#pragma region Macros

#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,fma,abm,mmx,avx,avx2")

#include <bits/extc++.h>
// #include <atcoder/all>
// using namespace atcoder;
using namespace std;
using namespace __gnu_pbds;

// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// using Bint = mp::cpp_int;
// using Bdouble = mp::number<mp::cpp_dec_float<256>>;

#define pb emplace_back
#define int ll
#define endl '\n'

#define sqrt __builtin_sqrtl
#define cbrt __builtin_cbrtl
#define hypot __builtin_hypotl

using ll = long long;
using ld = long double;
const ld PI = acosl(-1);
const int INF = 1 << 30;
const ll INFL = 1LL << 61;
const int MOD = 998244353;
// const int MOD = 1000000007;

const ld EPS = 1e-10;
const bool equals(ld a, ld b) { return fabs((a) - (b)) < EPS; }

const vector<int> dx = {0, 1, 0, -1, 1, 1, -1, -1}; // → ↓ ← ↑ ↘ ↙ ↖ ↗
const vector<int> dy = {1, 0, -1, 0, 1, -1, -1, 1};

struct Edge {
    int from, to;
    ll cost;
    Edge(int to, ll cost) : to(to), cost(cost) {}
    Edge(int from, int to, ll cost) : from(from), to(to), cost(cost) {}
};

chrono::system_clock::time_point  start, now;
__attribute__((constructor))
void constructor() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(10);
    start = chrono::system_clock::now();
}

__int128_t POW(__int128_t x, int n) {
    __int128_t ret = 1;
    assert(n >= 0);
    if (x == 1 or n == 0) ret = 1;
    else if (x == -1 && n % 2 == 0) ret = 1; 
    else if (x == -1) ret = -1; 
    else if (n % 2 == 0) {
        assert(x < INFL);
        ret = POW(x * x, n / 2);
    } else {
        assert(x < INFL);
        ret = x * POW(x, n - 1);
    }
    return ret;
}
int per(int x, int y) { // x = qy + r (0 <= r < y) を満たすq
    assert(y != 0);
    if (x >= 0 && y > 0) return x / y;
    if (x >= 0 && y < 0) return x / y - (x % y < 0);
    if (x < 0 && y < 0) return x / y + (x % y < 0);
    return x / y - (x % y < 0); //  (x < 0 && y > 0) 
}
// int perl(ld x, ld y) { // perld(4.5, 2.1) = 2  // TODO
//     if (-EPS < x && x < 0 or 0 < x && x < EPS) x = 0;
//     if (-EPS < y && y < 0 or 0 < x && x < EPS) y = 0;
//     assert(!equals(y, 0));
//     if (x >= 0 && y > 0) return floor(x / y)+EPS;
//     if (x >= 0 && y < 0) return floor(x / y) - (x - floor(x/y)*y < -EPS);
//     if (x < 0 && y < 0) return floor(x / y) + (x - floor(x/y)*y < -EPS);
//     return floor(x / y) - (x - floor(x/y)*y < -EPS); //  (x < 0 && y > 0) 
// }
int mod(int x, int y) { // x = qy + r (0 <= r < y) を満たすr
    assert(y != 0);
    if (x >= 0) return x % y;
    __int128_t ret = x % y; // (x < 0)
    ret += (__int128_t)abs(y) * INFL;
    ret %= abs(y);
    return ret;
}
// ld modl(ld x, ld y) { // TODO
//     assert(!equals(y, 0));
//     if (x >= -EPS) return (x - floor(x/y)*y);
//     ld ret = x - floor(x/y)*y; // (x < 0)
//     ret += abs(y) * INFL; // TODO : オーバーフローする?
//     ret = x - floor(x/abs(y))*abs(y);
//     return ret;
// }
int floor(int x, int y) { // (ld)x / y 以下の最大の整数
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return x >= 0 ? x / y : (x + 1) / y - 1;
}
int ceil(int x, int y) { // (ld)x / y 以上の最小の整数
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return x > 0 ? (x - 1) / y + 1 : x / y;
}
int floor(ld x, ld y) {
    assert(!equals(y, 0));
    return floor(x / y) + EPS;
}
int ceil(ld x, ld y) {
    assert(!equals(y, 0));
    return ceil(x / y) + EPS;
}
int seisuu(ld x) { // 整数部分
    return (int)(x + EPS);
}
int seisuu(int x, int y) {
    assert(y != 0);
    return x / y;
}
int seisuu(ld x, ld y) {
    return (int)(x / y + EPS);
}

