/**
 * date    : 2026-10-23 21:57:15
 * author  : yamadanull
 * library : https://github.com/yamadanull/yamadalib/
 */

// ===== BEGIN INCLUDE: ../../template/template.hpp =====

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

// ===== BEGIN INCLUDE: util.hpp =====
namespace yamada {
using ll = long long;
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using lld = long double;

template <typename T>
using vc = vector<T>;
template <typename T>
using vvc = vector<vector<T>>;
template <typename T>
using vvvc = vector<vector<vector<T>>>;
template <typename T>
using vvvvc = vector<vector<vector<vector<T>>>>;
using vint = vector<int>;
using vl = vector<long long>;
using vd = vector<double>;
using vs = vector<string>;
using vvl = vector<vector<long long>>;
using vvvl = vector<vector<vector<long long>>>;
using vvvvl = vector<vector<vector<vector<long long>>>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxpq = priority_queue<T, vector<T>, less<T>>;

using pint = pair<int, int>;
using pl = pair<ll, ll>;
using vp = vc<pl>;
using vvp = vvc<pl>;

template <typename T>
int len(const T &t) { return t.size(); }

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T, typename U>
inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template <typename T, typename U>
inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) { return make_pair(t, u); }
template <typename... Args>
tuple<Args...> mkt(const Args&... args) { return make_tuple(args...); }

template <ranges::input_range R>
ranges::range_value_t<R> Sum(const R &v) { return ranges::fold_left(v, ranges::range_value_t<R>(0), plus()); }

template <typename T>
int lb(const vector<T> &v, const T &a) { return ranges::lower_bound(v, a) - v.begin(); }
template <typename T>
int ub(const vector<T> &v, const T &a) { return ranges::upper_bound(v, a) - v.begin(); }

constexpr long long TEN(int n) {
	long long ret = 1, x = 10;
	for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
	return ret;
}

template <typename T>
vector<T> mkrui(const vector<T> &v, const bool rev = false) {
	vector<T> ret(v.size() + 1);
	if (rev) {
		for (int i = (int)v.size() - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
	} else {
		for (int i = 0; i < (int)v.size(); i++) ret[i + 1] = ret[i] + v[i];
	}
	return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
	vector<T> ret(v);
	ranges::sort(ret);
	ret.erase(ranges::unique(ret).begin(), ret.end());
	return ret;
}

template <typename F>
vector<int> mkord(int N, const F &f) {
	vector<int> ord = views::iota(0, N) | ranges::to<vector>();
	ranges::sort(ord, f);
	return ord;
}

template <typename T>
vector<int> mkinv(const vector<T> &v) {
	vector<int> inv(ranges::max(v) + 1, -1);
	for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
	return inv;
}

vector<int> mkiota(int N) { return views::iota(0, N) | ranges::to<vector>(); }

vector<int> p_mrg(const vector<int> &f, const vector<int> &g) { // g o f
	return f | views::transform([&](auto a) { return g[a]; }) | ranges::to<vector>();
}

template <typename T> // f: old_idx -> new_idx
vector<T> p_shf(const vector<T>& A, const vector<int>& f, const bool inv = false) {
	int n = A.size();
	vector<T> ret(n);
	if (!inv) for (int i = 0; i < n; i++) ret[f[i]] = A[i];
	else for (int i = 0; i < n; i++) ret[i] = A[f[i]];
	return ret;
}

template <typename T>
T mkrev(const T &v) { return v | views::reverse | ranges::to<vector>(); }

template <typename C>
bool nxp(C &v) { return ranges::next_permutation(v).found; }
template <typename F>
void nxp(int N, F f) {
	auto a = views::iota(0, N) | ranges::to<vector>();
	do { f(a); } while (nxp(a));
}

// i 要素目 : [0, A[i])
template <typename F>
void Product(const vector<int> &A, const F& f) {
	vector<int> cur;
	[&](this auto dfs, int i) -> void {
		if (i == (int)A.size()) { f(cur); return; }
		for (int j = 0; j < A[i]; j++) cur.emplace_back(j), dfs(i + 1), cur.pop_back();
	}(0);
}
// i 要素目 : [0, M)
template <typename F>
void Product(const int N, const int M, const F& f) { vector<int> A(N, M); Product(A, f); }

template <typename T, typename U>
vector<U> Digit(T a, const U &x, int siz = -1) {
	vector<U> ret;
	while (a > 0) {
		ret.emplace_back(a % x);
		a /= x;
	}
	if (siz >= 0) ret.resize(siz);
	return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
	T res = I;
	for (; n; f(a = a * a), n >>= 1) {
		if (n & 1) f(res = res * a);
	}
	return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
	return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

template <typename T>
vector<T> Transpose(const vector<T> &A) {
	if (A.empty()) return {};
	return views::iota(0, (int)A[0].size()) | views::transform([&](auto j) {
		return A | views::transform([&](auto&& a) { return a[j]; }) | ranges::to<T>();
	}) | ranges::to<vector<T>>();
}

template <typename T>
vector<T> RotateGrid(const vector<T> &A) {
	if (A.empty()) return {};
	return views::iota(0, (int)A[0].size()) | views::transform([&](auto j) {
		return A | views::transform([&](auto&& a) { return a[j]; }) | ranges::to<T>();
	}) | views::reverse | ranges::to<vector<T>>();
}

template <typename T, typename F>
T bisect(T ok, T ng, F f) { // ok < ng でも ok > ng でも可能 // f(ok) && !f(ng) が必要
	while (abs(ok - ng) > 1) { T mid = (ok + ng) / 2; (f(mid) ? ok : ng) = mid; } 
	return ok;
}

