#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#include <bits/extc++.h>
using namespace std;
/*
#include <atcoder/all>
using namespace atcoder;
*/
/*
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
using bll = boost::multiprecision::cpp_int;
using bdouble = boost::multiprecision::number<boost::multiprecision::cpp_dec_float<100>>;
using namespace boost::multiprecision;
*/
#if defined(LOCAL_TEST) || defined(LOCAL_DEV)
	#define BOOST_STACKTRACE_USE_ADDR2LINE
	#define BOOST_STACKTRACE_ADDR2LINE_LOCATION /usr/local/opt/binutils/bin/addr2line
	#define _GNU_SOURCE 1
	#include <boost/stacktrace.hpp>
#endif
#ifdef LOCAL_TEST
	namespace std {
		template <typename T> class dvector : public std::vector<T> {
		public:
			using std::vector<T>::vector;
			template <typename T_ = T, typename std::enable_if_t<std::is_same_v<T_, bool>, std::nullptr_t> = nullptr>
			std::vector<bool>::reference operator[](std::size_t n) {
				if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n);
			}
			template <typename T_ = T, typename std::enable_if_t<std::is_same_v<T_, bool>, std::nullptr_t> = nullptr>
			const T_ operator[](std::size_t n) const {
				if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n);
			}
			template <typename T_ = T, typename std::enable_if_t<!std::is_same_v<T_, bool>, std::nullptr_t> = nullptr>
			T_& operator[](std::size_t n) {
				if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n);
			}
			template <typename T_ = T, typename std::enable_if_t<!std::is_same_v<T_, bool>, std::nullptr_t> = nullptr>
			const T_& operator[](std::size_t n) const {
				if (this->size() <= n) { std::cerr << boost::stacktrace::stacktrace() << '\n' << "vector::_M_range_check: __n (which is " << n << ") >= this->size() (which is " << this->size() << ")" << '\n'; } return this->at(n);
			}
		};
		template <typename T, typename Compare = std::less<T>, typename Allocator = std::allocator<T>> class dmultiset : public std::multiset<T,Compare,Allocator> {
		public:
			using std::multiset<T,Compare,Allocator>::multiset;
			const typename std::multiset<T,Compare,Allocator>::iterator erase(const typename std::multiset<T,Compare,Allocator>::iterator it) {
				return std::multiset<T,Compare,Allocator>::erase(it);
			}
			std::size_t erase([[maybe_unused]] const T& x) {
				std::cerr << boost::stacktrace::stacktrace() << '\n'; assert(false);
			}
			std::size_t erase_all_elements(const T& x) {
				return std::multiset<T,Compare,Allocator>::erase(x);
			}
		};
	}
	#define vector dvector
	#define multiset dmultiset
	class SIGFPE_exception : std::exception {};
	class SIGSEGV_exception : std::exception {};
	void catch_SIGFPE([[maybe_unused]] int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGFPE_exception(); }
	void catch_SIGSEGV([[maybe_unused]] int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGSEGV_exception(); }
	signed convertedmain();
	signed main() { signal(SIGFPE, catch_SIGFPE); signal(SIGSEGV, catch_SIGSEGV); return convertedmain(); }
	#define main() convertedmain()
#else
	#define erase_all_elements erase
#endif
#ifdef LOCAL_DEV
	template <typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::pair<T1, T2>& p) {
		return s << "(" << p.first << ", " << p.second << ")"; }
	template <typename T, std::size_t N> std::ostream& operator<<(std::ostream& s, const std::array<T, N>& a) {
		s << "{ "; for (std::size_t i = 0; i < N; ++i){ s << a[i] << "\t"; } s << "}"; return s; }
	template <typename T, typename Compare> std::ostream& operator<<(std::ostream& s, const std::set<T, Compare>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
	template <typename T, typename Compare> std::ostream& operator<<(std::ostream& s, const std::multiset<T, Compare>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
	template <typename T1, typename T2, typename Compare> std::ostream& operator<<(std::ostream& s, const std::map<T1, T2, Compare>& m) {
		s << "{\n"; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << "\n"; } s << "}"; return s; }
	template <typename T> std::ostream& operator<<(std::ostream& s, const std::deque<T>& v) {