pair<int, int> max(const pair<int, int> &a, const pair<int, int> &b) {
    if (a.first > b.first or a.first == b.first && a.second > b.second) {
        return a;
    }
    return b;
}
pair<int, int> min(const pair<int, int> &a, const pair<int, int> &b) {
    if (a.first < b.first or a.first == b.first && a.second < b.second) {
        return a;
    }
    return b;
}

template <class T> bool chmax(T &a, const T& b) {
    if (a < b) { a = b; return true; }
    return false;
}
template <class T> bool chmin(T &a, const T& b) {
    if (a > b) { a = b; return true; }
    return false;
}
template <class T> T mid(T a, T b, T c) {
    return a + b + c - max({a, b, c}) - min({a, b, c});
}
template <class T> void sort(T &a, T &b, T &c, bool rev = false) {
    if (rev == false) { 
        if (a > b) swap(a, b);
        if (a > c) swap(a, c);
        if (b > c) swap(b, c);
    } else {
        if (c > b) swap(c, b);
        if (c > a) swap(c, a);
        if (b > a) swap(b, a);
    }
}
template <class T> void sort(T &a, T &b, T &c, T &d, bool rev = false) {
    if (rev == false) { 
        if (a > b) swap(a, b); if (a > c) swap(a, c);  if (a > d) swap(a, d);
        if (b > c) swap(b, c); if (b > d) swap(b, d);
        if (c > d) swap(c, d);
    } else {
        if (d > c) swap(d, c); if (d > b) swap(d, b); if (d > a) swap(d, a);
        if (c > b) swap(c, b); if (c > a) swap(c, a);
        if (b > a) swap(b, a);
    }
}

int countl_zero(int x) { return __builtin_clzll(x); }
int countl_one(int x) {
    int ret = 0; while (x % 2) { x /= 2; ret++; }
    return ret;
}
int countr_zero(int x) { return __builtin_ctzll(x); }
int countr_one(int x) {
    int ret = 0, k = 63 - __builtin_clzll(x);
    while (k != -1 && (x & (1LL << k))) { k--; ret++; }
    return ret;
}
int popcount(int x) { return __builtin_popcountll(x); }
int unpopcount(int x) { return 64 - __builtin_clzll(x) - __builtin_popcountll(x); }

int top_bit(int x) { return 63 - __builtin_clzll(x);} // 2^kの位
int bot_bit(int x) { return __builtin_ctz(x);} // 2^kの位
int MSB(int x) { return 1 << (63 - __builtin_clzll(x)); } // mask
int LSB(int x) { return (x & -x); } // mask

int bit_width(int x) { return 64 - __builtin_clzll(x); } // 桁数
int ceil_log2(int x) { return 63 - __builtin_clzll(x); }
int bit_floor(int x) { return 1 << (63 - __builtin_clzll(x)); }
int floor_log2(int x) { return 64 - __builtin_clzll(x-1); }
int bit_ceil(int x) { return 1 << (64 - __builtin_clzll(x-1)) - (x==1); }

int hamming(int a, int b) { return popcount(a ^ b); }
int compcnt(int x) { return (popcount(x^(x >> 1)) + (x&1)) / 2; }

class UnionFind {
public:
	UnionFind() = default;
    UnionFind(int N) : par(N), sz(N, 1) {
        iota(par.begin(), par.end(), 0);
    }