template <typename T, typename F>
T bisect(F f) { // 判定回数は上限を決め打ちした場合の高々２倍程度 // f(0) && !f(inf) が必要
	T ok = 0, ng = 1;
	while (f(ng)) ng *= 2;
	while (ng - ok > 1) { T mid = ok + (ng - ok) / 2; (f(mid) ? ok : ng) = mid; } 
	return ng;
}

template <typename T, typename F>
T bisect_double(T ok, T ng, F f, int iter = 100) {
	if (ok == ng) return ok;
	while (iter--) { T mid = (ok + ng) / 2; (f(mid) ? ok : ng) = mid; } 
	return ng;
}

template <typename T0, typename T1, typename T2>
bool inLR(T0 L, T1 x, T2 R){ return L <= x && x < R; }
bool YESNO(bool b) { cout << (b ? "YES\n" : "NO\n"); return b; }
bool YesNo(bool b) { cout << (b ? "Yes\n" : "No\n"); return b; }
bool yesno(bool b) { cout << (b ? "yes\n" : "no\n"); return b; }

long long Isqrt(long long n) {
	if (n <= 0) return 0;
	long long x = sqrt(n);
	while ((x + 1) * (x + 1) <= n) x++;
	while (x * x > n) x--;
	return x;
}

template <typename T>
struct CumulativeSum {
	vector<T> S;
	CumulativeSum(vector<T> &A) : S(A.size() + 1) {
		for (int i = 0; i < (int)A.size(); i++) S[i + 1] = S[i] + A[i];
	}
	T query(int l, int r) { return (l <= r ? S[r] - S[l] : T(0)); }
	T query() { return S.back(); }
	inline T operator()(int l, int r) { return query(l, r); }
	inline T operator()() { return query(); }
};

// 速度よりオーバーフロー対策優先
template <typename T>
T floor(T a, T b) { assert(b); if (b < 0) a = -a, b = -b; return a / b - (a % b < 0); }
template <typename T>
T under(T a, T b) { assert(b); if (b < 0) a = -a, b = -b; return a / b - (a % b <= 0); }
template <typename T>
T ceil (T a, T b) { assert(b); if (b < 0) a = -a, b = -b; return a / b + (a % b > 0); }
template <typename T>
T over (T a, T b) { assert(b); if (b < 0) a = -a, b = -b; return a / b + (a % b >= 0); }
template <typename T>
T modulo(T a, T b) { assert(b > 0); T c = a % b; return c < 0 ? c + b : c; }

template <typename T>
pair<T, T> divmod(T a, T b) {
	assert(b > 0);
	T q = a / b, r = a % b;
	if (r < 0) --q, r += b;
	return {q, r};
}

template <typename mint, int iter = 1000>
string tof(const mint &a) {
	for (int deno = 1; deno <= iter; deno++) {
		mint inv = ((mint)deno).inverse();
		for (int nume = 0; nume <= iter; nume++) {
			mint val = inv * nume;
			if (val == a) {
				if (deno == 1) return to_string(nume);
				return to_string(nume) + "/" + to_string(deno);
			}
			else if (-val == a) {
				if (deno == 1) return to_string(-nume);
				return to_string(-nume) + "/" + to_string(deno);
			}
		}
	}
	return "!NF"; // Not Found
}

template <typename mint>
constexpr auto Tof = views::transform(tof<mint, 1000>);

} // namespace yamada
// ===== END INCLUDE: util.hpp =====
// ===== BEGIN INCLUDE: bitop.hpp =====
namespace yamada {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
	return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) { return (a >> i) & 1; }
template <typename T>
inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; }
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }

string tog(int msk, int N) {
	return views::iota(0, N) | views::transform([&](auto i) {
		return msk >> i & 1 ? '#' : '.';
	}) | ranges::to<string>();
}
}  // namespace yamada
// ===== END INCLUDE: bitop.hpp =====
// ===== BEGIN INCLUDE: io.hpp =====
namespace yamada {

istream& operator>>(istream& is, __int128_t& x) {
	string S; is >> S;
	x = 0;
	bool f{};
	for (auto &c : S) {
		if (c == '-') { f = 1; continue; }
		x *= 10;
		x += c - '0';
	}
	if (f) x = -x;
	return is;
}
istream& operator>>(istream& is, __uint128_t& x) {
	string S; is >> S;
	x = 0;
	for (auto &c : S) {
		x *= 10;
		x += c - '0';
	}
	return is;
}
ostream& operator<<(ostream& os, __int128_t x) {
	if (x == 0) return os << 0;
	if (x < 0) os << '-', x = -x;
	string S;
	while (x) S.push_back('0' + x % 10), x /= 10;
	ranges::reverse(S);
	return os << S;
}
ostream& operator<<(ostream& os, __uint128_t x) {
	if (x == 0) return os << 0;
	string S;
	while (x) S.push_back('0' + x % 10), x /= 10;
	ranges::reverse(S);
	return os << S;
}

template <class T> // tuple / pair / array
concept TupleLike = requires { tuple_size<remove_cvref_t<T>>::value; };
template <class R> // vector / set / ranges::view など（set は入力不可）
concept ListLike = ranges::input_range<R> && !convertible_to<R, string_view> && !TupleLike<R>;

template <TupleLike T> ostream& operator<<(ostream&, const T&);
template <TupleLike T> istream& operator>>(istream&, T&&);
template <ListLike  R> ostream& operator<<(ostream&, const R&);
template <ListLike  R> istream& operator>>(istream&, R&&);