		for (std::size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; }
	template <typename T> std::ostream& operator<<(std::ostream& s, const std::vector<T>& v) {
		for (std::size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; }
	template <typename T> std::ostream& operator<<(std::ostream& s, const std::vector<std::vector<T>>& vv) {
		s << "\\\n"; for (std::size_t i = 0; i < vv.size(); ++i){ s << vv[i] << "\n"; } return s; }
	template <typename T, std::size_t N, typename std::enable_if_t<!std::is_same_v<T, char>, std::nullptr_t> = nullptr> std::ostream& operator<<(std::ostream& s, const T (&v)[N]) {
		for (std::size_t i = 0; i < N; ++i){ s << v[i]; if (i < N - 1) s << "\t"; } return s; }
	template <typename T, std::size_t N, std::size_t M, typename std::enable_if_t<!std::is_same_v<T, char>, std::nullptr_t> = nullptr> std::ostream& operator<<(std::ostream& s, const T (&vv)[N][M]) {
		s << "\\\n"; for (std::size_t i = 0; i < N; ++i){ s << vv[i] << "\n"; } return s; }
	#if __has_include(<ext/pb_ds/assoc_container.hpp>)
		template <typename Key, typename Compare> std::ostream& operator<<(std::ostream& s, const __gnu_pbds::tree<Key, __gnu_pbds::null_type, Compare, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>& se) {
			s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
		template <typename Key, typename T, typename Hash> std::ostream& operator<<(std::ostream& s, const __gnu_pbds::gp_hash_table<Key, T, Hash>& m) {
			s << "{\n"; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << "\n"; } s << "}"; return s; }
	#endif
	void debug_impl() { std::cerr << '\n'; }
	template <typename Head, typename... Tail> void debug_impl(const Head& head, const Tail&... tail) { std::cerr << " " << head << (sizeof...(tail) ? "," : ""); debug_impl(tail...); }
	#define debug(...) do { std::cerr << ":" << __LINE__ << " (" << #__VA_ARGS__ << ") ="; debug_impl(__VA_ARGS__); } while (false)
	constexpr inline long long prodlocal([[maybe_unused]] long long prod, [[maybe_unused]] long long local) { return local; }
#else
	#define debug(...) do {} while (false)
	constexpr inline long long prodlocal([[maybe_unused]] long long prod, [[maybe_unused]] long long local) { return prod; }
#endif
//#define int long long
using ll = long long;
//INT_MAX = (1<<31)-1 = 2147483647, INT64_MAX = (1LL<<63)-1 = 9223372036854775807
constexpr ll INF = std::numeric_limits<ll>::max() == INT_MAX ? (ll)1e9 + 7 : (ll)1e18;
constexpr ll MOD = (ll)1e9 + 7; //primitive root = 5
//constexpr ll MOD = 998244353; //primitive root = 3
constexpr double EPS = 1e-9;
constexpr ll dx[4] = {1, 0, -1, 0};
constexpr ll dy[4] = {0, 1, 0, -1};
constexpr ll dx8[8] = {1, 0, -1, 0, 1, 1, -1, -1};
constexpr ll dy8[8] = {0, 1, 0, -1, 1, -1, 1, -1};
#define repoverload3(_1, _2, _3, name, ...) name
#define rep3(i, a, b) for(ll i=(a), i##_length=(b); i<i##_length; ++i)
#define rep2(i, n) rep3(i, 0, n)
#define rep1(n) rep3(i, 0, n)
#define rep(...) repoverload3(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define repeq3(i, a, b) rep3(i, (a)+1, (b)+1)
#define repeq2(i, n) rep3(i, 1, (n)+1)
#define repeq1(n) rep3(i, 1, (n)+1)
#define repeq(...) repoverload3(__VA_ARGS__, repeq3, repeq2, repeq1)(__VA_ARGS__)
#define rrep3(i, a, b) for(ll i=(b)-1; i>=(a); --i)
#define rrep2(i, n) rrep3(i, 0, n)
#define rrep1(n) rrep3(i, 0, n)
#define rrep(...) repoverload3(__VA_ARGS__, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define rrepeq3(i, a, b) rrep3(i, (a)+1, (b)+1)
#define rrepeq2(i, n) rrep3(i, 1, (n)+1)
#define rrepeq1(n) rrep3(i, 1, (n)+1)
#define rrepeq(...) repoverload3(__VA_ARGS__, rrepeq3, rrepeq2, rrepeq1)(__VA_ARGS__)
#define all(v) std::begin(v), std::end(v)
#define rall(v) std::rbegin(v), std::rend(v)
void p() { std::cout << '\n'; }
template <typename Head, typename... Tail> void p(const Head& head, const Tail&... tail) { std::cout << head << (sizeof...(tail) ? " " : ""); p(tail...); }
template <typename T> inline void pv(const std::vector<T>& v) { for(ll i=0, N=v.size(); i<N; i++) std::cout << v[i] << " \n"[i==N-1]; }
