#pragma GCC optimize("O3")
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize("Ofast")
#pragma GCC optimize("inline")
#pragma GCC optimize("-fgcse")
#pragma GCC optimize("-fgcse-lm")
#pragma GCC optimize("-fipa-sra")
#pragma GCC optimize("-ftree-pre")
#pragma GCC optimize("-ftree-vrp")
#pragma GCC optimize("-fpeephole2")
#pragma GCC optimize("-ffast-math")
#pragma GCC optimize("-fsched-spec")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("-falign-jumps")   
#pragma GCC optimize("-falign-loops")
#pragma GCC optimize("-falign-labels")
#pragma GCC optimize("-fdevirtualize")
#pragma GCC optimize("-fcaller-saves")
#pragma GCC optimize("-fcrossjumping")
#pragma GCC optimize("-fthread-jumps")
#pragma GCC optimize("-funroll-loops")
#pragma GCC optimize("-freorder-blocks")
#pragma GCC optimize("-fschedule-insns")
#pragma GCC optimize("inline-functions")
#pragma GCC optimize("-ftree-tail-merge")
#pragma GCC optimize("-fschedule-insns2")
#pragma GCC optimize("-fstrict-aliasing")
#pragma GCC optimize("-falign-functions")
#pragma GCC optimize("-fcse-follow-jumps")
#pragma GCC optimize("-fsched-interblock")
#pragma GCC optimize("-fpartial-inlining")
#pragma GCC optimize("no-stack-protector")
#pragma GCC optimize("-freorder-functions")
#pragma GCC optimize("-findirect-inlining")
#pragma GCC optimize("-fhoist-adjacent-loads")
#pragma GCC optimize("-frerun-cse-after-loop")
#pragma GCC optimize("inline-small-functions")
#pragma GCC optimize("-finline-small-functions")
#pragma GCC optimize("-ftree-switch-conversion")
#pragma GCC optimize("-foptimize-sibling-calls")
#pragma GCC optimize("-fexpensive-optimizations")
#pragma GCC optimize("inline-functions-called-once")
#pragma GCC optimize("-fdelete-null-Pointer-checks")
#pragma GCC optimize("Ofast")

#include <bits/stdc++.h>

using namespace std;


namespace atcoder {

    namespace internal {

        template <class T> struct simple_queue {
            std::vector<T> payload;
            int pos = 0;
            void reserve(int n) { payload.reserve(n); }
            int size() const { return int(payload.size()) - pos; }
            bool empty() const { return pos == int(payload.size()); }
            void push(const T& t) { payload.push_back(t); }
            T& front() { return payload[pos]; }
            void clear() {
                payload.clear();
                pos = 0;
            }
            void pop() { pos++; }
        };

    }  // namespace internal

}  // namespace atcoder


namespace atcoder {
    namespace internal {

        template <class E> struct csr {
            std::vector<int> start;
            std::vector<E> elist;
            explicit csr(int n, const std::vector<std::pair<int, E>>& edges)
                    : start(n + 1), elist(edges.size()) {
                for (auto e : edges) {
                    start[e.first + 1]++;
                }
                for (int i = 1; i <= n; i++) {
                    start[i] += start[i - 1];
                }
                auto counter = start;
                for (auto e : edges) {
                    elist[counter[e.first]++] = e.second;
                }
            }
        };

    }  // namespace internal

}  // namespace atcoder

namespace atcoder {

    namespace internal {

// @param m `1 <= m`
// @return x mod m
        constexpr long long safe_mod(long long x, long long m) {
            x %= m;
            if (x < 0) x += m;
            return x;
        }

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
        struct barrett {
            unsigned int _m;
            unsigned long long im;

            // @param m `1 <= m`
            explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

            // @return m
            unsigned int umod() const { return _m; }

            // @param a `0 <= a < m`
            // @param b `0 <= b < m`
            // @return `a * b % m`
            unsigned int mul(unsigned int a, unsigned int b) const {
                // [1] m = 1
                // a = b = im = 0, so okay

                // [2] m >= 2
                // im = ceil(2^64 / m)
                // -> im * m = 2^64 + r (0 <= r < m)
                // let z = a*b = c*m + d (0 <= c, d < m)
                // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
                // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
                // ((ab * im) >> 64) == c or c + 1
                unsigned long long z = a;
                z *= b;
#ifdef _MSC_VER
                unsigned long long x;
        _umul128(z, im, &x);
#else
                unsigned long long x =
                        (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
                unsigned long long y = x * _m;
                return (unsigned int)(z - y + (z < y ? _m : 0));
            }
        };

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
        constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
            if (m == 1) return 0;
            unsigned int _m = (unsigned int)(m);
            unsigned long long r = 1;
            unsigned long long y = safe_mod(x, m);
            while (n) {
                if (n & 1) r = (r * y) % _m;
                y = (y * y) % _m;
                n >>= 1;
            }
            return r;
        }

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
        constexpr bool is_prime_constexpr(int n) {
            if (n <= 1) return false;
            if (n == 2 || n == 7 || n == 61) return true;
            if (n % 2 == 0) return false;
            long long d = n - 1;
            while (d % 2 == 0) d /= 2;
            constexpr long long bases[3] = {2, 7, 61};
            for (long long a : bases) {
                long long t = d;
                long long y = pow_mod_constexpr(a, t, n);
                while (t != n - 1 && y != 1 && y != n - 1) {
                    y = y * y % n;
                    t <<= 1;
                }
                if (y != n - 1 && t % 2 == 0) {
                    return false;
                }
            }
            return true;
        }
        template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
        constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
            a = safe_mod(a, b);
            if (a == 0) return {b, 0};