template <TupleLike T>
istream& operator>>(istream& is, T&& t) {
	apply([&](auto&... x) { (..., (is >> x)); }, t);
	return is;
}
template <ListLike R>
istream& operator>>(istream& is, R&& a) {
	for (auto&& x : a) is >> x;
	return is;
}
template <TupleLike T>
ostream& operator<<(ostream& os, const T& t) {
	bool f{};
	apply([&](const auto&... x) { (..., (os << (exchange(f, 1) ? " " : "") << x)); }, t);
	return os;
}
template <ListLike R>
ostream& operator<<(ostream& os, const R& a) {
	bool f{};
	for (const auto& x : a) os << (exchange(f, 1) ? " " : "") << x;
	return os;
}

template <class... T>
void in(T&&... x) { (cin >> ... >> x); }
template <class... T>
void out (const T&... x) { bool f{}; (..., (cout << (exchange(f, 1) ? " " : "") << x)); cout << '\n'; }
template <class... T> // "Flush after OUT"
void fout(const T&... x) { bool f{}; (..., (cout << (exchange(f, 1) ? " " : "") << x)); cout << endl; }
template <class... T> // "WithOUT ln"
void wout(const T&... x) { bool f{}; (..., (cout << (exchange(f, 1) ? " " : "") << x)); }

struct IoSetupYamada {
	IoSetupYamada() {
		cin.tie(nullptr);
		ios::sync_with_stdio(false);
		cout << fixed << setprecision(15);
		cerr << fixed << setprecision(7);
	}
} iosetupyamada;

namespace DebugImpl {

void dump(const char&   t) { cerr << t; }
void dump(const string& t) { cerr << t; }
void dump(const bool&   t) { cerr << (t ? "true" : "false"); }
void dump(__int128_t    t) { cerr << t; }
void dump(__uint128_t   t) { cerr << t; }

template <integral T>
void dump(const T& t) {
	string res;
	if (t == yamada::inf) res = "inf";
	if constexpr (is_signed<T>::value) {
		if (t == -yamada::inf) res = "-inf";
	}
	if constexpr (sizeof(T) == 8) {
		if (t == yamada::infLL) res = "inf";
		if constexpr (is_signed<T>::value) {
			if (t == -yamada::infLL) res = "-inf";
		}
	}
	if (res.empty()) res = to_string(t);
	cerr << res;
}

template <typename T>
requires (!ListLike<T> && !TupleLike<T> && !integral<T>)
void dump(const T& t) { cerr << t; }

template <ListLike  R> void dump(const R&);
template <TupleLike T> void dump(const T&);

template <ListLike R>
void dump(const R& a) {
	bool f{};
	cerr << "[ ";
	for (const auto& x : a) {
		cerr << (exchange(f, 1) ? ", " : "");
		dump(x);
	}
	cerr << " ]";
}

template <TupleLike T>
void dump(const T& t) {
	bool f{};
	apply([&](const auto&... x) {
		(..., (cerr << (exchange(f, 1) ? ", " : "( "), dump(x)));
	}, t);
	cerr << " )";
}

template <class... T>
void trace(const T&... x) {
	bool f{};
	(..., (cerr << (exchange(f, 1) ? ", " : " "), dump(x)));
	cerr << endl;
}

}  // namespace DebugImpl
}  // namespace yamada


#ifdef yamadaDebug
#define err(...) \
	do { \
		std::cerr << "## " << #__VA_ARGS__ << " = "; \
		yamada::DebugImpl::trace(__VA_ARGS__); \
	} while (0)
#else
#define err(...) (void(0))
#endif
// ===== END INCLUDE: io.hpp =====
// ===== BEGIN INCLUDE: io-extension.hpp =====
namespace yamada {
namespace ioImpl {

struct EVAL_TAG {};
template <class T> T read() { T x{}; cin >> x; return x; }
template <class F>
struct GEN {
	F f;
	auto operator()(long long i = 0) const { return f(i); }
	auto operator=(EVAL_TAG) const { return (*this)(); }

	template<class A>
	auto to(auto n) const {
		auto g = [p = *this, n](long long) {
			long long size;
			if constexpr (requires { n(); }) size = n();
			else size = n;
			A a;
			if constexpr (requires { a.reserve(size); }) a.reserve(size);
			for (long long i = 0; i < size; ++i) a.insert(a.end(), p(i));
			return a;
		};
		return GEN<decltype(g)>{g};
	}
	template<template<class...> class A>
	auto to(auto n) const {
		return to<decltype(ranges::to<A>(declval<vector<decltype((*this)())>>() | views::as_rvalue))>(n);
	}
	auto operator* (auto n) const { return to<vector>(n); }
	auto operator[](auto n) const { return to<vector>(n); }
	template<size_t N>
	auto array() const {
		return ioImpl::GEN{[p = *this](long long) {
			std::array<decltype(p()), N> a;
			if constexpr (N > 0) for (size_t i = 0; i < N; ++i) a[i] = p(i);
			return a;
		}};
	}
	auto operator-(auto d) const {
		return ioImpl::GEN{[p = *this, d](long long i) { return p(i) - d; }};
	}
	auto operator+(auto d) const {
		return ioImpl::GEN{[p = *this, d](long long i) { return p(i) + d; }};
	}
	auto operator--() const { // 前置デクリメントで使う (例: --LL --INT) (後置だと CE)
		return ioImpl::GEN{[p = *this](long long i) { return p(i) - 1; }};
	}
	auto operator++() const {
		return ioImpl::GEN{[p = *this](long long i) { return p(i) + 1; }};
	}
	auto uz() { // UnZip
		return ioImpl::GEN{[p = *this](long long i) {
			auto v = p(i);
			using T = ranges::range_value_t<decltype(v)>;
			return [&]<size_t... I>(index_sequence<I...>) {
				tuple<vector<tuple_element_t<I, T>>...> ans;
				((get<I>(ans).reserve(v.size())), ...);
				for (auto &x : v) ((get<I>(ans).push_back(get<I>(x))), ...);
				return ans;
			}(make_index_sequence<tuple_size_v<T>>{});
		}};
	}
};