template <typename T> inline bool chmax(T& a, T b) { return a < b && (a = b, true); }
template <typename T> inline bool chmin(T& a, T b) { return a > b && (a = b, true); }
template <typename T> inline void uniq(std::vector<T>& v) { std::sort(v.begin(), v.end()); v.erase(std::unique(v.begin(), v.end()), v.end()); }
template <typename T> inline ll sz(const T& v) { return std::size(v); }
template <typename T, std::size_t N> std::vector<T> make_vector_impl(std::vector<ll>& sizes, typename std::enable_if<(N==1), const T&>::type x) { return std::vector<T>(sizes.front(),x); }
template <typename T, std::size_t N> auto make_vector_impl(std::vector<ll>& sizes, typename std::enable_if<(N>1), const T&>::type x) { ll size=sizes.back(); sizes.pop_back(); return std::vector<decltype(make_vector_impl<T,N-1>(sizes,x))>(size,make_vector_impl<T,N-1>(sizes,x)); }
template <typename T, std::size_t N> auto make_vector(const ll (&sizes)[N], const T& x=T()) { std::vector<ll> s(N); for(std::size_t i=0; i<N; ++i)s[i]=sizes[N-1-i]; return make_vector_impl<T,N>(s,x); }
#if __has_include(<ext/pb_ds/assoc_container.hpp>)
	template <typename Key, typename Mapped, typename Hash = std::hash<Key>, typename std::enable_if_t<std::is_integral_v<Key>, std::nullptr_t> = nullptr> class fmap : public __gnu_pbds::gp_hash_table<Key, Mapped, Hash> {
	public:
		using __gnu_pbds::gp_hash_table<Key, Mapped, Hash>::gp_hash_table;
		template <typename T> fmap(std::initializer_list<std::initializer_list<T>> il) : __gnu_pbds::gp_hash_table<Key, Mapped, Hash>() {
			for (auto&& x : il) __gnu_pbds::gp_hash_table<Key, Mapped, Hash>::insert(std::pair<Key, Mapped>(*x.begin(), *(x.begin() + 1)));
		}
		template <typename T> ll count(const T& x) const {
			return __gnu_pbds::gp_hash_table<Key, Mapped, Hash>::find(x) != __gnu_pbds::gp_hash_table<Key, Mapped, Hash>::end();
		}
	};
#else
	template <typename Key, typename Mapped> using fmap = std::map<Key, Mapped>;
#endif
template <typename T> class each_hepler {
public:
	class iterator {
	public:
		ll _pos;
		typename T::iterator _it;
		iterator(typename T::iterator it): _pos(0), _it(it) {}
		std::pair<ll, typename std::iterator_traits<typename T::iterator>::reference> operator*() const { return {_pos, *_it}; }
		iterator& operator++() { ++_pos; ++_it; return *this; }
		iterator operator++(int) { iterator tmp(*this); ++*this; return tmp; }
		bool operator==(iterator const& it) const { return _it == it._it; }
		bool operator!=(iterator const& it) const { return !(*this == it); }
	};
	T& _container;
	each_hepler(T& t): _container(t) {}
	iterator begin() const { return iterator(_container.begin()); }
	iterator end() const { return iterator(_container.end()); }
};
template <typename T> each_hepler<T> each(T& t) { return each_hepler<T>(t); } // for (auto&& [i, val] : each(v))
template <typename... T> class zip_helper {
public:
	class iterator : std::iterator<std::forward_iterator_tag, std::tuple<decltype(*std::declval<T>().begin())...>> {
	private:
		std::tuple<decltype(std::declval<T>().begin())...> iters_;
		template <std::size_t... I> auto deref(std::index_sequence<I...>) const { return typename iterator::value_type{*std::get<I>(iters_)...}; }
		template <std::size_t... I> void increment(std::index_sequence<I...>) { [[maybe_unused]] auto l = {(++std::get<I>(iters_), 0)...}; }
	public:
		explicit iterator(decltype(iters_) iters) : iters_{std::move(iters)} {}
		iterator& operator++() { increment(std::index_sequence_for<T...>{}); return *this; }
		iterator operator++(int) { auto saved{*this}; increment(std::index_sequence_for<T...>{}); return saved; }
		bool operator!=(const iterator& other) const { return iters_ != other.iters_; }
		auto operator*() const { return deref(std::index_sequence_for<T...>{}); }
	};
	zip_helper(T&... seqs) : begin_{std::make_tuple(seqs.begin()...)}, end_{std::make_tuple(seqs.end()...)} {}
	iterator begin() const { return begin_; }
	iterator end() const { return end_; }
private:
	iterator begin_, end_;
};
template <typename... T> auto zip(T&&... seqs) { return zip_helper<T...>{seqs...}; } // for (auto&& [a, b, c] : zip(A, B, C))

