#line 1 "/home/anqooqie/.proconlib/tools/util.hpp"



// To see the details of my library, visit my GitHub Pages.
// https://anqooqie.github.io/proconlib/

#ifdef LOCAL
  #ifndef _GLIBCXX_DEBUG
    #define _GLIBCXX_DEBUG
  #endif
#else
  #ifndef NDEBUG
    #define NDEBUG
  #endif
#endif

#include <bits/stdc++.h>
#line 1 "/home/anqooqie/.proconlib/tools/resize.hpp"



#line 8 "/home/anqooqie/.proconlib/tools/resize.hpp"

namespace tools {
  template <class T, class Allocator, typename Head>
  void resize(::std::vector<T, Allocator>& vector, const Head& head) {
    vector.resize(head);
  }
  template <class T, ::std::size_t N, typename Head>
  void resize([[maybe_unused]] ::std::array<T, N>& array, [[maybe_unused]] const Head& head) {
    assert(array.size() == static_cast<::std::size_t>(head));
  }

  template <class T, class Allocator, typename Head, typename... Tail>
  void resize(::std::vector<T, Allocator>& vector, const Head& head, const Tail&... tail);
  template <class T, ::std::size_t N, typename Head, typename... Tail>
  void resize(::std::array<T, N>& array, const Head& head, const Tail&... tail);

  template <class T, class Allocator, typename Head, typename... Tail>
  void resize(::std::vector<T, Allocator>& vector, const Head& head, const Tail&... tail) {
    vector.resize(head);
    for (auto& child : vector) {
      ::tools::resize(child, tail...);
    }
  }
  template <class T, ::std::size_t N, typename Head, typename... Tail>
  void resize(::std::array<T, N>& array, [[maybe_unused]] const Head& head, const Tail&... tail) {
    assert(array.size() == static_cast<::std::size_t>(head));
    for (auto& child : array) {
      ::tools::resize(child, tail...);
    }
  }
}


#line 1 "/home/anqooqie/.proconlib/tools/fill.hpp"



#include <type_traits>
#line 1 "/home/anqooqie/.proconlib/tools/is_range.hpp"



#line 7 "/home/anqooqie/.proconlib/tools/is_range.hpp"

namespace tools {
  template <typename T, typename = ::std::void_t<>>
  struct is_range : ::std::false_type {};

  template <typename T>
  struct is_range<T, ::std::void_t<decltype(::std::begin(::std::declval<T>()), ::std::end(::std::declval<T>()))>> : ::std::true_type {};

  template <typename T>
  inline constexpr bool is_range_v = ::tools::is_range<T>::value;
}


#line 11 "/home/anqooqie/.proconlib/tools/fill.hpp"

namespace tools {
  template <class T, class Allocator, typename V>
  ::std::enable_if_t<!::tools::is_range_v<T>, void> fill(::std::vector<T, Allocator>& vector, const V& value) {
    ::std::fill(::std::begin(vector), ::std::end(vector), value);
  }
  template <class T, ::std::size_t N, typename V>
  ::std::enable_if_t<!::tools::is_range_v<T>, void> fill(::std::array<T, N>& array, const V& value) {
    ::std::fill(::std::begin(array), ::std::end(array), value);
  }

  template <class T, class Allocator, typename V>
  ::std::enable_if_t<::tools::is_range_v<T>, void> fill(::std::vector<T, Allocator>& vector, const V& value);
  template <class T, ::std::size_t N, typename V>
  ::std::enable_if_t<::tools::is_range_v<T>, void> fill(::std::array<T, N>& array, const V& value);

  template <class T, class Allocator, typename V>
  ::std::enable_if_t<::tools::is_range_v<T>, void> fill(::std::vector<T, Allocator>& vector, const V& value) {
    for (auto& child : vector) {
      ::tools::fill(child, value);
    }
  }
  template <class T, ::std::size_t N, typename V>
  ::std::enable_if_t<::tools::is_range_v<T>, void> fill(::std::array<T, N>& array, const V& value) {
    for (auto& child : array) {
      ::tools::fill(child, value);
    }
  }
}


#line 1 "/home/anqooqie/.proconlib/tools/extend_input.hpp"



// WARNING:
// This file adds functions to std namespace for convenience.
// Strictly speaking, it is not allowed in C++.
// It makes the program ill-formed to include this file, and may cause undefined behavior.

