The sequence of integers a_1, a_2, ..., 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.

Input

The first line contains the number n~(1 ≤ n ≤ 10^3) — the length of the initial sequence. The following line contains n integers a_1, a_2, ..., a_n~(-10^9 ≤ a_i ≤ 10^9) — the sequence itself.

Output

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

Examples

Input

3
2 1 1


Output

2


Input

4
1 1 1 1


Output

7

Note

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].
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e3 + 7;
const int mod = 998244353;
int a[maxn], c[maxn][maxn];
long long dp[maxn];
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]), dp[i] = 1;
  for (int i = 0; i <= n; i++) {
    c[i][0] = 1;
    for (int j = 1; j <= i; j++)
      c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % mod;
  }
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    if (i + a[i] <= n && a[i] > 0) {
      ans = (ans + dp[i] * c[n - i][a[i]]) % mod;
      for (int j = i + a[i]; j <= n; j++)
        dp[j + 1] = (dp[j + 1] + dp[i] * c[j - i][a[i]]) % mod;
    }
  }
  cout << ans;
  return 0;
}