/*-----8<-----template-----8<-----*/

//[lib]modint.cpp
#include <atcoder/modint>
constexpr int ModintConstexprSize = prodlocal(30000, 10);
template <int N = ModintConstexprSize>
class ModintConstexpr {
public:
	unsigned int inv[N + 1];
	constexpr inline long long modpow(long long a, long long n) {
		long long res = 1;
		while (n) {
			if (n & 1) res = res * a % MOD;
			a = a * a % MOD;
			n >>= 1;
		}
		return res;
	}
	constexpr ModintConstexpr() : inv() {
		inv[1] = 1;
		for (int i = 2; i <= N; ++i) inv[i] = modpow(i, MOD - 2);
	}
};
#ifdef __INTELLISENSE__
	#pragma diag_suppress 28
#endif
constexpr auto modintconstexpr = ModintConstexpr<>();

namespace atcoder {

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

#if __has_include(<ext/pb_ds/assoc_container.hpp>)
	using inv_cache_type = __gnu_pbds::gp_hash_table<unsigned int, unsigned int>;
#else
	using inv_cache_type = map<unsigned int, unsigned int>;
#endif
	static inv_cache_type& inv_cache() {
		static inv_cache_type inv_cache;
		return inv_cache;
	}

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

	static_modint_custom() : _v(0) {}
	template <class T, internal::is_signed_int_t<T>* = nullptr>
	static_modint_custom(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_custom(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 {
		mint x = *this, r = 1;
		if (n < 0) {
			x = inv(), n = -n;
		}
		while (n) {
			if (n & 1) r *= x;
			x *= x;
			n >>= 1;
		}
		return r;
	}
	mint inv() const {
		if (umod() == MOD && _v <= ModintConstexprSize) return raw(modintconstexpr.inv[_v]);
		auto& cachemap = inv_cache();
		unsigned int cached = cachemap[_v];
		if (cached) return raw(cached);
		mint x = inv_calc();
		cachemap[_v] = x._v;
		return x;
	}
	mint inv_calc() 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;
	}

	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>;
};