            // Contracts:
            // [1] s - m0 * a = 0 (mod b)
            // [2] t - m1 * a = 0 (mod b)
            // [3] s * |m1| + t * |m0| <= b
            long long s = b, t = a;
            long long m0 = 0, m1 = 1;

            while (t) {
                long long u = s / t;
                s -= t * u;
                m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

                // [3]:
                // (s - t * u) * |m1| + t * |m0 - m1 * u|
                // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
                // = s * |m1| + t * |m0| <= b

                auto tmp = s;
                s = t;
                t = tmp;
                tmp = m0;
                m0 = m1;
                m1 = tmp;
            }
            // by [3]: |m0| <= b/g
            // by g != b: |m0| < b/g
            if (m0 < 0) m0 += b / s;
            return {s, m0};
        }

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
        constexpr int primitive_root_constexpr(int m) {
            if (m == 2) return 1;
            if (m == 167772161) return 3;
            if (m == 469762049) return 3;
            if (m == 754974721) return 11;
            if (m == 998244353) return 3;
            int divs[20] = {};
            divs[0] = 2;
            int cnt = 1;
            int x = (m - 1) / 2;
            while (x % 2 == 0) x /= 2;
            for (int i = 3; (long long)(i)*i <= x; i += 2) {
                if (x % i == 0) {
                    divs[cnt++] = i;
                    while (x % i == 0) {
                        x /= i;
                    }
                }
            }
            if (x > 1) {
                divs[cnt++] = x;
            }
            for (int g = 2;; g++) {
                bool ok = true;
                for (int i = 0; i < cnt; i++) {
                    if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                        ok = false;
                        break;
                    }
                }
                if (ok) return g;
            }
        }
        template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
        unsigned long long floor_sum_unsigned(unsigned long long n,
                                              unsigned long long m,
                                              unsigned long long a,
                                              unsigned long long b) {
            unsigned long long ans = 0;
            while (true) {
                if (a >= m) {
                    ans += n * (n - 1) / 2 * (a / m);
                    a %= m;
                }
                if (b >= m) {
                    ans += n * (b / m);
                    b %= m;
                }

                unsigned long long y_max = a * n + b;
                if (y_max < m) break;
                // y_max < m * (n + 1)
                // floor(y_max / m) <= n
                n = (unsigned long long)(y_max / m);
                b = (unsigned long long)(y_max % m);
                std::swap(m, a);
            }
            return ans;
        }

    }  // namespace internal

}  // namespace atcoder


namespace atcoder {

    namespace internal {

#ifndef _MSC_VER
        template <class T>
        using is_signed_int128 =
                typename std::conditional<std::is_same<T, __int128_t>::value ||
                                          std::is_same<T, __int128>::value,
                        std::true_type,
                        std::false_type>::type;

        template <class T>
        using is_unsigned_int128 =
                typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                          std::is_same<T, unsigned __int128>::value,
                        std::true_type,
                        std::false_type>::type;

        template <class T>
        using make_unsigned_int128 =
                typename std::conditional<std::is_same<T, __int128_t>::value,
                        __uint128_t,
                        unsigned __int128>;

        template <class T>
        using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                      is_signed_int128<T>::value ||
                                                      is_unsigned_int128<T>::value,
                std::true_type,
                std::false_type>::type;

        template <class T>
        using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                         std::is_signed<T>::value) ||
                                                        is_signed_int128<T>::value,
                std::true_type,
                std::false_type>::type;

        template <class T>
        using is_unsigned_int =
                typename std::conditional<(is_integral<T>::value &&
                                           std::is_unsigned<T>::value) ||
                                          is_unsigned_int128<T>::value,
                        std::true_type,
                        std::false_type>::type;

        template <class T>
        using to_unsigned = typename std::conditional<
                is_signed_int128<T>::value,
                make_unsigned_int128<T>,
                typename std::conditional<std::is_signed<T>::value,
                        std::make_unsigned<T>,
                        std::common_type<T>>::type>::type;

#else

        template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

        template <class T>
        using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

        template <class T>
        using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

        template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

    }  // namespace internal

}  // namespace atcoder

namespace atcoder {

    namespace internal {

        struct modint_base {};
        struct static_modint_base : modint_base {};

        template <class T> using is_modint = std::is_base_of<modint_base, T>;
        template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

    }  // namespace internal

    template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
    struct static_modint : internal::static_modint_base {
        using mint = static_modint;

    public:
        static constexpr int mod() { return m; }
        static mint raw(int v) {
            mint x;
            x._v = v;
            return x;
        }

        static_modint() : _v(0) {}
        template <class T, internal::is_signed_int_t<T>* = nullptr>
        static_modint(T v) {
            long long x = (long long)(v % (long long)(umod()));
            if (x < 0) x += umod();
            _v = (unsigned int)(x);
        }
        template <class T, internal::is_unsigned_int_t<T>* = nullptr>
        static_modint(T v) {
            _v = (unsigned int)(v % umod());
        }

        unsigned int val() const { return _v; }

        mint& operator++() {
            _v++;
            if (_v == umod()) _v = 0;
            return *this;
        }
        mint& operator--() {
            if (_v == 0) _v = umod();
            _v--;
            return *this;
        }
        mint operator++(int) {
            mint result = *this;
            ++*this;
            return result;
        }
        mint operator--(int) {
            mint result = *this;
            --*this;
            return result;
        }