#line 1 "/home/anqooqie/.proconlib/tools/has_mod.hpp"



#line 6 "/home/anqooqie/.proconlib/tools/has_mod.hpp"

namespace tools {
  template <typename T, typename = ::std::void_t<>>
  struct has_mod : ::std::false_type {};

  template <typename T>
  struct has_mod<T, ::std::void_t<decltype(::std::declval<T>().mod())>> : ::std::true_type {};

  template <typename T>
  inline constexpr bool has_mod_v = ::tools::has_mod<T>::value;
}


#line 16 "/home/anqooqie/.proconlib/tools/extend_input.hpp"

namespace tools {
  namespace detail {
    namespace extend_input {
      template <typename T>
      ::std::istream& read(::std::istream& is, T& container) {
        for (auto& v : container) {
          is >> v;
        }
        return is;
      }
    }
  }
}

namespace std {
  template <class T, ::std::size_t N>
  ::std::istream& operator>>(::std::istream& is, ::std::array<T, N>& array) {
    return ::tools::detail::extend_input::read(is, array);
  }

  template <class T1, class T2>
  ::std::istream& operator>>(::std::istream& is, ::std::pair<T1, T2>& pair) {
    return is >> pair.first >> pair.second;
  }

  template <int I = 0, typename... Args>
  ::std::istream& operator>>(::std::istream& is, ::std::tuple<Args...>& tuple) {
    if constexpr (I < int(sizeof...(Args))) {
        is >> ::std::get<I>(tuple);
        return operator>><I + 1>(is, tuple);
      } else {
      return is;
    }
  }

  template <class T, class Allocator>
  ::std::istream& operator>>(::std::istream& is, ::std::vector<T, Allocator>& vector) {
    return ::tools::detail::extend_input::read(is, vector);
  }

  template <typename T>
  ::std::enable_if_t<::tools::has_mod_v<T>, ::std::istream&> operator>>(::std::istream& is, T& x) {
    long long n;
    is >> n;
    x = T(n);
    return is;
  }
}


#line 1 "/home/anqooqie/.proconlib/tools/extend_output.hpp"



// WARNING:
// This file adds functions to std namespace for convenience.
// Strictly speaking, it is not allowed in C++.
// It makes the program ill-formed to include this file, and may cause undefined behavior.

#line 12 "/home/anqooqie/.proconlib/tools/extend_output.hpp"
#include <optional>
#line 24 "/home/anqooqie/.proconlib/tools/extend_output.hpp"

namespace tools {
  namespace detail {
    namespace extend_output {
      template <typename T>
      ::std::ostream& debug_print(::std::ostream& os, const T& container) {
        ::std::string delimiter = "";
        os << '[';
        for (const auto& v : container) {
          os << delimiter << v;
          delimiter = ", ";
        }
        os << ']';
        return os;
      }
    }
  }
}

namespace std {
  template <class T, ::std::size_t N>
  ::std::ostream& operator<<(::std::ostream& os, const ::std::array<T, N>& array) {
    return ::tools::detail::extend_output::debug_print(os, array);
  }
  
  template <class Key, class T, class Compare, class Allocator>
  ::std::ostream& operator<<(::std::ostream& os, const ::std::map<Key, T, Compare, Allocator>& map) {
    return ::tools::detail::extend_output::debug_print(os, map);
  }

  template <typename T>
  ::std::ostream& operator<<(::std::ostream& os, const ::std::optional<T>& optional) {
    if (optional) {
      return os << *optional;
    } else {
      return os << "null";
    }
  }
  
  template <class T1, class T2>
  ::std::ostream& operator<<(::std::ostream& os, const ::std::pair<T1, T2>& pair) {
    return os << '[' << pair.first << ", " << pair.second << ']';
  }
  
  template <class T, class Container>
  ::std::ostream& operator<<(::std::ostream& os, ::std::queue<T, Container>& queue) {
    ::std::queue<T, Container> other = queue;
    ::std::string delimiter = "";
    os << '[';
    while (!queue.empty()) {
      os << delimiter << queue.front();
      delimiter = ", ";
      queue.pop();
    }
    os << ']';
  
