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 . 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 ). Print a single integer, the answer to the problem. 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 .