        mint& operator+=(const mint& rhs) {
            _v += rhs._v;
            if (_v >= umod()) _v -= umod();
            return *this;
        }
        mint& operator-=(const mint& rhs) {
            _v -= rhs._v;
            if (_v >= umod()) _v += umod();
            return *this;
        }
        mint& operator*=(const mint& rhs) {
            unsigned long long z = _v;
            z *= rhs._v;
            _v = (unsigned int)(z % umod());
            return *this;
        }
        mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

        mint operator+() const { return *this; }
        mint operator-() const { return mint() - *this; }

        mint pow(long long n) const {
            assert(0 <= n);
            mint x = *this, r = 1;
            while (n) {
                if (n & 1) r *= x;
                x *= x;
                n >>= 1;
            }
            return r;
        }
        mint inv() const {
            if (prime) {
                assert(_v);
                return pow(umod() - 2);
            } else {
                auto eg = internal::inv_gcd(_v, m);
                assert(eg.first == 1);
                return eg.second;
            }
        }

        friend mint operator+(const mint& lhs, const mint& rhs) {
            return mint(lhs) += rhs;
        }
        friend mint operator-(const mint& lhs, const mint& rhs) {
            return mint(lhs) -= rhs;
        }
        friend mint operator*(const mint& lhs, const mint& rhs) {
            return mint(lhs) *= rhs;
        }
        friend mint operator/(const mint& lhs, const mint& rhs) {
            return mint(lhs) /= rhs;
        }
        friend bool operator==(const mint& lhs, const mint& rhs) {
            return lhs._v == rhs._v;
        }
        friend bool operator!=(const mint& lhs, const mint& rhs) {
            return lhs._v != rhs._v;
        }

    private:
        unsigned int _v;
        static constexpr unsigned int umod() { return m; }
        static constexpr bool prime = internal::is_prime<m>;
    };

    template <int id> struct dynamic_modint : internal::modint_base {
        using mint = dynamic_modint;

    public:
        static int mod() { return (int)(bt.umod()); }
        static void set_mod(int m) {
            assert(1 <= m);
            bt = internal::barrett(m);
        }
        static mint raw(int v) {
            mint x;
            x._v = v;
            return x;
        }

        dynamic_modint() : _v(0) {}
        template <class T, internal::is_signed_int_t<T>* = nullptr>
        dynamic_modint(T v) {
            long long x = (long long)(v % (long long)(mod()));
            if (x < 0) x += mod();
            _v = (unsigned int)(x);
        }
        template <class T, internal::is_unsigned_int_t<T>* = nullptr>
        dynamic_modint(T v) {
            _v = (unsigned int)(v % mod());
        }

        unsigned int val() const { return _v; }

        mint& operator++() {
            _v++;
            if (_v == umod()) _v = 0;
            return *this;
        }
        mint& operator--() {
            if (_v == 0) _v = umod();
            _v--;
            return *this;
        }
        mint operator++(int) {
            mint result = *this;
            ++*this;
            return result;
        }
        mint operator--(int) {
            mint result = *this;
            --*this;
            return result;
        }

        mint& operator+=(const mint& rhs) {
            _v += rhs._v;
            if (_v >= umod()) _v -= umod();
            return *this;
        }
        mint& operator-=(const mint& rhs) {
            _v += mod() - rhs._v;
            if (_v >= umod()) _v -= umod();
            return *this;
        }
        mint& operator*=(const mint& rhs) {
            _v = bt.mul(_v, rhs._v);
            return *this;
        }
        mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

        mint operator+() const { return *this; }
        mint operator-() const { return mint() - *this; }

        mint pow(long long n) const {
            assert(0 <= n);
            mint x = *this, r = 1;
            while (n) {
                if (n & 1) r *= x;
                x *= x;
                n >>= 1;
            }
            return r;
        }
        mint inv() const {
            auto eg = internal::inv_gcd(_v, mod());
            assert(eg.first == 1);
            return eg.second;
        }

        friend mint operator+(const mint& lhs, const mint& rhs) {
            return mint(lhs) += rhs;
        }
        friend mint operator-(const mint& lhs, const mint& rhs) {
            return mint(lhs) -= rhs;
        }
        friend mint operator*(const mint& lhs, const mint& rhs) {
            return mint(lhs) *= rhs;
        }
        friend mint operator/(const mint& lhs, const mint& rhs) {
            return mint(lhs) /= rhs;
        }
        friend bool operator==(const mint& lhs, const mint& rhs) {
            return lhs._v == rhs._v;
        }
        friend bool operator!=(const mint& lhs, const mint& rhs) {
            return lhs._v != rhs._v;
        }

    private:
        unsigned int _v;
        static internal::barrett bt;
        static unsigned int umod() { return bt.umod(); }
    };
    template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

    using modint998244353 = static_modint<998244353>;
    using modint1000000007 = static_modint<1000000007>;
    using modint = dynamic_modint<-1>;

    namespace internal {

        template <class T>
        using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

        template <class T>
        using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

        template <class> struct is_dynamic_modint : public std::false_type {};
        template <int id>
        struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

        template <class T>
        using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

