Don't Exceed
Description
You generate real numbers s1, s2, ..., sn as follows:
- s0 = 0;
- si = si - 1 + ti, where ti is a real number chosen independently uniformly at random between 0 and 1, inclusive.
You are given real numbers x1, x2, ..., xn. You are interested in the probability that si ≤ xi is true for all i simultaneously.
It can be shown that this can be represented as 
, where P and Q are coprime integers, and 
. Print the value of P·Q - 1 modulo 998244353.
The first line contains integer n (1 ≤ n ≤ 30).
The next n lines contain real numbers x1, x2, ..., xn, given with at most six digits after the decimal point (0 < xi ≤ n).
Print a single integer, the answer to the problem.
Input
The first line contains integer n (1 ≤ n ≤ 30).
The next n lines contain real numbers x1, x2, ..., xn, given with at most six digits after the decimal point (0 < xi ≤ n).
Output
Print a single integer, the answer to the problem.
4<br>1.00<br>2<br>3.000000<br>4.0<br>
1<br>0.50216<br>
2<br>0.5<br>1.0<br>
6<br>0.77<br>1.234567<br>2.1<br>1.890<br>2.9999<br>3.77<br>
1<br>
342677322<br>
623902721<br>
859831967<br>
Note
In the first example, the sought probability is 1 since the sum of i real numbers which don't exceed 1 doesn't exceed i.
In the second example, the probability is x1 itself.
In the third example, the sought probability is 3 / 8.