There are n+2 towns situated on an arrange line, numbered from 0 to n+1. The I-th town is situated at the point I. You fabricate a radio pinnacle in every one of the towns 1,2,… ,n with likelihood 12 (these occasions are autonomous). From that point forward, you need to set the sign power on each pinnacle to some integer from 1 to n (signal powers are not really the equivalent, yet in addition not really unique)
Correct answer will be upvoted else Multiple Downvoted. Computer science.
There are n+2 towns situated on an arrange line, numbered from 0 to n+1. The I-th town is situated at the point I.
You fabricate a radio pinnacle in every one of the towns 1,2,… ,n with likelihood 12 (these occasions are autonomous). From that point forward, you need to set the sign power on each pinnacle to some integer from 1 to n (signal powers are not really the equivalent, yet in addition not really unique). The sign from a pinnacle situated in a town I with signal power p arrives at each city c to such an extent that |c−i|<p.
Subsequent to building the pinnacles, you need to pick signal powers so that:
towns 0 and n+1 don't get any transmission from the radio pinnacles;
towns 1,2,… ,n get signal from precisely one radio pinnacle each.
For instance, if n=5, and you have assembled the pinnacles in towns 2, 4 and 5, you might set the sign force of the pinnacle around 2 to 2, and the sign force of the pinnacles in towns 4 and 5 to 1. That way, towns 0 and n+1 don't get the sign from any pinnacle, towns 1, 2 and 3 get the sign from the pinnacle around 2, town 4 gets the sign from the pinnacle around 4, and town 5 gets the sign from the pinnacle around 5.
Compute the likelihood that, in the wake of building the pinnacles, you will have a way of setting signal abilities to meet all imperatives.
Input
The sole line of the input contains one integer n (1≤n≤2⋅105).
Output
Print one integer — the likelihood that there will be a way of setting signal powers so all limitations are met, taken modulo 998244353.
Officially, the likelihood can be communicated as a final portion xy. You need to print the worth of x⋅y−1mod998244353, where y−1 is an integer with the end goal that y⋅y−1mod998244353=1.
Step by step
Solved in 4 steps with 1 images