	int root(int x) {
		if (par[x] == x) return x;
		return (par[x] = root(par[x]));
	}

	bool unite(int x, int y) {
		int rx = root(x);
		int ry = root(y);

        if (rx == ry) return false;
		if (sz[rx] < sz[ry]) swap(rx, ry);

		sz[rx] += sz[ry];
		par[ry] = rx;

        return true;
	}

	bool issame(int x, int y) { return (root(x) == root(y)); }
	int size(int x) { return sz[root(x)]; }

    vector<vector<int>> groups(int N) {
        vector<vector<int>> G(N);
        for (int x = 0; x < N; x++) {
            G[root(x)].push_back(x);
        }
		G.erase(
            remove_if(G.begin(), G.end(),
                [&](const vector<int>& V) { return V.empty(); }),
                    G.end());
        return G;
    }
private:
	vector<int> par;
	vector<int> sz;
};

template<int mod> class Modint{
public:
    int val = 0;
    Modint(int x = 0) { while (x < 0) x += mod; val = x % mod; }
    Modint(const Modint &r) { val = r.val; }

    Modint operator -() { return Modint(-val); } // 単項
    Modint operator +(const Modint &r) { return Modint(*this) += r; }
    Modint operator +(const int &q) { Modint r(q); return Modint(*this) += r; }
    Modint operator -(const Modint &r) { return Modint(*this) -= r; }
    Modint operator -(const int &q) { Modint r(q); return Modint(*this) -= r; }
    Modint operator *(const Modint &r) { return Modint(*this) *= r; }
    Modint operator *(const int &q) { Modint r(q); return Modint(*this) *= r; }
    Modint operator /(const Modint &r) { return Modint(*this) /= r; }
    Modint operator /(const int &q) { Modint r(q); return Modint(*this) /= r; }
    
    Modint& operator ++() { val++; if (val >= mod) val -= mod; return *this; } // 前置
    Modint operator ++(signed) { ++*this; return *this; } // 後置
    Modint& operator --() { val--; if (val < 0) val += mod; return *this; }
    Modint operator --(signed) { --*this; return *this; }
    Modint &operator +=(const Modint &r) { val += r.val; if (val >= mod) val -= mod; return *this; }
    Modint &operator +=(const int &q) { Modint r(q); val += r.val; if (val >= mod) val -= mod; return *this; }
    Modint &operator -=(const Modint &r) { if (val < r.val) val += mod; val -= r.val; return *this; }
    Modint &operator -=(const int &q) { Modint r(q);  if (val < r.val) val += mod; val -= r.val; return *this; }
    Modint &operator *=(const Modint &r) { val = val * r.val % mod; return *this; }
    Modint &operator *=(const int &q) { Modint r(q); val = val * r.val % mod; return *this; }
    Modint &operator /=(const Modint &r) {
        int a = r.val, b = mod, u = 1, v = 0;
        while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);}
        val = val * u % mod; if (val < 0) val += mod;
        return *this;
    }
    Modint &operator /=(const int &q) {
        Modint r(q); int a = r.val, b = mod, u = 1, v = 0;
        while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);}
        val = val * u % mod; if (val < 0) val += mod;
        return *this;
    }

    bool operator ==(const Modint& r) { return this -> val == r.val; }
    bool operator <(const Modint& r) { return this -> val < r.val; }
    bool operator >(const Modint& r) { return this -> val > r.val; }
    bool operator !=(const Modint& r) { return this -> val != r.val; }
};

using mint = Modint<MOD>;
// using Mint = modint998244353;

istream &operator >>(istream &is, mint& x) {
    int t; is >> t;
    x = t;
    return (is);
}
ostream &operator <<(ostream &os, const mint& x) {
    return os << x.val;
}
mint modpow(const mint &x, int n) {
    assert(n >= 0); // TODO: n <= -1
    if (n == 0) return 1;
    mint t = modpow(x, n / 2);
    t = t * t;
    if (n & 1) t = t * x;
    return t;
}