template <class T>
const auto RD = GEN{[](long long) { return read<T>(); }};
[[maybe_unused]] const auto IDX = GEN{[](long long i) { return i; }};
[[maybe_unused]] const auto INT = RD<int>;
[[maybe_unused]] const auto LL  = RD<long long>;
[[maybe_unused]] const auto CHR = RD<char>;
[[maybe_unused]] const auto STR = RD<string>;
[[maybe_unused]] const auto DBL = RD<double>;
[[maybe_unused]] const auto LLD = RD<long double>;
auto CON(auto x) { return GEN{[x = move(x)](long long) { return x; }}; } // CONstant
auto PR(auto p, auto q) { return GEN{[=](ll i) { return pair{p(i), q(i)}; }}; } // PaiR
auto TP(auto... p) { return GEN{[=](long long i) { return tuple{p(i)...}; }}; } // TuPle

} // namespace ioImpl

using ioImpl::RD;
using ioImpl::IDX;
using ioImpl::INT;
using ioImpl::LL;
using ioImpl::CHR;
using ioImpl::STR;
using ioImpl::DBL;
using ioImpl::LLD;
using ioImpl::CON;
using ioImpl::PR;
using ioImpl::TP;

}  // namespace yamada

#define FN(i,...) yamada::ioImpl::GEN{[&](long long i) { return (__VA_ARGS__); }} // これ衝突怖い
#define IN(...) __VA_OPT__(IOIMPL_E3(IOIMPL_EACH(__VA_ARGS__))) // これ衝突怖い
#define BIND(...) ([__VA_ARGS__])

#define IOIMPL_E0(...) __VA_ARGS__
#define IOIMPL_E1(...) IOIMPL_E0(IOIMPL_E0(IOIMPL_E0(__VA_ARGS__)))
#define IOIMPL_E2(...) IOIMPL_E1(IOIMPL_E1(IOIMPL_E1(__VA_ARGS__)))
#define IOIMPL_E3(...) IOIMPL_E2(IOIMPL_E2(IOIMPL_E2(__VA_ARGS__)))
#define IOIMPL_LP ()
#define IOIMPL_NEXT() IOIMPL_EACH
#define IOIMPL_EACH(e,...) IOIMPL_ITEM(e) __VA_OPT__(IOIMPL_NEXT IOIMPL_LP (__VA_ARGS__))
#define IOIMPL_ITEM(e) auto IOIMPL_NORMALIZE(e) = [] { \
	if constexpr (std::string_view{#e}.contains('=')) return yamada::ioImpl::EVAL_TAG{}; \
	else return yamada::ioImpl::LL(); \
}();

#define IOIMPL_PROBE(...) ~, 1,
#define IOIMPL_CHECK_N(_0, _1, ...) _1
#define IOIMPL_CHECK(...) IOIMPL_CHECK_N(__VA_ARGS__, 0)
#define IOIMPL_IS_PAREN(x) IOIMPL_CHECK(IOIMPL_PROBE x)

#define IOIMPL_UNPAREN(...) __VA_ARGS__
#define IOIMPL_STRIP_0(x) x
#define IOIMPL_STRIP_1(x) IOIMPL_UNPAREN x
#define IOIMPL_STRIP_IMPL(b,x) IOIMPL_STRIP_##b(x)
#define IOIMPL_STRIP(b,x) IOIMPL_STRIP_IMPL(b,x)
#define IOIMPL_NORMALIZE(x) IOIMPL_STRIP(IOIMPL_IS_PAREN(x),x)
// ===== END INCLUDE: io-extension.hpp =====
// ===== BEGIN INCLUDE: ranges.hpp =====
namespace yamada {
constexpr auto All = ranges::all_of; // of なし (Python に合わせている）
constexpr auto Any = ranges::any_of; // 同上
constexpr auto BinarySearch = ranges::binary_search;
constexpr auto Contains = ranges::contains;
constexpr auto Copy = ranges::copy;
constexpr auto Count = ranges::count;
constexpr auto CountIf = ranges::count_if;
constexpr auto Fill = ranges::fill;
constexpr auto Find = ranges::find;
constexpr auto FindIf = ranges::find_if;
constexpr auto FoldLeft = ranges::fold_left;
constexpr auto FoldRight = ranges::fold_right;
constexpr auto IsSorted = ranges::is_sorted;
constexpr auto IsSortedUntil = ranges::is_sorted_until;
constexpr auto LowerBound = ranges::lower_bound;
constexpr auto Max = ranges::max;
constexpr auto MaxElement = ranges::max_element;
constexpr auto Min = ranges::min;
constexpr auto MinElement = ranges::min_element;
constexpr auto MinMax = ranges::minmax;
constexpr auto MinMaxElement = ranges::minmax_element;
constexpr auto Reverse = ranges::reverse;
constexpr auto Rotate = ranges::rotate;
constexpr auto Sort = ranges::sort;
constexpr auto UpperBound = ranges::upper_bound;

template <int K>
constexpr auto Adjacent = views::adjacent<K>;
constexpr auto Chunk = views::chunk;
constexpr auto Drop = views::drop;
constexpr auto DropWhile = views::drop_while;
constexpr auto Enumerate = views::enumerate;
constexpr auto Filter = views::filter;
constexpr auto Join = views::join;
constexpr auto Slide = views::slide;
constexpr auto Stride = views::stride;
constexpr auto Take = views::take;
constexpr auto TakeWhile = views::take_while;
constexpr auto Zip = views::zip;

