#D12099. Don't Exceed
Don't Exceed
Don't Exceed
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.
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.
Examples
Input
4 1.00 2 3.000000 4.0
Output
1
Input
1 0.50216
Output
342677322
Input
2 0.5 1.0
Output
623902721
Input
6 0.77 1.234567 2.1 1.890 2.9999 3.77
Output
859831967
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.
inputFormat
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).
outputFormat
Output
Print a single integer, the answer to the problem.
Examples
Input
4 1.00 2 3.000000 4.0
Output
1
Input
1 0.50216
Output
342677322
Input
2 0.5 1.0
Output
623902721
Input
6 0.77 1.234567 2.1 1.890 2.9999 3.77
Output
859831967
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.
样例
1
0.50216
342677322