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 $a_1 \gt 0$. 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.

整数序列 $a_1, a_2, \dots, a_k$ 被称为好数组，当且仅当 $a_1 = k - 1$ 且 $a_1 \gt 0$。例如，序列 $[3, -1, 44, 0]$、$[1, -99]$ 是好数组；而序列 $[3, 7, 8]$、$[2, 5, 4, 1]$、$[0]$ 则不是。

一个整数序列被称为好序列，当且仅当它可以被划分为若干个（正整数个）好数组。每个好数组必须是该序列的一个连续子段，且序列中的每个元素恰好属于其中一个好数组。例如，序列 $[2, -3, 0, 1, 4]$、$[1, 2, 3, -3, -9, 4]$ 是好序列；而序列 $[2, -3, 0, 1]$、$[1, 2, 3, -3 -9, 4, 1]$ 则不是。

给定一个整数序列，求其所有子序列中是好序列的个数，并将结果对 $998244353$ 取模后输出。

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.

第一行包含一个整数 $n~(1 \le n \le 10^3)$ —— 初始序列的长度。
接下来的一行包含 $n$ 个整数 $a_1, a_2, \dots, a_n~(-10^9 \le a_i \le 10^9)$ —— 序列本身。

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

在单行输出一个整数——原序列中“好序列”子序列的个数，对 998244353 取模。

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 $[a_3, a_4]$.

在第一个测试用例中，有两个好数组：$[a_1, a_2, a_3]$ 和 $[a_2, a_3]$。

在第二个测试用例中，有七个好数组：$[a_1, a_2, a_3, a_4], [a_1, a_2], [a_1, a_3], [a_1, a_4], [a_2, a_3], [a_2, a_4]$ 和 $[a_3, a_4]$。