}  // namespace atcoder
namespace std {
	template <int m> class numeric_limits<atcoder::static_modint_custom<m>> {
	public:
		static constexpr atcoder::static_modint_custom<m> min() noexcept { return 0; }
		static constexpr atcoder::static_modint_custom<m> max() noexcept { return m-1; }
	};
}
using Modint = atcoder::static_modint_custom<MOD>;
std::istream& operator>>(std::istream& is, Modint& x){ ll a; is>>a; x = a; return is; }
std::ostream& operator<<(std::ostream& os, const Modint& x){ return os << x.val(); }
inline Modint operator""_M(unsigned long long x) noexcept { return Modint(x); }
std::vector<Modint> fac_vec(1, 1), inv_vec(1, 1);
inline void reserve_fac_vec(size_t a){
	if(fac_vec.size() >= a) return;
	if(a < fac_vec.size() * 2) a = fac_vec.size() * 2;
	if(a >= (size_t)Modint::mod()) a = Modint::mod();
	fac_vec.reserve(a);
	while(fac_vec.size() < a) fac_vec.push_back(fac_vec.back() * Modint(fac_vec.size()));
	inv_vec.resize(fac_vec.size());
	inv_vec.back() = fac_vec.back().inv();
	for(ll i = inv_vec.size() - 1; !inv_vec[i - 1].val(); i--) inv_vec[i - 1] = inv_vec[i] * i;
}
inline Modint factorial(ll n){ if(n < 0) return 0; reserve_fac_vec(n + 1); return fac_vec[n]; }
inline Modint nPk(ll n, ll r){
	if(r < 0 || n < r) return 0;
	if(n >> 24){ Modint ans = 1; for(ll i = 0; i < r; i++) ans *= n--; return ans; }
	reserve_fac_vec(n + 1); return fac_vec[n] * inv_vec[n - r];
}
inline Modint nCk(ll n, ll r){ if(r < 0 || n < r) return 0; r = min(r, n - r); reserve_fac_vec(r + 1); return inv_vec[r] * nPk(n, r); }
inline Modint nHk(ll n, ll r){ return nCk(n + r - 1, n - 1); } //n種類のものから重複を許してr個選ぶ=玉r個と仕切りn-1個
inline Modint catalan(ll n){ reserve_fac_vec(n * 2 + 1); return fac_vec[n * 2] * inv_vec[n] * inv_vec[n + 1]; }

//[lib]BIT.cpp
//一点add, 区間sum ができる
template< typename T >
class BinaryIndexedTreeNaive {
public:
	ll size;
	vector<T> data;
	BinaryIndexedTreeNaive(ll N) : size(N), data(size, 0) {}
	// add x to i
	void add(ll i, const T& x) {
		for(; i<size; i|=i+1) data[i] += x;
	}
	// sum [0, i)
	T sum(ll i) const {
		T ret = 0;
		for(--i; i>=0; i=(i&(i+1))-1) ret += data[i];
		return ret;
	}
	// sum [i, j)
	T sum(ll i, ll j) const {
		return sum(j) - sum(i);
	}
};
template<typename T> std::ostream& operator<<(std::ostream& s, const BinaryIndexedTreeNaive<T>& bit) { 
	for(ll i=0; i<bit.size; i++) s << bit.sum(i, i+1) << "\t\n"[i==bit.size-1];
	return s;
}
//区間add, 区間sum ができる
template< typename T >
class BinaryIndexedTree {
public:
	ll size;
	BinaryIndexedTreeNaive<T> b, c;
	BinaryIndexedTree(ll N) : size(N), b(size+1), c(size+1) {}
	// add x to [i, j) 
	void add(ll i, ll j, const T& x) {
		if (i>=j) return;
		b.add(i,x*-i);
		b.add(j,x*j);
		c.add(i,x);
		c.add(j,x*-1);
	}
	// sum [0, i)
	T sum(ll i) const { 
		return b.sum(i+1) + c.sum(i+1)*i;
	}
	// sum [i, j)
	T sum(ll i, ll j) const {
		if (i>=j) return 0;
		return sum(j) - sum(i);
	}
};
template<typename T> std::ostream& operator<<(std::ostream& s, const BinaryIndexedTree<T>& bit) { 
	for(ll i=0; i<bit.size; i++) s << bit.sum(i, i+1) << "\t\n"[i==bit.size-1];
	return s;
}

