#include <bits/stdc++.h>
using namespace std;

#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;

vi pi(const string &s)
{
    vi p(sz(s));
    rep(i, 1, sz(s))
    {
        int g = p[i - 1];
        while (g && s[i] != s[g])
            g = p[g - 1];
        p[i] = g + (s[i] == s[g]);
    }
    return p;
}

#define int long long
const int M = 998244353;
const int MAXN = 1000000;

vector<int> dv[MAXN + 1];
int phi[MAXN + 1];

void calculatePhi()
{
    rep(i, 0, MAXN + 1) phi[i] = i & 1 ? i : i / 2;
    for (int i = 3; i < MAXN + 1; i += 2)
        if (phi[i] == i)
            for (int j = i; j < MAXN + 1; j += i)
                phi[j] -= phi[j] / i;
}

void init()
{
    calculatePhi();
    for (int i = 1; i <= MAXN; i++)
    {
        for (int j = i; j <= MAXN; j += i)
        {
            dv[j].push_back(i);
        }
    }
}

int hist[MAXN + 1];

void dfs(int now, vector<vector<int>> &adj, vi &kmp, vector<int> &ans)
{
    for (int j : dv[now+1])
    {
        ans[now] += hist[j] * phi[j];
    }
    for (int j : dv[now+1])
    {
        hist[j]++;
    }

    for (int u : adj[now])
    {
        dfs(u, adj, kmp, ans);
    }
    for (int j : dv[now+1])
    {
        hist[j]--;
    }
}

void solve()
{
    string s;
    cin >> s;
    int n = s.size();

    vi kmp = pi(s);
    vector<vector<int>> adj(n);
    for (int i = 0; i < n; i++)
    {
        if (kmp[i] != 0)
        {
            adj[kmp[i] - 1].push_back(i);
        }
    }

    vector<int> ans(n);
    for (int i = 0; i < n; i++)
    {
        if (kmp[i] == 0)
        {
            dfs(i, adj, kmp, ans);
        }
    }
    int res = 1;
    for (int i : ans)
    {
        res = (res * (i % M + 1)) % M;
    }
    cout << res << '\n';
}

signed main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    init();

    int t;
    cin >> t;
    while (t--)
    {
        solve();
    }

    return 0;
}