - 10^{-4}
$$
**Objective**
Find any $ \vec{p}_0 = (S_x, S_y) \in \mathbb{R}^2 $ such that the above constraint holds for all $ k $.