int modpow(__int128_t x, int n, int mod) {
    assert(n >= 0 && mod > 0); // TODO: n <= -1
    __int128_t ret = 1;
    while (n > 0) {
        if (n % 2 == 1) ret = ret * x % mod;
        x = x * x % mod;
        n /= 2;
    }
    return ret;
}

int modinv(__int128_t x, int mod) {
    assert(mod > 0 && x > 0);
    if (x == 1) return 1;
    return mod - modinv(mod % x, mod) * (mod / x) % mod;
}

istream &operator >>(istream &is, __int128_t& x) {
    string S; is >> S;
    __int128_t ret = 0;
    int f = 1;
    if (S[0] == '-') f = -1; 
    for (int i = 0; i < S.length(); i++)
        if ('0' <= S[i] && S[i] <= '9')
            ret = ret * 10 + S[i] - '0';
    x = ret * f;
    return (is);
}
ostream &operator <<(ostream &os, __int128_t x) {
    ostream::sentry s(os);
    if (s) {
        __uint128_t tmp = x < 0 ? -x : x;
        char buffer[128];
        char *d = end(buffer);

        do {
            --d;
            *d = "0123456789"[tmp % 10];
            tmp /= 10;
        } while (tmp != 0);

        if (x < 0) {
            --d;
            *d = '-';
        }
        int len = end(buffer) - d;

        if (os.rdbuf()->sputn(d, len) != len) {
            os.setstate(ios_base::badbit);
        }
    }
    return os;
}

__int128_t stoll(string &S) {
    __int128_t ret = 0;
    int f = 1;
    if (S[0] == '-') f = -1; 
    for (int i = 0; i < S.length(); i++)
        if ('0' <= S[i] && S[i] <= '9')
            ret = ret * 10 + S[i] - '0';
    return ret * f;
}
__int128_t gcd(__int128_t a, __int128_t b) {
    return b ? gcd(b, a % b) : a;
}
__int128_t lcm(__int128_t a, __int128_t b) {
    return a / gcd(a, b) * b;
    // lcmが__int128_tに収まる必要あり
}

string to_string(ld x, int k) { // xの小数第k位までをstring化する
    assert(k >= 0);
    stringstream ss;
    ss << setprecision(k + 2) << x;
    string s = ss.str();
    if (s.find('.') == string::npos) s += '.';
    int pos = s.find('.');
    for (int i = 0; k >= (int)s.size() - 1 - pos; i++) s += '0';
    s.pop_back();
    if (s.back() == '.') s.pop_back();
    return s;

    // stringstream ss; // 第k+1位を四捨五入して第k位まで返す
    // ss << setprecision(k + 1) << x;
    // string s = ss.str();
    // if (s.find('.') == string::npos) s += '.';
    // int pos = s.find('.');
    // for (int i = 0; k > (int)s.size() - 1 - pos; i++) s += '0';
    // if (s.back() == '.') s.pop_back();
    // return s;
}

string to_string(__int128_t x) {
    string ret = "";
    if (x < 0) {
        ret += "-";
        x *= -1;
    }
    while (x) {
        ret += (char)('0' + x % 10);
        x /= 10;
    }
    reverse(ret.begin(), ret.end());
    return ret;
}
string to_string(char c) {
    string s = "";
    s += c;
    return s;
}

struct SXor128 {
    uint64_t x = 88172645463325252LL;
    unsigned Int() {
        x = x ^ (x << 7);
        return x = x ^ (x >> 9);
    }
    unsigned Int(unsigned mod) {
        x = x ^ (x << 7);
        x = x ^ (x >> 9);
        return x % mod;
    }
    unsigned Int(unsigned l, unsigned r) {
        x = x ^ (x << 7);
        x = x ^ (x >> 9);
        return x % (r - l + 1) + l;
    }
    double Double() {
        return double(Int()) / UINT_MAX;
    }
} rnd;