    }  // namespace internal

}  // namespace atcoder

namespace atcoder {

    namespace internal {

// @return same with std::bit::bit_ceil
        unsigned int bit_ceil(unsigned int n) {
            unsigned int x = 1;
            while (x < (unsigned int)(n)) x *= 2;
            return x;
        }

// @param n `1 <= n`
// @return same with std::bit::countr_zero
        int countr_zero(unsigned int n) {
#ifdef _MSC_VER
            unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
            return __builtin_ctz(n);
#endif
        }

// @param n `1 <= n`
// @return same with std::bit::countr_zero
        constexpr int countr_zero_constexpr(unsigned int n) {
            int x = 0;
            while (!(n & (1 << x))) x++;
            return x;
        }

    }  // namespace internal

}  // namespace atcoder


namespace atcoder {

    namespace internal {

#ifndef _MSC_VER
        template <class T>
        using is_signed_int128 =
                typename std::conditional<std::is_same<T, __int128_t>::value ||
                                          std::is_same<T, __int128>::value,
                        std::true_type,
                        std::false_type>::type;

        template <class T>
        using is_unsigned_int128 =
                typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                          std::is_same<T, unsigned __int128>::value,
                        std::true_type,
                        std::false_type>::type;

        template <class T>
        using make_unsigned_int128 =
                typename std::conditional<std::is_same<T, __int128_t>::value,
                        __uint128_t,
                        unsigned __int128>;

        template <class T>
        using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                      is_signed_int128<T>::value ||
                                                      is_unsigned_int128<T>::value,
                std::true_type,
                std::false_type>::type;

        template <class T>
        using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                         std::is_signed<T>::value) ||
                                                        is_signed_int128<T>::value,
                std::true_type,
                std::false_type>::type;

        template <class T>
        using is_unsigned_int =
                typename std::conditional<(is_integral<T>::value &&
                                           std::is_unsigned<T>::value) ||
                                          is_unsigned_int128<T>::value,
                        std::true_type,
                        std::false_type>::type;

        template <class T>
        using to_unsigned = typename std::conditional<
                is_signed_int128<T>::value,
                make_unsigned_int128<T>,
                typename std::conditional<std::is_signed<T>::value,
                        std::make_unsigned<T>,
                        std::common_type<T>>::type>::type;

#else

        template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

        template <class T>
        using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

        template <class T>
        using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

        template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

    }  // namespace internal

}  // namespace atcoder


namespace atcoder {

// Reference: https://en.wikipedia.org/wiki/Fenwick_tree
    template <class T> struct fenwick_tree {
        using U = internal::to_unsigned_t<T>;

    public:
        fenwick_tree() : _n(0) {}
        explicit fenwick_tree(int n) : _n(n), data(n) {}

        void add(int p, T x) {
            assert(0 <= p && p < _n);
            p++;
            while (p <= _n) {
                data[p - 1] += U(x);
                p += p & -p;
            }
        }

        T sum(int l, int r) {
            assert(0 <= l && l <= r && r <= _n);
            return sum(r) - sum(l);
        }

    private:
        int _n;
        std::vector<U> data;

        U sum(int r) {
            U s = 0;
            while (r > 0) {
                s += data[r - 1];
                r -= r & -r;
            }
            return s;
        }
    };

}  // namespace atcoder


namespace atcoder {

#if __cplusplus >= 201703L

    template <class S, auto op, auto e> struct segtree {
        static_assert(std::is_convertible_v<decltype(op), std::function<S(S, S)>>,
                      "op must work as S(S, S)");
        static_assert(std::is_convertible_v<decltype(e), std::function<S()>>,
                      "e must work as S()");

#else

        template <class S, S (*op)(S, S), S (*e)()> struct segtree {

#endif

    public:
        segtree() : segtree(0) {}
        explicit segtree(int n) : segtree(std::vector<S>(n, e())) {}
        explicit segtree(const std::vector<S>& v) : _n(int(v.size())) {
            size = (int)internal::bit_ceil((unsigned int)(_n));
            log = internal::countr_zero((unsigned int)size);
            d = std::vector<S>(2 * size, e());
            for (int i = 0; i < _n; i++) d[size + i] = v[i];
            for (int i = size - 1; i >= 1; i--) {
                update(i);
            }
        }

        void clear_and_update(const std::vector<S>& v)
        {
            _n = (int)v.size();
            size = (int)internal::bit_ceil((unsigned int)(_n));
            log = internal::countr_zero((unsigned int)size);
            d = std::vector<S>(2 * size, e());
            for (int i = 0; i < _n; i++) d[size + i] = v[i];
            for (int i = size - 1; i >= 1; i--) {
                update(i);
            }
        }

        void set(int p, S x) {
            assert(0 <= p && p < _n);
            p += size;
            d[p] = x;
            for (int i = 1; i <= log; i++) update(p >> i);
        }

        S get(int p) const {
            assert(0 <= p && p < _n);
            return d[p + size];
        }

        S prod(int l, int r) const {
            assert(0 <= l && l <= r && r <= _n);
            S sml = e(), smr = e();
            l += size;
            r += size;

            while (l < r) {
                if (l & 1) sml = op(sml, d[l++]);
                if (r & 1) smr = op(d[--r], smr);
                l >>= 1;
                r >>= 1;
            }
            return op(sml, smr);
        }

