Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-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 tags yet

No tag edit access

G. Graphic Settings

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputRecently Ivan bought a new computer. Excited, he unpacked it and installed his favourite game. With his old computer Ivan had to choose the worst possible graphic settings (because otherwise the framerate would be really low), but now he wants to check, maybe his new computer can perform well even with the best possible graphics?

There are *m* graphics parameters in the game. *i*-th parameter can be set to any positive integer from 1 to *a*_{i}, and initially is set to *b*_{i} (*b*_{i} ≤ *a*_{i}). So there are different combinations of parameters. Ivan can increase or decrease any of these parameters by 1; after that the game will be restarted with new parameters (and Ivan will have the opportunity to check chosen combination of parameters).

Ivan wants to try all *p* possible combinations. Also he wants to return to the initial settings after trying all combinations, because he thinks that initial settings can be somehow best suited for his hardware. But Ivan doesn't really want to make a lot of restarts.

So he wants you to tell the following:

- If there exists a way to make exactly
*p*changes (each change either decreases or increases some parameter by 1) to try all possible combinations and return to initial combination, then Ivan wants to know this way. - Otherwise, if there exists a way to make exactly
*p*- 1 changes to try all possible combinations (including the initial one), then Ivan wants to know this way.

Help Ivan by showing him the way to change parameters!

Input

The first line of input contains one integer number *m* (1 ≤ *m* ≤ 6).

The second line contains *m* integer numbers *a*_{1}, *a*_{2}, ..., *a*_{m} (2 ≤ *a*_{i} ≤ 1000). It is guaranteed that .

The third line contains *m* integer numbers *b*_{1}, *b*_{2}, ..., *b*_{m} (1 ≤ *b*_{i} ≤ *a*_{i}).

Output

If there is a way to make exactly *p* changes (each change either decreases or increases some parameter by 1) to try all possible combinations and return to initial combination, then output Cycle in the first line. Then *p* lines must follow, each desribing a change. The line must be either inc x (increase parameter *x* by 1) or dec x (decrease it).

Otherwise, if there is a way to make exactly *p* - 1 changes to try all possible combinations (including the initial one), then output Path in the first line. Then *p* - 1 lines must follow, each describing the change the same way as mentioned above.

Otherwise, output No.

Examples

Input

1

3

1

Output

Path

inc 1

inc 1

Input

1

3

2

Output

No

Input

2

3 2

1 1

Output

Cycle

inc 1

inc 1

inc 2

dec 1

dec 1

dec 2

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Dec/12/2017 17:27:04 (c5).

Desktop version, switch to mobile version.

User lists

Name |
---|