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

template<class T> size_t HashCombine(const size_t seed,const T &v) {
    return seed^(hash<T>()(v)+0x9e3779b9+(seed<<6)+(seed>>2));
}
template<class T,class S> struct hash<pair<T,S>>{
    size_t operator()(const pair<T,S> &keyval) const noexcept {
        return HashCombine(hash<T>()(keyval.first), keyval.second);
    }
};
template<class T> struct hash<vector<T>>{
    size_t operator()(const vector<T> &keyval) const noexcept {
        size_t s=0;
        for (auto&& v: keyval) s=HashCombine(s,v);
        return s;
    }
};
template<int N> struct HashTupleCore{
    template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{
        size_t s=HashTupleCore<N-1>()(keyval);
        return HashCombine(s,get<N-1>(keyval));
    }
};
template <> struct HashTupleCore<0>{
    template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{ return 0; }
};
template<class... Args> struct hash<tuple<Args...>>{
    size_t operator()(const tuple<Args...> &keyval) const noexcept {
        return HashTupleCore<tuple_size<tuple<Args...>>::value>()(keyval);
    }
};

vector<mint> _fac, _finv, _inv;
void COMinit(int N) {
    _fac.resize(N + 1);
    _finv.resize(N + 1);
    _inv.resize(N + 1);
    _fac[0] = _fac[1] = 1;
    _finv[0] = _finv[1] = 1;
    _inv[1] = 1;
    for (int i = 2; i <= N; i++) {
        _fac[i] = _fac[i-1] * mint(i);
        _inv[i] = -_inv[MOD % i] * mint(MOD / i);
        _finv[i] = _finv[i - 1] * _inv[i];
    }
}

mint FAC(int N) {
    if (N < 0) return 0;
    return _fac[N];
}
mint COM(int N, int K) {
    if (N < K) return 0;
    if (N < 0 or K < 0) return 0;
    return _fac[N] * _finv[K] * _finv[N - K];
}
mint PERM(int N, int K) {
    if (N < K) return 0;
    if (N < 0 or K < 0) return 0;
    return _fac[N] *  _finv[N - K];
}
mint NHK(int N, int K) {
    if (N == 0 && K == 0)  return 1;
    return COM(N + K - 1, K);
}

#pragma endregion

template <typename Key, typename Val>
struct HashMap {
    using u32 = uint32_t;
    using u64 = uint64_t;

    u32 cap, s;
    vector<Key> keys;
    vector<Val> vals;
    vector<bool> flag;
    u64 r;
    u32 shift;
    Val DefaultValue;

    static u64 rng() {
        u64 m = chrono::duration_cast<chrono::nanoseconds>(
                    chrono::high_resolution_clock::now().time_since_epoch())
                    .count();
        m ^= m >> 16;
        m ^= m << 32;
        return m;
    }

    void reallocate() {
        cap <<= 1;
        vector<Key> k(cap);
        vector<Val> v(cap);
        vector<bool> f(cap);
        u32 sh = shift - 1;
        for (int i = 0; i < (int)flag.size(); i++) {
            if (flag[i]) {
                u32 hash = (u64(keys[i]) * r) >> sh;
                while (f[hash]) hash = (hash + 1) & (cap - 1);
                k[hash] = keys[i];
                v[hash] = vals[i];
                f[hash] = 1;
            }
        }
        keys.swap(k);
        vals.swap(v);
        flag.swap(f);
        --shift;
    }

    explicit HashMap()
        : cap(8),
            s(0),
            keys(cap),
            vals(cap),
            flag(cap),
            r(rng()),
            shift(64 - __lg(cap)),
            DefaultValue(Val()) {}

    Val& operator[](const Key& i) {
        u32 hash = (u64(i) * r) >> shift;
        while (true) {
            if (!flag[hash]) {
                if (s + s / 4 >= cap) {
                reallocate();
                return (*this)[i];
                }
                keys[hash] = i;
                flag[hash] = 1;
                ++s;
                return vals[hash] = DefaultValue;
            }
            if (keys[hash] == i) return vals[hash];
            hash = (hash + 1) & (cap - 1);
        }
    }