        S all_prod() const { return d[1]; }

        template <bool (*f)(S)> int max_right(int l) const {
            return max_right(l, [](S x) { return f(x); });
        }
        template <class F> int max_right(int l, F f) const {
            assert(0 <= l && l <= _n);
            assert(f(e()));
            if (l == _n) return _n;
            l += size;
            S sm = e();
            do {
                while (l % 2 == 0) l >>= 1;
                if (!f(op(sm, d[l]))) {
                    while (l < size) {
                        l = (2 * l);
                        if (f(op(sm, d[l]))) {
                            sm = op(sm, d[l]);
                            l++;
                        }
                    }
                    return l - size;
                }
                sm = op(sm, d[l]);
                l++;
            } while ((l & -l) != l);
            return _n;
        }

        template <bool (*f)(S)> int min_left(int r) const {
            return min_left(r, [](S x) { return f(x); });
        }
        template <class F> int min_left(int r, F f) const {
            assert(0 <= r && r <= _n);
            assert(f(e()));
            if (r == 0) return 0;
            r += size;
            S sm = e();
            do {
                r--;
                while (r > 1 && (r % 2)) r >>= 1;
                if (!f(op(d[r], sm))) {
                    while (r < size) {
                        r = (2 * r + 1);
                        if (f(op(d[r], sm))) {
                            sm = op(d[r], sm);
                            r--;
                        }
                    }
                    return r + 1 - size;
                }
                sm = op(d[r], sm);
            } while ((r & -r) != r);
            return 0;
        }

    private:
        int _n, size, log;
        std::vector<S> d;

        void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
    };

}  // namespace atcoder


namespace atcoder {

#if __cplusplus >= 201703L

    template <class S,
            auto op,
            auto e,
            class F,
            auto mapping,
            auto composition,
            auto id>
    struct lazy_segtree {
        static_assert(std::is_convertible_v<decltype(op), std::function<S(S, S)>>,
                      "op must work as S(S, S)");
        static_assert(std::is_convertible_v<decltype(e), std::function<S()>>,
                      "e must work as S()");
        static_assert(
                std::is_convertible_v<decltype(mapping), std::function<S(F, S)>>,
                "mapping must work as F(F, S)");
        static_assert(
                std::is_convertible_v<decltype(composition), std::function<F(F, F)>>,
                "compostiion must work as F(F, F)");
        static_assert(std::is_convertible_v<decltype(id), std::function<F()>>,
                      "id must work as F()");

#else

        template <class S,
          S (*op)(S, S),
          S (*e)(),
          class F,
          S (*mapping)(F, S),
          F (*composition)(F, F),
          F (*id)()>
struct lazy_segtree {

#endif

    public:
        lazy_segtree() : lazy_segtree(0) {}
        explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
        explicit lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
            size = (int)internal::bit_ceil((unsigned int)(_n));
            log = internal::countr_zero((unsigned int)size);
            d = std::vector<S>(2 * size, e());
            lz = std::vector<F>(size, id());
            for (int i = 0; i < _n; i++) d[size + i] = v[i];
            for (int i = size - 1; i >= 1; i--) {
                update(i);
            }
        }

        void set(int p, S x) {
            assert(0 <= p && p < _n);
            p += size;
            for (int i = log; i >= 1; i--) push(p >> i);
            d[p] = x;
            for (int i = 1; i <= log; i++) update(p >> i);
        }

        S get(int p) {
            assert(0 <= p && p < _n);
            p += size;
            for (int i = log; i >= 1; i--) push(p >> i);
            return d[p];
        }

        S prod(int l, int r) {
            assert(0 <= l && l <= r && r <= _n);
            if (l == r) return e();

            l += size;
            r += size;

            for (int i = log; i >= 1; i--) {
                if (((l >> i) << i) != l) push(l >> i);
                if (((r >> i) << i) != r) push((r - 1) >> i);
            }

            S sml = e(), smr = e();
            while (l < r) {
                if (l & 1) sml = op(sml, d[l++]);
                if (r & 1) smr = op(d[--r], smr);
                l >>= 1;
                r >>= 1;
            }

            return op(sml, smr);
        }

        S all_prod() { return d[1]; }

        void apply(int p, F f) {
            assert(0 <= p && p < _n);
            p += size;
            for (int i = log; i >= 1; i--) push(p >> i);
            d[p] = mapping(f, d[p]);
            for (int i = 1; i <= log; i++) update(p >> i);
        }
        void apply(int l, int r, F f) {
            assert(0 <= l && l <= r && r <= _n);
            if (l == r) return;

            l += size;
            r += size;

            for (int i = log; i >= 1; i--) {
                if (((l >> i) << i) != l) push(l >> i);
                if (((r >> i) << i) != r) push((r - 1) >> i);
            }

            {
                int l2 = l, r2 = r;
                while (l < r) {
                    if (l & 1) all_apply(l++, f);
                    if (r & 1) all_apply(--r, f);
                    l >>= 1;
                    r >>= 1;
                }
                l = l2;
                r = r2;
            }

            for (int i = 1; i <= log; i++) {
                if (((l >> i) << i) != l) update(l >> i);
                if (((r >> i) << i) != r) update((r - 1) >> i);
            }
        }

        template <bool (*g)(S)> int max_right(int l) {
            return max_right(l, [](S x) { return g(x); });
        }
        template <class G> int max_right(int l, G g) {
            assert(0 <= l && l <= _n);
            assert(g(e()));
            if (l == _n) return _n;
            l += size;
            for (int i = log; i >= 1; i--) push(l >> i);
            S sm = e();
            do {
                while (l % 2 == 0) l >>= 1;
                if (!g(op(sm, d[l]))) {
                    while (l < size) {
                        push(l);
                        l = (2 * l);
                        if (g(op(sm, d[l]))) {
                            sm = op(sm, d[l]);
                            l++;
                        }
                    }
                    return l - size;
                }
                sm = op(sm, d[l]);
                l++;
            } while ((l & -l) != l);
            return _n;
        }

