#include <bits/stdc++.h>

using i64 = long long;

constexpr int P = 998244353;

std::string pref;

using i128 = __int128;

i128 find(i128 n) {
    n--;
    i128 ans = 0;
    int len = 1;
    for (i128 p = 1; p <= n; p *= 10, len++) {
        ans += std::min(9 * p, n - p + 1) * len;
    }
    return ans;
}

std::string toString(i128 n) {
    std::string s;
    while (n) {
        s += '0' + n % 10;
        n /= 10;
    }
    std::reverse(s.begin(), s.end());
    return s;
}

std::mt19937 rng;
void solve() {
    // i64 v = rng() % 1000000000;
    // std::string s0;
    // for (int i = 0; i < 100; i++) {
    //     s0 += std::to_string(v + i);
    // }
    
    std::string s;
    std::cin >> s;
    // s = s0.substr(25, 25);
    // std::cerr << s << "\n";
    // for (int i = 0; i < 25; i++) {
    //     if (rng() % 2) {
    //         s[i] = '?';
    //     }
    // }
    // std::cerr << s << "\n";
    
    for (int i = 0; i + s.size() <= pref.size(); i++) {
        int ok = 1;
        for (int j = 0; j < s.size(); j++) {
            if (s[j] != '?' && pref[i + j] != s[j]) {
                ok = 0;
                break;
            }
        }
        if (ok) {
            std::cout << i + 1 << "\n";
            return;
        }
    }
    
    i128 ans = 0;
    
    const int n = s.size();
    // case 1: 1 number
    for (int i = 0; i < n; i++) {
        if (i == 0) {
            if (s[i] == '0') {
                ans = 10;
            } else if (s[i] == '?') {
                ans = 1;
            } else {
                ans = s[i] - '0';
            }
        } else if (s[i] == '?') {
            ans = 10 * ans;
        } else {
            ans = 10 * ans + s[i] - '0';
        }
    }
    ans = find(ans);
    if (s[0] == '0') {
        ans++;
    }
    
    bool verbose = false;
    auto checkv = [&](i128 v, int l) {
        if (v < 10000) {
            return;
        }
        i128 pos = find(v) - l;
        const i128 v0 = v;
        const int l0 = l;
        int r = l;
        i64 vl = v;
        std::string t(n, '?');
        while (l > 0) {
            vl--;
            std::string s = toString(vl);
            for (int i = s.size() - 1; i >= 0; i--) {
                if (l > 0) {
                    t[--l] = s[i];
                }
            }
        }
        while (r < n) {
            std::string s = toString(v);
            v++;
            for (int i = 0; i < s.size(); i++) {
                if (r < n) {
                    t[r++] = s[i];
                }
            }
        }
        if (verbose) {
            std::cerr << "checkv " << toString(v0) << " " << l0 << "\n";
            std::cerr << t << "\n";
        }
        for (int i = 0; i < n; i++) {
            if (s[i] != '?' && s[i] != t[i]) {
                return;
            }
        }
        ans = std::min(ans, pos);
    };
    
    auto check = [&](const std::vector<int> &a, int l) {
        for (int i = 0; i < a.size(); i++) {
            if (a[i] < 0 || a[i] >= 10) {
                return;
            }
        }
        if (a[0] == 0) {
            return;
        }
        i64 v = 0;
        for (int i = 0; i < a.size(); i++) {
            v = 10 * v + a[i];
        }
        checkv(v, l);
    };
    
    // case 2: 9...9 or 10...0
    for (i128 p = 10000, len = 5; len <= 26; p *= 10, len++) {
        for (int i = 0; i < n; i++) {
            checkv(p - 1, i);
            checkv(p, i);
        }
    }
    
    // case 3: 2 numbers
    for (int i = 1; i < n; i++) {
        for (int len = std::max({5, n - i, i}); len <= n + 1; len++) {
            for (int c = 0; c < len; c++) {
                std::vector<int> a(len, -1);
                for (int j = 0; j < i; j++) {
                    if (s[j] != '?') {
                        a[len - i + j] = s[j] - '0';
                    }
                }
                for (int j = i; j < n; j++) {
                    if (s[j] != '?') {
                        a[j - i] = s[j] - '0';
                    }
                }
                for (int j = 0; j < len; j++) {
                    if (a[j] == -1) {
                        a[j] = j == 0 ? 1 : 0;
                    }
                }
                for (int j = len - c; j < len; j++) {
                    a[j] = 0;
                }
                check(a, i);
                a[len - 1 - c]++;
                check(a, i);
            }
        }
    }
    
    // case 4: 3+ numbers
    
    for (int i = 0; i < n; i++) {
        for (int len = 5; len <= n - i; len++) {
            for (int c = 0; c < len; c++) {
                std::vector<int> a(len, -1);
                for (int j = 0; j < n; j++) {
                    if (s[j] != '?') {
                        a[(j - i + len * 100) % len] = s[j] - '0';
                    }
                }
                for (int j = i; j < i + len; j++) {
                    if (s[j] != '?') {
                        a[j - i] = s[j] - '0';
                    }
                }
                for (int j = 0; j < len; j++) {
                    if (a[j] == -1) {
                        a[j] = j == 0 ? 1 : 0;
                    }
                }
                for (int j = len - c; j < len; j++) {
                    a[j] = 0;
                }
                for (int v = 0; v < 10; v++) {
                    a[len - 1 - c] = v;
                    check(a, i);
                }
                for (int j = len - c; j < len; j++) {
                    a[j] = 9;
                }
                for (int v = 0; v < 10; v++) {
                    a[len - 1 - c] = v;
                    check(a, i);
                }
            }
        }
    }
    
    // assert(ans <= find(v) + 25);
    std::cout << int((ans + 1) % P) << "\n";
}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    
    int n = 1;
    while (pref.size() < 100000) {
        pref += std::to_string(n);
        n++;
    }
    
    int t;
    std::cin >> t;
    
    while (t--) {
        solve();
    }
    
    return 0;
}