CF1000D Yet Another Problem On a Subsequence

The 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.

The 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.

In the single line output one integer — the number of subsequences of the original sequence that are good sequences, taken modulo 998244353.

In 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] $ .