        template <bool (*g)(S)> int min_left(int r) {
            return min_left(r, [](S x) { return g(x); });
        }
        template <class G> int min_left(int r, G g) {
            assert(0 <= r && r <= _n);
            assert(g(e()));
            if (r == 0) return 0;
            r += size;
            for (int i = log; i >= 1; i--) push((r - 1) >> i);
            S sm = e();
            do {
                r--;
                while (r > 1 && (r % 2)) r >>= 1;
                if (!g(op(d[r], sm))) {
                    while (r < size) {
                        push(r);
                        r = (2 * r + 1);
                        if (g(op(d[r], sm))) {
                            sm = op(d[r], sm);
                            r--;
                        }
                    }
                    return r + 1 - size;
                }
                sm = op(d[r], sm);
            } while ((r & -r) != r);
            return 0;
        }

    private:
        int _n, size, log;
        std::vector<S> d;
        std::vector<F> lz;

        void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
        void all_apply(int k, F f) {
            d[k] = mapping(f, d[k]);
            if (k < size) lz[k] = composition(f, lz[k]);
        }
        void push(int k) {
            all_apply(2 * k, lz[k]);
            all_apply(2 * k + 1, lz[k]);
            lz[k] = id();
        }
    };

}  // namespace atcoder


namespace atcoder {

    namespace internal {

        template <class mint,
                int g = internal::primitive_root<mint::mod()>,
                internal::is_static_modint_t<mint>* = nullptr>
        struct fft_info {
            static constexpr int rank2 = countr_zero_constexpr(mint::mod() - 1);
            std::array<mint, rank2 + 1> root;   // root[i]^(2^i) == 1
            std::array<mint, rank2 + 1> iroot;  // root[i] * iroot[i] == 1

            std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
            std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;

            std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
            std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;

            fft_info() {
                root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
                iroot[rank2] = root[rank2].inv();
                for (int i = rank2 - 1; i >= 0; i--) {
                    root[i] = root[i + 1] * root[i + 1];
                    iroot[i] = iroot[i + 1] * iroot[i + 1];
                }

                {
                    mint prod = 1, iprod = 1;
                    for (int i = 0; i <= rank2 - 2; i++) {
                        rate2[i] = root[i + 2] * prod;
                        irate2[i] = iroot[i + 2] * iprod;
                        prod *= iroot[i + 2];
                        iprod *= root[i + 2];
                    }
                }
                {
                    mint prod = 1, iprod = 1;
                    for (int i = 0; i <= rank2 - 3; i++) {
                        rate3[i] = root[i + 3] * prod;
                        irate3[i] = iroot[i + 3] * iprod;
                        prod *= iroot[i + 3];
                        iprod *= root[i + 3];
                    }
                }
            }
        };

        template <class mint, internal::is_static_modint_t<mint>* = nullptr>
        void butterfly(std::vector<mint>& a) {
            int n = int(a.size());
            int h = internal::countr_zero((unsigned int)n);

            static const fft_info<mint> info;

            int len = 0;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
            while (len < h) {
                if (h - len == 1) {
                    int p = 1 << (h - len - 1);
                    mint rot = 1;
                    for (int s = 0; s < (1 << len); s++) {
                        int offset = s << (h - len);
                        for (int i = 0; i < p; i++) {
                            auto l = a[i + offset];
                            auto r = a[i + offset + p] * rot;
                            a[i + offset] = l + r;
                            a[i + offset + p] = l - r;
                        }
                        if (s + 1 != (1 << len))
                            rot *= info.rate2[countr_zero(~(unsigned int)(s))];
                    }
                    len++;
                } else {
                    // 4-base
                    int p = 1 << (h - len - 2);
                    mint rot = 1, imag = info.root[2];
                    for (int s = 0; s < (1 << len); s++) {
                        mint rot2 = rot * rot;
                        mint rot3 = rot2 * rot;
                        int offset = s << (h - len);
                        for (int i = 0; i < p; i++) {
                            auto mod2 = 1ULL * mint::mod() * mint::mod();
                            auto a0 = 1ULL * a[i + offset].val();
                            auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
                            auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
                            auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
                            auto a1na3imag =
                                    1ULL * mint(a1 + mod2 - a3).val() * imag.val();
                            auto na2 = mod2 - a2;
                            a[i + offset] = a0 + a2 + a1 + a3;
                            a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
                            a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
                            a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
                        }
                        if (s + 1 != (1 << len))
                            rot *= info.rate3[countr_zero(~(unsigned int)(s))];
                    }
                    len += 2;
                }
            }
        }

        template <class mint, internal::is_static_modint_t<mint>* = nullptr>
        void butterfly_inv(std::vector<mint>& a) {
            int n = int(a.size());
            int h = internal::countr_zero((unsigned int)n);

            static const fft_info<mint> info;