//[lib]BIT_2D(1点add矩形sum).cpp
//1点update, 矩形sumができる
template< typename T >
class BinaryIndexedTree2D {
public:
	ll h, w;
	T identity;
	vector< T > data;
	BinaryIndexedTree2D(ll h, ll w, T identity = T(0))
			: h(h), w(w), identity(identity), data(h * w, identity) {}
	// add val to data[x][y]	
	void add(ll x, ll y, T val) {
		for(; y < w; y|=y+1) addX(x, y, val);
	}
	// set val to data[x][y]
	void set(ll x, ll y, T val) { add(x, y, val - get(x, y)); }
	// get data[x][y]
	T get(ll x, ll y) const { return sum(x, x + 1, y, y + 1); }
	// sum [0, x) x [0, y)
	T sum(ll x, ll y) const {
		if(x < 0 || y < 0) return identity;
		T r = identity;
		for(--y; y>=0; y=(y&(y+1))-1) r += sumX(x, y);
		return r;
	}
	// sum [x1, x2) x [y1, y2)
	T sum(ll x1, ll x2, ll y1, ll y2) const {
		if (x1 >= x2 || y1 >= y2) return 0;
		return sum(x2, y2) - sum(x2, y1) - sum(x1, y2) + sum(x1, y1);
	}

private:
	inline ll id(ll x, ll y) const { return x * w + y; }
	void addX(ll x, ll y, T const &val) {
		for(; x < h; x|=x+1) data[id(x, y)] += val;
	}
	T sumX(ll x, ll y) const {
		T r = identity;
		for(--x; x>=0; x=(x&(x+1))-1) r += data[id(x, y)];
		return r;
	}
};
template< typename T>
std::ostream& operator<<(std::ostream& s, const BinaryIndexedTree2D<T>& bit) {
	s << "\\\n";
	for(ll i=0; i<bit.h; i++) for(ll j=0; j<bit.w; j++) s << bit.sum(i, i+1, j, j+1) << "\t\n"[j==bit.w-1];
	return s;
}

/*-----8<-----library-----8<-----*/

// nextc[i][c] := S の i 文字目以降で最初に文字 c が登場する index(i自体を含む)
vector<vector<ll> > calcNext(const string &S, char initc = 'a') {
	int n = S.size();
	vector<vector<ll> > res(n+1, vector<ll>(27, n));
	for (int i = n-1; i >= 0; --i) {
		for (int j = 0; j < 27; ++j) res[i][j] = res[i+1][j];
		int x = S[i]=='?' ? 26 : S[i] - initc;
		res[i][x] = i;
	}
	return res;
}

void solve() {
	ll N;
	string S;
	cin >> N >> S;
	vector<vector<ll>> nextv = calcNext(S);
	debug(nextv);
	string T = "yukicoder";
	BinaryIndexedTree2D<Modint> dp(N+1, 2);
	dp.add(0, 0, 1);

	rep(j,9){
		BinaryIndexedTree2D<Modint> ndp(N+1, 2);
		rep(i,N){
			if (S[i] == T[j]){
				//普通文字
				rep(k,2){
					Modint t = dp.sum(0, i+1, k, k + 1);
					ndp.add(i, k, t);
				}
			}
			if(S[i]=='?'){
				Modint t = dp.sum(0, i+1, 0, 1);
				ndp.add(i, 1, t);
			}
		}
		dp = move(ndp);
		debug(dp);
	}

	Modint ans = dp.sum(0, N, 0, 2);
	p(ans);
}

signed main() {
#ifndef LOCAL_DEV
	//std::cin.tie(nullptr);
	//std::ios::sync_with_stdio(false);
#endif
	//ll Q; cin >> Q; while(Q--)solve();
	solve();
	return 0;
}