constexpr auto Rev = views::reverse; // ranges の方と混同しない
constexpr auto Transform = views::transform; // ranges の方は多分使わない
constexpr auto Iota = views::iota; // ranges の方は多分使わない

constexpr auto rtov = ranges::to<vector>();
constexpr auto rtos = ranges::to<string>();

using namespace placeholders;
constexpr auto Ofs(const int K = 1) { return views::transform(bind(plus(), _1, K)); }
} // namespace yamada
// ===== END INCLUDE: ranges.hpp =====
// ===== BEGIN INCLUDE: macro.hpp =====
#define FORE1(x, v) for (auto&& x : v)
#define FORE2(x, y, v) for (auto&& [x, y] : v)
#define FORE3(x, y, z, v) for (auto&& [x, y, z] : v)
#define FORE4(x, y, z, u, v) for (auto&& [x, y, z, u] : v)
#define FORE5(x, y, z, t, u, v) for (auto&& [x, y, z, t, u] : v)
#define FORE6(x, y, z, s, t, u, v) for (auto&& [x, y, z, s, t, u] : v)
#define OVERLOAD7(a, b, c, d, e, f, g, h, ...) h
#define each(...) OVERLOAD7(__VA_ARGS__, FORE6, FORE5, FORE4, FORE3, FORE2, FORE1)(__VA_ARGS__)

#define FOR1(a) for (long long _ = 0; _ < (long long)(a); ++_)
#define FOR2(i, a) for (long long i = 0; i < (long long)(a); ++i)
#define FOR3(i, a, b) for (long long i = a; i < (long long)(b); ++i)
#define FOR4(i, a, b, c) for (long long i = a; i < (long long)(b); i += c)
#define OVERLOAD4(a, b, c, d, e, ...) e
#define rep(...) OVERLOAD4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)

#define FOR_R1(a) for (long long i = (long long)(a)-1; i >= 0LL; --i)
#define FOR_R2(i, a) for (long long i = (long long)(a)-1; i >= 0LL; --i)
#define FOR_R3(i, a, b) for (long long i = (long long)(b)-1; i >= (long long)(a); --i)
#define OVERLOAD3(a, b, c, d, ...) d
#define repr(...) OVERLOAD3(__VA_ARGS__, FOR_R3, FOR_R2, FOR_R1)(__VA_ARGS__)

#define eb emplace_back
#define pb push_back
#define fi first
#define se second

#define VV(type, name, h, ...) \
	vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define VVV(type, name, h, w, ...) \
	vector<vector<vector<type>>> name( \
			h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define VVVV(type, name, a, b, c, ...) \
	vector<vector<vector<vector<type>>>> name( \
			a, vector<vector<vector<type>>>( \
				b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

#define DIE(...) do { yamada::out(__VA_ARGS__); return; } while (0)
// ===== END INCLUDE: macro.hpp =====

namespace yamada {
void solve();
}
int main() { yamada::solve(); }
// ===== END INCLUDE: ../../template/template.hpp =====
// ===== BEGIN INCLUDE: ../../modint/montgomery-modint.hpp =====

#include <cstdint>
#include <iostream>
#include <ostream>

template <std::uint32_t mod>
struct LazyMontgomeryModInt {
	using mint = LazyMontgomeryModInt;
	using i32 = std::int32_t;
	using u32 = std::uint32_t;
	using u64 = std::uint64_t;

	static constexpr u32 get_r() {
		u32 ret = mod;
		for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
		return ret;
	}

	static constexpr u32 r = get_r();
	static constexpr u32 n2 = -u64(mod) % mod;
	static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
	static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
	static_assert(r * mod == 1, "this code has bugs.");

	u32 a;

	constexpr LazyMontgomeryModInt() : a(0) {}
	constexpr LazyMontgomeryModInt(const int64_t &b)
			: a(reduce(u64(b % mod + mod) * n2)){};

	static constexpr u32 reduce(const u64 &b) {
		return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
	}

	constexpr mint &operator+=(const mint &b) {
		if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
		return *this;
	}

	constexpr mint &operator-=(const mint &b) {
		if (i32(a -= b.a) < 0) a += 2 * mod;
		return *this;
	}

	constexpr mint &operator*=(const mint &b) {
		a = reduce(u64(a) * b.a);
		return *this;
	}

	constexpr mint &operator/=(const mint &b) {
		*this *= b.inverse();
		return *this;
	}

	constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
	constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
	constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
	constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
	constexpr bool operator==(const mint &b) const {
		return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
	}
	constexpr bool operator!=(const mint &b) const {
		return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
	}
	constexpr mint operator-() const { return mint() - mint(*this); }
	constexpr mint operator+() const { return mint(*this); }

	constexpr mint pow(u64 n) const {
		mint ret(1), mul(*this);
		while (n > 0) {
			if (n & 1) ret *= mul;
			mul *= mul;
			n >>= 1;
		}
		return ret;
	}

	constexpr mint inverse() const {
		int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
		while (y > 0) {
			t = x / y;
			x -= t * y, u -= t * v;
			tmp = x, x = y, y = tmp;
			tmp = u, u = v, v = tmp;
		}
		return mint{u};
	}

	friend std::ostream &operator<<(std::ostream &os, const mint &b) {
		return os << b.get();
	}

	friend std::istream &operator>>(std::istream &is, mint &b) {
		int64_t t;
		is >> t;
		b = LazyMontgomeryModInt<mod>(t);
		return (is);
	}

	constexpr u32 get() const {
		u32 ret = reduce(a);
		return ret >= mod ? ret - mod : ret;
	}

	static constexpr u32 get_mod() { return mod; }
};
// ===== END INCLUDE: ../../modint/montgomery-modint.hpp =====
// ===== BEGIN INCLUDE: ../../prime/fast-factorize.hpp =====