            int len = h;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
            while (len) {
                if (len == 1) {
                    int p = 1 << (h - len);
                    mint irot = 1;
                    for (int s = 0; s < (1 << (len - 1)); s++) {
                        int offset = s << (h - len + 1);
                        for (int i = 0; i < p; i++) {
                            auto l = a[i + offset];
                            auto r = a[i + offset + p];
                            a[i + offset] = l + r;
                            a[i + offset + p] =
                                    (unsigned long long)(mint::mod() + l.val() - r.val()) *
                                    irot.val();
                            ;
                        }
                        if (s + 1 != (1 << (len - 1)))
                            irot *= info.irate2[countr_zero(~(unsigned int)(s))];
                    }
                    len--;
                } else {
                    // 4-base
                    int p = 1 << (h - len);
                    mint irot = 1, iimag = info.iroot[2];
                    for (int s = 0; s < (1 << (len - 2)); s++) {
                        mint irot2 = irot * irot;
                        mint irot3 = irot2 * irot;
                        int offset = s << (h - len + 2);
                        for (int i = 0; i < p; i++) {
                            auto a0 = 1ULL * a[i + offset + 0 * p].val();
                            auto a1 = 1ULL * a[i + offset + 1 * p].val();
                            auto a2 = 1ULL * a[i + offset + 2 * p].val();
                            auto a3 = 1ULL * a[i + offset + 3 * p].val();

                            auto a2na3iimag =
                                    1ULL *
                                    mint((mint::mod() + a2 - a3) * iimag.val()).val();

                            a[i + offset] = a0 + a1 + a2 + a3;
                            a[i + offset + 1 * p] =
                                    (a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
                            a[i + offset + 2 * p] =
                                    (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
                                    irot2.val();
                            a[i + offset + 3 * p] =
                                    (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
                                    irot3.val();
                        }
                        if (s + 1 != (1 << (len - 2)))
                            irot *= info.irate3[countr_zero(~(unsigned int)(s))];
                    }
                    len -= 2;
                }
            }
        }

        template <class mint, internal::is_static_modint_t<mint>* = nullptr>
        std::vector<mint> convolution_naive(const std::vector<mint>& a,
                                            const std::vector<mint>& b) {
            int n = int(a.size()), m = int(b.size());
            std::vector<mint> ans(n + m - 1);
            if (n < m) {
                for (int j = 0; j < m; j++) {
                    for (int i = 0; i < n; i++) {
                        ans[i + j] += a[i] * b[j];
                    }
                }
            } else {
                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < m; j++) {
                        ans[i + j] += a[i] * b[j];
                    }
                }
            }
            return ans;
        }

        template <class mint, internal::is_static_modint_t<mint>* = nullptr>
        std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
            int n = int(a.size()), m = int(b.size());
            int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
            a.resize(z);
            internal::butterfly(a);
            b.resize(z);
            internal::butterfly(b);
            for (int i = 0; i < z; i++) {
                a[i] *= b[i];
            }
            internal::butterfly_inv(a);
            a.resize(n + m - 1);
            mint iz = mint(z).inv();
            for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
            return a;
        }

    }  // namespace internal

    template <class mint, internal::is_static_modint_t<mint>* = nullptr>
    std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {
        int n = int(a.size()), m = int(b.size());
        if (!n || !m) return {};

        int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
        assert((mint::mod() - 1) % z == 0);

        if (std::min(n, m) <= 60) return convolution_naive(a, b);
        return internal::convolution_fft(a, b);
    }
    template <class mint, internal::is_static_modint_t<mint>* = nullptr>
    std::vector<mint> convolution(const std::vector<mint>& a,
                                  const std::vector<mint>& b) {
        int n = int(a.size()), m = int(b.size());
        if (!n || !m) return {};

        int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
        assert((mint::mod() - 1) % z == 0);

        if (std::min(n, m) <= 60) return convolution_naive(a, b);
        return internal::convolution_fft(a, b);
    }

    template <unsigned int mod = 998244353,
            class T,
            std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
    std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
        int n = int(a.size()), m = int(b.size());
        if (!n || !m) return {};

        using mint = static_modint<mod>;

        int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
        assert((mint::mod() - 1) % z == 0);

        std::vector<mint> a2(n), b2(m);
        for (int i = 0; i < n; i++) {
            a2[i] = mint(a[i]);
        }
        for (int i = 0; i < m; i++) {
            b2[i] = mint(b[i]);
        }
        auto c2 = convolution(std::move(a2), std::move(b2));
        std::vector<T> c(n + m - 1);
        for (int i = 0; i < n + m - 1; i++) {
            c[i] = c2[i].val();
        }
        return c;
    }

    std::vector<long long> convolution_ll(const std::vector<long long>& a,
                                          const std::vector<long long>& b) {
        int n = int(a.size()), m = int(b.size());
        if (!n || !m) return {};

        static constexpr unsigned long long MOD1 = 754974721;  // 2^24
        static constexpr unsigned long long MOD2 = 167772161;  // 2^25
        static constexpr unsigned long long MOD3 = 469762049;  // 2^26
        static constexpr unsigned long long M2M3 = MOD2 * MOD3;
        static constexpr unsigned long long M1M3 = MOD1 * MOD3;
        static constexpr unsigned long long M1M2 = MOD1 * MOD2;
        static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;

        static constexpr unsigned long long i1 =
                internal::inv_gcd(MOD2 * MOD3, MOD1).second;
        static constexpr unsigned long long i2 =
                internal::inv_gcd(MOD1 * MOD3, MOD2).second;
        static constexpr unsigned long long i3 =
                internal::inv_gcd(MOD1 * MOD2, MOD3).second;

