Code : Hop Sugoroku

#include <atcoder/modint>
#include <bits/stdc++.h>

using namespace std;

using namespace atcoder;
using mint = modint998244353;

int solve(vector<long long> &a) {
    int n = a.size();

    int rootn = sqrt(n);

    vector<mint> dp(n);
    vector<vector<mint>> delta(n, vector<mint>(rootn + 1, 0));
    dp[0] = 1;
    for (int i = 0; i < n; i++) {
        for (int j = 1; j <= rootn; j++) {
            dp[i] += delta[i][j];
        }

        if (a[i] > rootn) {
            for (int j = i + a[i]; j < n; j += a[i]) {
                dp[j] += dp[i];
            }
        } else if (i + a[i] < n) {
            delta[i + a[i]][a[i]] += dp[i];
        }

        for (int j = 1; j <= rootn; j++) {
            if (i + j < n) {
                delta[i + j][j] += delta[i][j];
            }
        }
    }

    mint ans = 0;
    for (int i = 0; i < n; i++) {
        ans += dp[i];
    }
    return ans.val();
}

int main() {
    int n;
    cin >> n;
    vector<long long> a(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    cout << solve(a) << endl;
    return 0;
}

#include <atcoder/modint>
#include <bits/stdc++.h>

using namespace std;

using namespace atcoder;
using mint = modint998244353;

int solve(vector<long long> &a) {
    int n = a.size();

    vector<mint> dp(n);
    dp[0] = 1;
    for (int i = 0; i < n; i++) {
        for (int j = i + a[i]; j < n; j += a[i]) {
            dp[j] += dp[i];
        }
    }
    mint ans = 0;
    for (int i = 0; i < n; i++) {
        ans += dp[i];
    }
    return ans.val();
}

int main() {
    int n;
    cin >> n;
    vector<long long> a(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    cout << solve(a) << endl;
    return 0;
}

#include <atcoder/modint>
#include <bits/stdc++.h>

using namespace std;

using namespace atcoder;
using mint = modint998244353;

int solve(vector<long long> &a) {
    int n = a.size();

    vector<mint> dp(n);
    vector<vector<mint>> delta(n, vector<mint>(n + 1, 0));
    dp[0] = 1;
    for (int i = 0; i < n; i++) {
        for (int j = 1; j <= n; j++) {
            dp[i] += delta[i][j];
        }

        if (i + a[i] < n) {
            delta[i + a[i]][a[i]] += dp[i];
        }

        for (int j = 1; j <= n; j++) {
            if (i + j < n) {
                delta[i + j][j] += delta[i][j];
            }
        }
    }

    mint ans = 0;
    for (int i = 0; i < n; i++) {
        ans += dp[i];
    }
    return ans.val();
}

int main() {
    int n;
    cin >> n;
    vector<long long> a(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    cout << solve(a) << endl;
    return 0;
}

#include <atcoder/modint>
#include <bits/stdc++.h>

using namespace std;

using namespace atcoder;
using mint = modint998244353;

int solve(vector<long long> &a) {
    int n = a.size();

    // dp[i] is the number of black subsets of the first i elements such that
    // the i-th element is necessarily painted black.
    vector<mint> dp(n), offload(n);
    dp[0] = 1;
    for (int i = 0; i < n; i++) {
        for (int j = i + a[i]; j < n; j += a[i]) {
            dp[j] += dp[i] + offload[i];
            if (a[j] == a[i]) {
                offload[j] += offload[i] + dp[i];
                break;
            }
        }
    }

    mint ans = 0;
    for (int i = 0; i < n; i++) {
        ans += dp[i];
    }
    return ans.val();
}

int main() {
    int n;
    cin >> n;
    vector<long long> a(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    cout << solve(a) << endl;
    return 0;
}