You generate real numbers $*s*_{1}, *s*_{2}, ..., *s*_{*n*}$ as follows:

• $*s*_{0} = 0$;
• $*s*_{*i*} = *s*_{*i* - 1} + *t*_{*i*}$, where $*t*_{*i*}$ is a real number chosen independently uniformly at random between 0 and 1, inclusive.

You are given real numbers $*x*_{1}, *x*_{2}, ..., *x*_{*n*}$. You are interested in the probability that $*s*_{*i*} ≤ *x*_{*i*}$ 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 $*x*_{1}, *x*_{2}, ..., *x*_{*n*}$, given with at most six digits after the decimal point ($0 < *x*_{*i*} ≤ *n*$).

Output

Print a single integer, the answer to the problem.

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 $*x*_{1}$ itself.

In the third example, the sought probability is $3 / 8$.