        static constexpr int MAX_AB_BIT = 24;
        static_assert(MOD1 % (1ull << MAX_AB_BIT) == 1, "MOD1 isn't enough to support an array length of 2^24.");
        static_assert(MOD2 % (1ull << MAX_AB_BIT) == 1, "MOD2 isn't enough to support an array length of 2^24.");
        static_assert(MOD3 % (1ull << MAX_AB_BIT) == 1, "MOD3 isn't enough to support an array length of 2^24.");
        assert(n + m - 1 <= (1 << MAX_AB_BIT));

        auto c1 = convolution<MOD1>(a, b);
        auto c2 = convolution<MOD2>(a, b);
        auto c3 = convolution<MOD3>(a, b);

        std::vector<long long> c(n + m - 1);
        for (int i = 0; i < n + m - 1; i++) {
            unsigned long long x = 0;
            x += (c1[i] * i1) % MOD1 * M2M3;
            x += (c2[i] * i2) % MOD2 * M1M3;
            x += (c3[i] * i3) % MOD3 * M1M2;
            // B = 2^63, -B <= x, r(real value) < B
            // (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
            // r = c1[i] (mod MOD1)
            // focus on MOD1
            // r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
            // r = x,
            //     x - M' + (0 or 2B),
            //     x - 2M' + (0, 2B or 4B),
            //     x - 3M' + (0, 2B, 4B or 6B) (without mod!)
            // (r - x) = 0, (0)
            //           - M' + (0 or 2B), (1)
            //           -2M' + (0 or 2B or 4B), (2)
            //           -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
            // we checked that
            //   ((1) mod MOD1) mod 5 = 2
            //   ((2) mod MOD1) mod 5 = 3
            //   ((3) mod MOD1) mod 5 = 4
            long long diff =
                    c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
            if (diff < 0) diff += MOD1;
            static constexpr unsigned long long offset[5] = {
                    0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
            x -= offset[diff % 5];
            c[i] = x;
        }

        return c;
    }

}  // namespace atcoder

namespace atcoder {

long long pow_mod(long long x, long long n, int m) {
    assert(0 <= n && 1 <= m);
    if (m == 1) return 0;
    internal::barrett bt((unsigned int)(m));
    unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
    while (n) {
        if (n & 1) r = bt.mul(r, y);
        y = bt.mul(y, y);
        n >>= 1;
    }
    return r;
}

long long inv_mod(long long x, long long m) {
    assert(1 <= m);
    auto z = internal::inv_gcd(x, m);
    assert(z.first == 1);
    return z.second;
}

// (rem, mod)
std::pair<long long, long long> crt(const std::vector<long long>& r,
                                    const std::vector<long long>& m) {
    assert(r.size() == m.size());
    int n = int(r.size());
    // Contracts: 0 <= r0 < m0
    long long r0 = 0, m0 = 1;
    for (int i = 0; i < n; i++) {
        assert(1 <= m[i]);
        long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
        if (m0 < m1) {
            std::swap(r0, r1);
            std::swap(m0, m1);
        }
        if (m0 % m1 == 0) {
            if (r0 % m1 != r1) return {0, 0};
            continue;
        }
        // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1)

        // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1));
        // r2 % m0 = r0
        // r2 % m1 = r1
        // -> (r0 + x*m0) % m1 = r1
        // -> x*u0*g = r1-r0 (mod u1*g) (u0*g = m0, u1*g = m1)
        // -> x = (r1 - r0) / g * inv(u0) (mod u1)

        // im = inv(u0) (mod u1) (0 <= im < u1)
        long long g, im;
        std::tie(g, im) = internal::inv_gcd(m0, m1);

        long long u1 = (m1 / g);
        // |r1 - r0| < (m0 + m1) <= lcm(m0, m1)
        if ((r1 - r0) % g) return {0, 0};

        // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1)
        long long x = (r1 - r0) / g % u1 * im % u1;

        // |r0| + |m0 * x|
        // < m0 + m0 * (u1 - 1)
        // = m0 + m0 * m1 / g - m0
        // = lcm(m0, m1)
        r0 += x * m0;
        m0 *= u1;  // -> lcm(m0, m1)
        if (r0 < 0) r0 += m0;
    }
    return {r0, m0};
}

long long floor_sum(long long n, long long m, long long a, long long b) {
    //assert(0 <= n && n < (1LL << 32));
    //assert(1 <= m && m < (1LL << 32));
    unsigned long long ans = 0;
    if (a < 0) {
        unsigned long long a2 = internal::safe_mod(a, m);
        ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m);
        a = a2;
    }
    if (b < 0) {
        unsigned long long b2 = internal::safe_mod(b, m);
        ans -= 1ULL * n * ((b2 - b) / m);
        b = b2;
    }
    return ans + internal::floor_sum_unsigned(n, m, a, b);
}

}  // namespace atcoder

using namespace atcoder;

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
//using mint = modint;
using mint = modint998244353;

#include <bits/stdc++.h>

using namespace std;

int main(void)
{
	cin.tie(0);
	ios::sync_with_stdio(false);

    int n,t;
    vector <int> A;

    cin >> n;
    for(int i=0;i<n;i++)
    {
        cin >> t;
        A.push_back(t);
    }

    mint res = 0;

    sort(A.begin(),A.end());

    for(int i=0;i<n;i++)
    {
        res = res*10 + A[i];
    }

    cout << res.val() << '\n';
    
	return 0;
}