#include <cstdint>
#include <numeric>
#include <vector>
using namespace std;

// ===== BEGIN INCLUDE: ../internal/internal-math.hpp =====

// ===== BEGIN INCLUDE: internal-type-traits.hpp =====

#include <type_traits>
using namespace std;

namespace internal {
template <typename T>
using is_broadly_integral =
    typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
                               is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_signed =
    typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_unsigned =
    typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

#define ENABLE_VALUE(x) \
  template <typename T> \
  constexpr bool x##_v = x<T>::value;

ENABLE_VALUE(is_broadly_integral);
ENABLE_VALUE(is_broadly_signed);
ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE

#define ENABLE_HAS_TYPE(var)                                   \
  template <class, class = void>                               \
  struct has_##var : false_type {};                            \
  template <class T>                                           \
  struct has_##var<T, void_t<typename T::var>> : true_type {}; \
  template <class T>                                           \
  constexpr auto has_##var##_v = has_##var<T>::value;

#define ENABLE_HAS_VAR(var)                                     \
  template <class, class = void>                                \
  struct has_##var : false_type {};                             \
  template <class T>                                            \
  struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \
  template <class T>                                            \
  constexpr auto has_##var##_v = has_##var<T>::value;

#define ENABLE_HAS_FUNCTION(var)                                              \
  template <class, class = void>                                              \
  struct has_##var : false_type {};                                           \
  template <class T>                                                          \
  struct has_##var<T, void_t<decltype(&T::var)>>                              \
      : bool_constant<is_member_function_pointer<decltype(&T::var)>::value> { \
  };                                                                          \
  template <class T>                                                          \
  inline constexpr bool has_##var##_v = has_##var<T>::value;

}  // namespace internal
// ===== END INCLUDE: internal-type-traits.hpp =====

namespace internal {

#include <cassert>
#include <utility>
#include <vector>
using namespace std;

// a mod p
template <typename T>
T safe_mod(T a, T p) {
	a %= p;
	if constexpr (is_broadly_signed_v<T>) {
		if (a < 0) a += p;
	}
	return a;
}

// 返り値：pair(g, x)
// s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
template <typename T>
pair<T, T> inv_gcd(T a, T p) {
	static_assert(is_broadly_signed_v<T>);
	a = safe_mod(a, p);
	if (a == 0) return {p, 0};
	T b = p, x = 1, y = 0;
	while (a != 0) {
		T q = b / a;
		swap(a, b %= a);
		swap(x, y -= q * x);
	}
	if (y < 0) y += p / b;
	return {b, y};
}

// 返り値 : a^{-1} mod p
// gcd(a, p) == 1 が必要
template <typename T>
T inv(T a, T p) {
	static_assert(is_broadly_signed_v<T>);
	a = safe_mod(a, p);
	T b = p, x = 1, y = 0;
	while (a != 0) {
		T q = b / a;
		swap(a, b %= a);
		swap(x, y -= q * x);
	}
	assert(b == 1);
	return y < 0 ? y + p : y;
}

// T : 底の型
// U : T*T がオーバーフローしない かつ 指数の型
template <typename T, typename U>
T modpow(T a, U n, T p) {
	a = safe_mod(a, p);
	T ret = 1 % p;
	while (n != 0) {
		if (n % 2 == 1) ret = U(ret) * a % p;
		a = U(a) * a % p;
		n /= 2;
	}
	return ret;
}

// 返り値 : pair(rem, mod)
// 解なしのときは {0, 0} を返す
template <typename T>
pair<T, T> crt(const vector<T>& r, const vector<T>& m) {
	static_assert(is_broadly_signed_v<T>);
	assert(r.size() == m.size());
	int n = int(r.size());
	T r0 = 0, m0 = 1;
	for (int i = 0; i < n; i++) {
		assert(1 <= m[i]);
		T r1 = safe_mod(r[i], m[i]), m1 = m[i];
		if (m0 < m1) swap(r0, r1), swap(m0, m1);
		if (m0 % m1 == 0) {
			if (r0 % m1 != r1) return {0, 0};
			continue;
		}
		auto [g, im] = inv_gcd(m0, m1);
		T u1 = m1 / g;
		if ((r1 - r0) % g) return {0, 0};
		T x = (r1 - r0) / g % u1 * im % u1;
		r0 += x * m0;
		m0 *= u1;
		if (r0 < 0) r0 += m0;
	}
	return {r0, m0};
}

// calc x s.t. Ax + B = 0 (mod M)
template <typename T>
pair<T, T> zero_linear(const T A, const T B, const T M) {
	static_assert(is_broadly_signed_v<T>);
	if (A == 0) {
		if (B == 0) return {0, 1};
		return {0, 0};
	}
	auto [ans, bns] = crt<T>({T(0), -B}, {A, M});
	assert(ans % A == 0);
	assert(bns % A == 0);
	return {ans / A, bns / A};
}

}  // namespace internal
// ===== END INCLUDE: ../internal/internal-math.hpp =====
// ===== BEGIN INCLUDE: ../misc/rng.hpp =====

// ===== BEGIN INCLUDE: ../internal/internal-seed.hpp =====

#include <chrono>
using namespace std;

namespace internal {
unsigned long long non_deterministic_seed() {
  unsigned long long m =
      chrono::duration_cast<chrono::nanoseconds>(
          chrono::high_resolution_clock::now().time_since_epoch())
          .count();
  m ^= 9845834732710364265uLL;
  m ^= m << 24, m ^= m >> 31, m ^= m << 35;
  return m;
}
unsigned long long deterministic_seed() { return 88172645463325252UL; }