    queue = ::std::move(other);
    return os;
  }
  
  template <class Key, class Compare, class Allocator>
  ::std::ostream& operator<<(::std::ostream& os, const ::std::set<Key, Compare, Allocator>& set) {
    return ::tools::detail::extend_output::debug_print(os, set);
  }

  template <class T, class Container>
  ::std::ostream& operator<<(::std::ostream& os, ::std::stack<T, Container>& stack) {
    ::std::stack<T, Container> other;
    while (!stack.empty()) {
      other.push(stack.top());
      stack.pop();
    }
  
    ::std::string delimiter = "";
    os << '[';
    while (!other.empty()) {
      os << delimiter << other.top();
      delimiter = ", ";
      stack.push(other.top());
      other.pop();
    }
    os << ']';
  
    return os;
  }
  
  template <int I = -1, typename... Args>
  ::std::ostream& operator<<(::std::ostream& os, const ::std::tuple<Args...>& tuple) {
    if constexpr (I == -1) {
      os << '[';
    } else if constexpr (I == int(sizeof...(Args))) {
      os << ']';
    } else if constexpr (I == 0) {
      os << ::std::get<I>(tuple);
    } else {
      os << ", " << ::std::get<I>(tuple);
    }
  
    if constexpr (I < int(sizeof...(Args))) {
      return operator<<<I + 1>(os, tuple);
    } else {
      return os;
    }
  }
  
  template <class Key, class T, class Hash, class Pred, class Allocator>
  ::std::ostream& operator<<(::std::ostream& os, const ::std::unordered_map<Key, T, Hash, Pred, Allocator>& unordered_map) {
    return ::tools::detail::extend_output::debug_print(os, unordered_map);
  }
  
  template <class Key, class Hash, class Pred, class Allocator>
  ::std::ostream& operator<<(::std::ostream& os, const ::std::unordered_set<Key, Hash, Pred, Allocator>& unordered_set) {
    return ::tools::detail::extend_output::debug_print(os, unordered_set);
  }
  
  template <class T, class Allocator>
  ::std::ostream& operator<<(::std::ostream& os, const ::std::vector<T, Allocator>& vector) {
    return ::tools::detail::extend_output::debug_print(os, vector);
  }
  
  template <typename T>
  ::std::enable_if_t<::tools::has_mod_v<T>, ::std::ostream&> operator<<(::std::ostream& os, const T& x) {
    return os << x.val();
  }
}


#line 1 "/home/anqooqie/.proconlib/tools/extend_hash.hpp"



// WARNING:
// This file adds partial specializations for classes in std namespace, for convenience.
// Strictly speaking, it is not allowed in C++.
// It makes the program ill-formed to include this file, and may cause undefined behavior.

#line 1 "/home/anqooqie/.proconlib/tools/tuple_hash.hpp"



#line 1 "/home/anqooqie/.proconlib/tools/now.hpp"



#line 5 "/home/anqooqie/.proconlib/tools/now.hpp"

namespace tools {
  inline long long now() {
    return ::std::chrono::duration_cast<::std::chrono::nanoseconds>(::std::chrono::high_resolution_clock::now().time_since_epoch()).count();
  }
}


#line 1 "/home/anqooqie/.proconlib/tools/hash_combine.hpp"



#line 6 "/home/anqooqie/.proconlib/tools/hash_combine.hpp"

// Source: https://github.com/google/cityhash/blob/f5dc54147fcce12cefd16548c8e760d68ac04226/src/city.h
// License: MIT
// Author: Google Inc.

