//たぶん終わらない

#include <iostream>
#include <cmath>
#include <algorithm>

using namespace std;

typedef long long ll;
typedef __int128_t int128;

const ll MOD = 998244353;

/**
 * xy <= n (x, y >= 1)
 * Stern-Brocot
*/
struct LatticeCounter {
    ll N;
    int128 count;

    void solve_recursive(ll n, ll a, ll b, ll c, ll d, ll x, ll y) {
        ll m = a + c, p = b + d;
        if (m * (int128)y + (int128)p * x * y > n) return;

        if (m * (int128)y + (int128)p * x * y <= n) {
            ll x_next = (n - p * (int128)x * y) / (p * y + m);
            ll y_next = (n - m * (int128)x * y) / (m * x + p);

            count += (int128)x_next * y_next;
            
            solve_recursive(n, a, b, m, p, x, y);
            solve_recursive(n, m, p, c, d, x, y);
        }
    }

    ll get_S(ll n) {
        if (n <= 0) return 0;
        if (n == 1) return 1;
        
        ll k = pow(n, 0.5);
        while ((k + 1) * (int128)(k + 1) <= n) k++;
        while (k * (int128)k > n) k--;

        int128 sum_val = 0;
        for (ll l = 1, r; l <= k; l = r + 1) {
            r = n / (n / l);
            if (r > k) r = k;
            sum_val += (int128)(n / l) * (r - l + 1);
        }
        
        int128 res = sum_val * 2 - (int128)k * k;
        return (ll)(res % MOD);
    }
};

ll fast_S(ll n) {
    if (n <= 0) return 0;
    ll k = sqrtl(n);
    while ((k + 1) * (int128)(k + 1) <= n) k++;
    while (k * (int128)k > n) k--;

    int128 res = 0;
    for (ll i = 1; i <= k; ++i) {
        res += n / i;
    }
    res = res * 2 - (int128)k * k;
    return (ll)(res % MOD);
}

void solve() {
    ll N;
    if (!(cin >> N)) return;

    ll K = 2 * N + 1;

    ll sK = fast_S(K);
    ll sK2 = fast_S(K / 2);
    ll sK4 = fast_S(K / 4);

    ll fK = (sK - 2 * sK2 % MOD + sK4 + 2LL * MOD) % MOD;

    ll ans = (fK - (K % MOD) + MOD) % MOD;

    cout << ans << endl;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int T;
    if (!(cin >> T)) return 0;
    while (T--) {
        solve();
    }
    return 0;
}