Training Site

# Hopscotch

Input: Standard Input (stdin)
Output: Standard Output (stdout)
Memory limit: 32 megabytes
Time limit: 5.0 seconds

While it commonly refers to the popular children's jumping game, Hopscotch is also the name of the most adorable rabbit (in the world). Hopscotch is a simple creature, and spends his entire existence in one of three states: sleeping, exploring, and nibbling.

• When Hopscotch is sleeping, he can either keep sleeping or wake up and begin exploring.
• When Hopscotch is exploring, he will inevitably find something he considers to be edible, and begin nibbling.
• When Hopscotch is nibbling, he will either return to exploring or spontaneously begin sleeping.

We have been trying to document Hopscotch's day. We've recorded a log of $N$ states that we've observed Hopscotch in. Unfortunately, Hopscotch is very fast and we're worried that we might have missed recording a state. Given our log of the $N$ recorded states, please tell us whether they describe a plausible sequence (the state transitions follow the rules described above) or whether the sequence described is impossible. The sequence may begin in any state.

## Input

The first line will contain a single non-negative integer $N$, describing the number of states that have been recorded in the log.

The following $N$ lines each contain a single character representing the recorded state. 'S' represents sleeping, 'E' represents exploring, and 'N' represents nibbling.

## Output

If the sequence described is plausible, output a single line containing the text plausible (without quotes).

If the sequence described is impossible, output a single line containing the text impossible (without quotes).

• Subtask 1 (20%): $N \leq 1,000$, the sequence only contains entries of sleeping.
• Subtask 2 (30%): $N \leq 1,000$, the sequence contains no entries of sleeping.
• Subtask 3 (50%): $N \leq 1,000,000$, no further restrictions apply.
• ### Sample Input 1

10
S
S
S
E
N
S
S
S
E
N


### Sample Output 1

plausible

• ### Sample Input 2

10
E
N
N
E
E
N
S
S
E
N


### Sample Output 2

impossible