    // exist -> return pointer of Val
    // not exist -> return nullptr
    const Val* find(const Key& i) const {
        u32 hash = (u64(i) * r) >> shift;
        while (true) {
            if (!flag[hash]) return nullptr;
            if (keys[hash] == i) return &(vals[hash]);
        hash = (hash + 1) & (cap - 1);
        }
    }

    // return vector< pair<const Key&, val& > >
    vector<pair<Key, Val>> enumerate() const {
        vector<pair<Key, Val>> ret;
        for (u32 i = 0; i < cap; ++i)
            if (flag[i]) ret.emplace_back(keys[i], vals[i]);
        return ret;
    }

    int size() const { return s; }

    // set default_value
    void set_default(const Val& val) { DefaultValue = val; }
};

template <typename S, typename T>
struct DynamicBITwa {
    S N;
    HashMap<S, T> data;
    explicit DynamicBITwa() = default;
    explicit DynamicBITwa(S size) { N = size + 1; }

    void add(S k, T x) {
        for (++k; k < N; k += k & -k) data[k] += x;
    }

    // [0, k)
    T sum(S k) const {
        if (k < 0) return 0;
        T ret = T();
        for (; k > 0; k -= k & -k) {
            const T* p = data.find(k);
            ret += p ? *p : T();
        }
        return ret;
    }

    // [a, b)
    T sum(S a, S b) const { return sum(b) - sum(a); }

    T operator[](S k) const { return sum(k + 1) - sum(k); }

    S lower_bound(T w) {
        if (w <= 0) return 0;
        S x = 0;
        for (S k = 1 << __lg(N); k; k >>= 1) {
            if (x + k <= N - 1 && data[x + k] < w) {
                w -= data[x + k];
                x += k;
            }
        }
        return x;
    }
};

template <typename T>
struct DynamicBIT2Dwa {
    using BITwa = DynamicBITwa<int, T>;
    int N, M;
    vector<BITwa*> bit;
    DynamicBIT2Dwa() = default;
    DynamicBIT2Dwa(int n, int m) : N(n + 1), M(m) {
        for (int _ = 0; _ < N; ++_) bit.push_back(new BITwa(M));
    }
  
    void add(int i, int j, const T& x) {
        for (++i; i < N; i += i & -i) (*bit[i]).add(j, x);
    }

    // i = [0, n), j = [0, m)
    T sum(int n, int m) const {
        if (n < 0 || m < 0) return T();
        T ret = T();
        for (; n; n -= n & -n) ret += (*bit[n]).sum(m);
        return ret;
    }

    // i = [x1, x2), j = [y1, y2)
    T sum(int x1, int y1, int x2, int y2) const {
        T ret = T();
        while (x1 != x2) {
            if (x1 < x2) {
                ret += (*bit[x2]).sum(y1, y2);
                x2 -= x2 & -x2;
            } else {
                ret -= (*bit[x1]).sum(y1, y2);
                x1 -= x1 & -x1;
            }
        }
        return ret;
    }

    T get(int x, int y) {
        return sum(x, y, x + 1, y + 1);
    }
    void set(int x, int y, T w) {
        T s = get(x, y);
        add(x, y, s + w);
    }
};

template <typename S, typename T>
struct DynamicBITseki {
    S N;
    HashMap<S, mint> data;
    explicit DynamicBITseki() = default;
    explicit DynamicBITseki(S size) { N = size + 1; }

    void apply(S k, mint x) {
        for (++k; k < N; k += k & -k) {
            const mint* p = data.find(k);
            if (p) data[k] *= x;
            else data[k] = x;
        }
    }

    // [0, k)
    mint prod(S k) const {
        if (k < 0) return 1;
        mint ret = 1;
        for (; k > 0; k -= k & -k) {
            const mint* p = data.find(k);
            ret *= p ? *p : (mint)1;
        }
        return ret;
    }