// Copyright (c) 2011 Google, Inc.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.

namespace tools {
  template <typename T>
  void hash_combine(::std::size_t& seed, const T& v) {
    static const ::std::hash<T> hasher;
    static constexpr ::std::size_t k_mul = 0x9ddfea08eb382d69ULL;
    ::std::size_t a = (hasher(v) ^ seed) * k_mul;
    a ^= (a >> 47);
    ::std::size_t b = (seed ^ a) * k_mul;
    b ^= (b >> 47);
    seed = b * k_mul;
  }
}


#line 11 "/home/anqooqie/.proconlib/tools/tuple_hash.hpp"

namespace tools {
  template <typename... Ts>
  struct tuple_hash {
    template <::std::size_t I = sizeof...(Ts) - 1>
    ::std::size_t operator()(const ::std::tuple<Ts...>& key) const {
      if constexpr (I == ::std::numeric_limits<::std::size_t>::max()) {
        static const ::std::size_t seed = ::tools::now();
        return seed;
      } else {
        ::std::size_t seed = this->operator()<I - 1>(key);
        ::tools::hash_combine(seed, ::std::get<I>(key));
        return seed;
      }
    }
  };
}


#line 14 "/home/anqooqie/.proconlib/tools/extend_hash.hpp"

namespace std {
  template <class T1, class T2>
  struct hash<::std::pair<T1, T2>> {
    ::std::size_t operator()(const ::std::pair<T1, T2>& key) const {
      static const ::tools::tuple_hash<T1, T2> hasher;
      return hasher(::std::make_tuple(key.first, key.second));
    }
  };

  template <class... Args>
  struct hash<::std::tuple<Args...>> {
    ::std::size_t operator()(const ::std::tuple<Args...>& key) const {
      static const ::tools::tuple_hash<Args...> hasher;
      return hasher(key);
    }
  };
}


#line 23 "/home/anqooqie/.proconlib/tools/util.hpp"

using ll = long long;
using ull = unsigned long long;
using i32 = ::std::int32_t;
using u32 = ::std::uint32_t;
using i64 = ::std::int64_t;
using u64 = ::std::uint64_t;

#define ALL(x) ::std::begin(x), ::std::end(x)
#define REP(i, n) for (long long i = 0, i##_len = static_cast<long long>(n); i < i##_len; ++i)


#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"



#line 7 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"

#ifdef _MSC_VER
#include <intrin.h>
#endif

#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_math.hpp"



#line 5 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_math.hpp"

#ifdef _MSC_VER
#include <intrin.h>
#endif

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


#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_type_traits.hpp"



#line 7 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_type_traits.hpp"

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


#line 14 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"

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


#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/segtree.hpp"



#line 8 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/segtree.hpp"

#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_bit.hpp"



#ifdef _MSC_VER
#include <intrin.h>
#endif

#if __cplusplus >= 202002L
#include <bit>
#endif

namespace atcoder {

namespace internal {

#if __cplusplus >= 202002L

using std::bit_ceil;

#else

// @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;
}

#endif

// @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


#line 10 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/segtree.hpp"

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 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


#line 1 "/home/anqooqie/.proconlib/tools/less_by_first.hpp"



#line 5 "/home/anqooqie/.proconlib/tools/less_by_first.hpp"

namespace tools {

  class less_by_first {
  public:
    template <class T1, class T2>
    bool operator()(const ::std::pair<T1, T2>& x, const ::std::pair<T1, T2>& y) const {
      return x.first < y.first;
    }
  };
}


#line 5 "main.cpp"

using mint = atcoder::modint1000000007;

struct monoid {
  using T = std::pair<ll, mint>;
  static T op(const T& x, const T& y) {
    return x.first == y.first ? T(x.first, x.second + y.second) : std::max(x, y, tools::less_by_first{});
  }
  static T e() {
    return T(0, mint::raw(0));
  }
};

int main() {
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);

  ll N;
  std::cin >> N;
  std::vector<ll> A(N);
  std::cin >> A;

  std::vector<std::pair<ll, ll>> sorted;
  REP(i, N) {
    sorted.emplace_back(A[i], -i);
  }
  std::sort(ALL(sorted));
  REP(i, N) {
    A[i] = std::distance(sorted.begin(), std::lower_bound(ALL(sorted), std::make_pair(A[i], -i)));
  }

  atcoder::segtree<typename monoid::T, monoid::op, monoid::e> dp(N);
  REP(i, N) {
    const auto [n, k] = dp.prod(0, A[i]);
    dp.set(A[i], std::make_pair(n + 1, n == 0 ? mint::raw(1) : k));
  }

  std::cout << dp.all_prod().second.val() << '\n';
  return 0;
}