// 64 bit の seed 値を生成 (手元では seed 固定)
// 連続で呼び出すと同じ値が何度も返ってくるので注意
// #define RANDOMIZED_SEED するとシードがランダムになる
unsigned long long seed() {
#if defined(NyaanLocal) && !defined(RANDOMIZED_SEED)
  return deterministic_seed();
#else
  return non_deterministic_seed();
#endif
}

}  // namespace internal
// ===== END INCLUDE: ../internal/internal-seed.hpp =====

namespace my_rand {
using i64 = long long;
using u64 = unsigned long long;

// [0, 2^64 - 1)
u64 rng() {
	static u64 _x = internal::seed();
	return _x ^= _x << 7, _x ^= _x >> 9;
}

// [l, r]
i64 rng(i64 l, i64 r) {
	assert(l <= r);
	return l + rng() % u64(r - l + 1);
}

// [l, r)
i64 randint(i64 l, i64 r) {
	assert(l < r);
	return l + rng() % u64(r - l);
}

// choose N numbers from [l, r) without overlapping
vector<i64> randset(i64 l, i64 r, i64 N) {
	assert(l <= r && N <= r - l);
	unordered_set<i64> s;
	for (i64 i = N; i; --i) {
		i64 m = randint(l, r + 1 - i);
		if (s.find(m) != s.end()) m = r - i;
		s.insert(m);
	}
	vector<i64> ret;
	for (auto& x : s) ret.push_back(x);
	sort(begin(ret), end(ret));
	return ret;
}

// [0.0, 1.0)
double rnd() { return rng() * 5.42101086242752217004e-20; }
// [l, r)
double rnd(double l, double r) {
	assert(l < r);
	return l + rnd() * (r - l);
}

template <typename T>
void randshf(vector<T>& v) {
	int N = v.size();
	for (int i = 1; i < N; i++) swap(v[i], v[randint(0, i + 1)]);
}

}  // namespace my_rand

using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;
// ===== END INCLUDE: ../misc/rng.hpp =====
// ===== BEGIN INCLUDE: ../modint/arbitrary-montgomery-modint.hpp =====

#include <iostream>
using namespace std;

template <typename Int, typename UInt, typename Long, typename ULong, int id>
struct ArbitraryLazyMontgomeryModIntBase {
  using mint = ArbitraryLazyMontgomeryModIntBase;

  inline static UInt mod;
  inline static UInt r;
  inline static UInt n2;
  static constexpr int bit_length = sizeof(UInt) * 8;

  static UInt get_r() {
    UInt ret = mod;
    while (mod * ret != 1) ret *= UInt(2) - mod * ret;
    return ret;
  }
  static void set_mod(UInt m) {
    assert(m < (UInt(1u) << (bit_length - 2)));
    assert((m & 1) == 1);
    mod = m, n2 = -ULong(m) % m, r = get_r();
  }
  UInt a;

  ArbitraryLazyMontgomeryModIntBase() : a(0) {}
  ArbitraryLazyMontgomeryModIntBase(const Long &b)
      : a(reduce(ULong(b % mod + mod) * n2)){};

  static UInt reduce(const ULong &b) {
    return (b + ULong(UInt(b) * UInt(-r)) * mod) >> bit_length;
  }

  mint &operator+=(const mint &b) {
    if (Int(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }
  mint &operator-=(const mint &b) {
    if (Int(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }
  mint &operator*=(const mint &b) {
    a = reduce(ULong(a) * b.a);
    return *this;
  }
  mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  mint operator+(const mint &b) const { return mint(*this) += b; }
  mint operator-(const mint &b) const { return mint(*this) -= b; }
  mint operator*(const mint &b) const { return mint(*this) *= b; }
  mint operator/(const mint &b) const { return mint(*this) /= b; }

  bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  mint operator-() const { return mint(0) - mint(*this); }
  mint operator+() const { return mint(*this); }

  mint pow(ULong n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul, n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    Long t;
    is >> t;
    b = ArbitraryLazyMontgomeryModIntBase(t);
    return (is);
  }

  mint inverse() const {
    Int x = get(), y = get_mod(), u = 1, v = 0;
    while (y > 0) {
      Int t = x / y;
      swap(x -= t * y, y);
      swap(u -= t * v, v);
    }
    return mint{u};
  }

  UInt get() const {
    UInt ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static UInt get_mod() { return mod; }
};

// id に適当な乱数を割り当てて使う
template <int id>
using ArbitraryLazyMontgomeryModInt =
    ArbitraryLazyMontgomeryModIntBase<int, unsigned int, long long,
                                      unsigned long long, id>;
template <int id>
using ArbitraryLazyMontgomeryModInt64bit =
    ArbitraryLazyMontgomeryModIntBase<long long, unsigned long long, __int128_t,
                                      __uint128_t, id>;
// ===== END INCLUDE: ../modint/arbitrary-montgomery-modint.hpp =====
// ===== BEGIN INCLUDE: miller-rabin.hpp =====

#include <vector>
using namespace std;


namespace fast_factorize {

template <typename T, typename U>
bool miller_rabin(const T& n, vector<T> ws) {
  if (n <= 2) return n == 2;
  if (n % 2 == 0) return false;

