D. Yet Another Problem On a Subsequencetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe sequence of integers a_1, a_2, \dots, a_k is called a good array if a_1 = k - 1 and a_1 > 0. For example, the sequences [3, -1, 44, 0], [1, -99] are good arrays, and the sequences [3, 7, 8], [2, 5, 4, 1], [0] — are not.A sequence of integers is called good if it can be divided into a positive number of good arrays. Each good array should be a subsegment of sequence and each element of the sequence should belong to exactly one array. For example, the sequences [2, -3, 0, 1, 4], [1, 2, 3, -3, -9, 4] are good, and the sequences [2, -3, 0, 1], [1, 2, 3, -3 -9, 4, 1] — are not.For a given sequence of numbers, count the number of its subsequences that are good sequences, and print the number of such subsequences modulo 998244353.InputThe first line contains the number n~(1 \le n \le 10^3) — the length of the initial sequence. The following line contains n integers a_1, a_2, \dots, a_n~(-10^9 \le a_i \le 10^9) — the sequence itself.OutputIn the single line output one integer — the number of subsequences of the original sequence that are good sequences, taken modulo 998244353.ExamplesInput32 1 1Output2Input41 1 1 1Output7NoteIn the first test case, two good subsequences — [a_1, a_2, a_3] and [a_2, a_3].In the second test case, seven good subsequences — [a_1, a_2, a_3, a_4], [a_1, a_2], [a_1, a_3], [a_1, a_4], [a_2, a_3], [a_2, a_4] and [a_3, a_4].
Input32 1 1
Output2
['combinatorics', 'dp', '*1900']