    // [a, b)
    mint prod(S a, S b) const { return prod(b) / prod(a); }

    mint operator[](S k) const { return prod(k + 1) / prod(k); }
};

template <typename T>
struct DynamicBIT2Dseki {
    using BITseki = DynamicBITseki<int, mint>;
    int N, M;
    vector<BITseki*> bit;
    DynamicBIT2Dseki() = default;
    DynamicBIT2Dseki(int n, int m) : N(n + 1), M(m) {
        for (int _ = 0; _ < N; ++_) bit.push_back(new BITseki(M));
    }
  
    void apply(int i, int j, const mint& x) {
        for (++i; i < N; i += i & -i) (*bit[i]).apply(j, x);
    }

    // i = [0, n), j = [0, m)
    mint prod(int n, int m) const {
        if (n < 0 or m < 0) return (mint)1;
        mint ret = 1;
        for (; n; n -= n & -n) ret *= (*bit[n]).prod(m);
        return ret;
    }

    // i = [x1, x2), j = [y1, y2)
    mint prod(int x1, int y1, int x2, int y2) const {
        mint ret = 1;
        while (x1 != x2) {
            if (x1 < x2) {
                ret *= (*bit[x2]).prod(y1, y2);
                x2 -= x2 & -x2;
            } else {
                ret /= (*bit[x1]).prod(y1, y2);
                x1 -= x1 & -x1;
            }
        }
        return ret;
    }

    mint get(int x, int y) {
        return prod(x, y, x + 1, y + 1);
    }
    // void set(int x, int y, mint w) {
    //     apply(x, y, get(x, y)*w);
    // }
};

signed main() {
    int H, W;
    cin >> H >> W;

    DynamicBIT2Dseki<mint> bit(H, W);
    DynamicBIT2Dwa<int> cnt(H, W);
    vector<vector<int>> A(H, vector<int>(W));
    for (int i = 0; i < H; i++) {
        for (int j = 0; j < W; j++) {
            cin >> A[i][j];
            if (A[i][j] != 0) bit.apply(i, j, A[i][j]);
            else cnt.add(i, j, 1);
        }
    }

    int Q;
    cin >> Q;
    for (int q = 0; q < Q; q++) {
        int r, c;
        cin >> r >> c;
        r--; c--;

        int i1 = 0, j1 = 0, i2 = r - 1, j2 = c - 1;
        mint tot1 = 1;
        if (i1 <= i2 && j1 <= j2) tot1 *= bit.prod(i1, j1, i2 + 1, j2 + 1);
        if (i1 <= i2 && j1 <= j2 && cnt.sum(i1, j1, i2 + 1, j2 + 1) > 0) tot1 = 0;

        i1 = 0, j1 = c + 1, i2 = r - 1, j2 = W - 1;
        mint tot2 = 1;
        if (i1 <= i2 && j1 <= j2) tot2 *= bit.prod(i1, j1, i2 + 1, j2 + 1);
        if (i1 <= i2 && j1 <= j2 && cnt.sum(i1, j1, i2 + 1, j2 + 1) > 0) tot2 = 0;

        i1 = r + 1, j1 = 0, i2 = H - 1, j2 = c - 1;
        mint tot3 = 1;
        if (i1 <= i2 && j1 <= j2) tot3 *= bit.prod(i1, j1, i2 + 1, j2 + 1);
        if (i1 <= i2 && j1 <= j2 && cnt.sum(i1, j1, i2 + 1, j2 + 1) > 0) tot3 = 0;

        i1 = r + 1, j1 = c + 1, i2 = H - 1, j2 = W - 1;
        mint tot4 = 1;
        if (i1 <= i2 && j1 <= j2) tot4 *= bit.prod(i1, j1, i2 + 1, j2 + 1);
        if (i1 <= i2 && j1 <= j2 && cnt.sum(i1, j1, i2 + 1, j2 + 1) > 0) tot4 = 0;

        cout << tot1 * tot2 * tot3 * tot4 << endl;
    }
}