  T d = n - 1;
  while (d % 2 == 0) d /= 2;
  U e = 1, rev = n - 1;
  for (T w : ws) {
    if (w % n == 0) continue;
    T t = d;
    U y = internal::modpow<T, U>(w, t, n);
    while (t != n - 1 && y != e && y != rev) y = y * y % n, t *= 2;
    if (y != rev && t % 2 == 0) return false;
  }
  return true;
}

bool miller_rabin_u64(unsigned long long n) {
  return miller_rabin<unsigned long long, __uint128_t>(
      n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}

template <typename mint>
bool miller_rabin(unsigned long long n, vector<unsigned long long> ws) {
  if (n <= 2) return n == 2;
  if (n % 2 == 0) return false;

  if (mint::get_mod() != n) mint::set_mod(n);
  unsigned long long d = n - 1;
  while (~d & 1) d >>= 1;
  mint e = 1, rev = n - 1;
  for (unsigned long long w : ws) {
    if (w % n == 0) continue;
    unsigned long long t = d;
    mint y = mint(w).pow(t);
    while (t != n - 1 && y != e && y != rev) y *= y, t *= 2;
    if (y != rev && t % 2 == 0) return false;
  }
  return true;
}

bool is_prime(unsigned long long n) {
  using mint32 = ArbitraryLazyMontgomeryModInt<96229631>;
  using mint64 = ArbitraryLazyMontgomeryModInt64bit<622196072>;

  if (n <= 2) return n == 2;
  if (n % 2 == 0) return false;
  if (n < (1uLL << 30)) {
    return miller_rabin<mint32>(n, {2, 7, 61});
  } else if (n < (1uLL << 62)) {
    return miller_rabin<mint64>(
        n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
  } else {
    return miller_rabin_u64(n);
  }
}

}  // namespace fast_factorize

using fast_factorize::is_prime;

/**
 * @brief Miller-Rabin primality test
 */
// ===== END INCLUDE: miller-rabin.hpp =====

namespace fast_factorize {
using u64 = uint64_t;

template <typename mint, typename T>
T pollard_rho(T n) {
  if (~n & 1) return 2;
  if (is_prime(n)) return n;
  if (mint::get_mod() != n) mint::set_mod(n);
  mint R, one = 1;
  auto f = [&](mint x) { return x * x + R; };
  auto rnd_ = [&]() { return rng() % (n - 2) + 2; };
  while (1) {
    mint x, y, ys, q = one;
    R = rnd_(), y = rnd_();
    T g = 1;
    constexpr int m = 128;
    for (int r = 1; g == 1; r <<= 1) {
      x = y;
      for (int i = 0; i < r; ++i) y = f(y);
      for (int k = 0; g == 1 && k < r; k += m) {
        ys = y;
        for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));
        g = gcd(q.get(), n);
      }
    }
    if (g == n) do
        g = gcd((x - (ys = f(ys))).get(), n);
      while (g == 1);
    if (g != n) return g;
  }
  exit(1);
}

using i64 = long long;

vector<i64> inner_factorize(u64 n) {
  using mint32 = ArbitraryLazyMontgomeryModInt<452288976>;
  using mint64 = ArbitraryLazyMontgomeryModInt64bit<401243123>;

  if (n <= 1) return {};
  u64 p;
  if (n <= (1LL << 30)) {
    p = pollard_rho<mint32, uint32_t>(n);
  } else if (n <= (1LL << 62)) {
    p = pollard_rho<mint64, uint64_t>(n);
  } else {
    exit(1);
  }
  if (p == n) return {i64(p)};
  auto l = inner_factorize(p);
  auto r = inner_factorize(n / p);
  copy(begin(r), end(r), back_inserter(l));
  return l;
}

vector<i64> factorize(u64 n) {
  auto ret = inner_factorize(n);
  sort(begin(ret), end(ret));
  return ret;
}

map<i64, i64> factor_count(u64 n) {
  map<i64, i64> mp;
  for (auto &x : factorize(n)) mp[x]++;
  return mp;
}

vector<i64> divisors(u64 n) {
  if (n == 0) return {};
  vector<pair<i64, i64>> v;
  for (auto &p : factorize(n)) {
    if (v.empty() || v.back().first != p) {
      v.emplace_back(p, 1);
    } else {
      v.back().second++;
    }
  }
  vector<i64> ret;
  auto f = [&](auto rc, int i, i64 x) -> void {
    if (i == (int)v.size()) {
      ret.push_back(x);
      return;
    }
    rc(rc, i + 1, x);
    for (int j = 0; j < v[i].second; j++) rc(rc, i + 1, x *= v[i].first);
  };
  f(f, 0, 1);
  sort(begin(ret), end(ret));
  return ret;
}

}  // namespace fast_factorize

using fast_factorize::divisors;
using fast_factorize::factor_count;
using fast_factorize::factorize;

/**
 * @brief 高速素因数分解(Miller Rabin/Pollard's Rho)
 * @docs docs/prime/fast-factorize.md
 */
// ===== END INCLUDE: ../../prime/fast-factorize.hpp =====

const int LG=20;
using mint = LazyMontgomeryModInt<998244353>;
void yamada::solve()
{
	vl cnt(LG);
	rep(t,1,LG){
		rep(x00,t+1)rep(x01,t-x00+1){
			rep(x10,t+1)rep(x11,t-x10+1){
				ll x02=t-x01-x00;
				ll x12=t-x11-x10;
				ll x20=t-x10-x00;
				ll x21=t-x11-x01;
				ll x22=t-x21-x20;
				bool fn=1;
				for(auto x:{x02,x12,x20,x21,x22}){
					if(x<0)fn=0;
				}
				cnt[t]+=fn;
			}
		}
	}

	IN(T);
	while(T--){
		IN(X);
		mint ans=1;
		each(p,c,factor_count(X)){
			ans*=cnt[c];
		}
		out(ans);
	}
}