#line 1 "main.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1144"

#include <cstdint>
#include <iostream>
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"



#include <cassert>
#include <numeric>
#include <type_traits>

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

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



#include <utility>

#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 < 2^31`
    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 int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

// @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);

}  // 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/tools/vector2.hpp"



#include <cmath>
#line 6 "/home/anqooqie/.proconlib/tools/vector2.hpp"
#include <cstddef>
#include <array>
#include <string>
#include <functional>
#include <limits>
#line 1 "/home/anqooqie/.proconlib/tools/pair_hash.hpp"



#line 6 "/home/anqooqie/.proconlib/tools/pair_hash.hpp"
#include <random>
#line 9 "/home/anqooqie/.proconlib/tools/pair_hash.hpp"

namespace tools {

  template <class T1, class T2>
  struct pair_hash {
    using result_type = ::std::size_t;
    using argument_type = ::std::pair<T1, T2>;
    ::std::size_t operator()(const ::std::pair<T1, T2>& key) const {
      static const ::std::size_t salt = ::std::random_device()();
      static const ::std::hash<T1> hasher1 = ::std::hash<T1>();
      static const ::std::hash<T2> hasher2 = ::std::hash<T2>();
      static const ::std::hash<::std::size_t> hasher3 = ::std::hash<::std::size_t>();
      ::std::size_t result = 0;
      result ^= hasher1(key.first) + static_cast<::std::size_t>(0x9e3779b9) + (result << static_cast<::std::size_t>(6)) + (result >> static_cast<::std::size_t>(2));
      result ^= hasher2(key.second) + static_cast<::std::size_t>(0x9e3779b9) + (result << static_cast<::std::size_t>(6)) + (result >> static_cast<::std::size_t>(2));
      result ^= hasher3(salt) + static_cast<::std::size_t>(0x9e3779b9) + (result << static_cast<::std::size_t>(6)) + (result >> static_cast<::std::size_t>(2));
      return result;
    }
  };

  template <>
  struct pair_hash<::std::uint64_t, ::std::uint64_t> {
    using result_type = ::std::size_t;
    using argument_type = ::std::pair<::std::uint64_t, ::std::uint64_t>;
    ::std::size_t operator()(const ::std::pair<::std::uint64_t, ::std::uint64_t>& key) const {
      static const ::std::hash<::std::uint64_t> hasher = ::std::hash<::std::uint64_t>();
      return hasher(((key.first << static_cast<::std::uint64_t>(32)) | (key.first >> static_cast<::std::uint64_t>(32))) ^ key.second);
    }
  };

  template <>
  struct pair_hash<::std::int64_t, ::std::int64_t> {
    using result_type = ::std::size_t;
    using argument_type = ::std::pair<::std::int64_t, ::std::int64_t>;
    ::std::size_t operator()(const ::std::pair<::std::int64_t, ::std::int64_t>& key) const {
      static const ::tools::pair_hash<::std::uint64_t, ::std::uint64_t> hasher = ::tools::pair_hash<::std::uint64_t, ::std::uint64_t>();
      return hasher(::std::make_pair<::std::uint64_t, ::std::uint64_t>(key.first, key.second));
    }
  };

  template <>
  struct pair_hash<::std::uint32_t, ::std::uint32_t> {
    using result_type = ::std::size_t;
    using argument_type = ::std::pair<::std::uint32_t, ::std::uint32_t>;
    ::std::size_t operator()(const ::std::pair<::std::uint32_t, ::std::uint32_t>& key) const {
      static const ::std::hash<::std::uint64_t> hasher = ::std::hash<::std::uint64_t>();
      return hasher((static_cast<::std::uint64_t>(key.first) << static_cast<::std::uint64_t>(32)) | static_cast<::std::uint64_t>(key.second));
    }
  };

  template <>
  struct pair_hash<::std::int32_t, ::std::int32_t> {
    using result_type = ::std::size_t;
    using argument_type = ::std::pair<::std::int32_t, ::std::int32_t>;
    ::std::size_t operator()(const ::std::pair<::std::int32_t, ::std::int32_t>& key) const {
      static const ::tools::pair_hash<::std::uint32_t, ::std::uint32_t> hasher = ::tools::pair_hash<::std::uint32_t, ::std::uint32_t>();
      return hasher(::std::make_pair<::std::uint32_t, ::std::uint32_t>(key.first, key.second));
    }
  };
}


#line 13 "/home/anqooqie/.proconlib/tools/vector2.hpp"

namespace tools {

  template <typename T>
  class vector2 {
  public:
    T x;
    T y;

    vector2() :
      vector2(T(), T()) {
    }

    vector2(const T& x, const T& y) :
      x(x),
      y(y) {
    }

    double norm() const {
      return ::std::sqrt(static_cast<double>(this->squared_norm()));
    }

    T squared_norm() const {
      return this->inner_product(*this);
    }

    template <typename SFINAE_T = T, typename ::std::enable_if<::std::is_same<SFINAE_T, double>::value, ::std::nullptr_t>::type = nullptr>
    ::tools::vector2<double> normalized() const {
      return *this / this->norm();
    }

    ::tools::vector2<T> operator+() const {
      return *this;
    }

    ::tools::vector2<T> operator-() const {
      return ::tools::vector2<T>(-this->x, -this->y);
    }

    friend ::tools::vector2<T> operator+(const ::tools::vector2<T>& lhs, const ::tools::vector2<T>& rhs) {
      return ::tools::vector2<T>(lhs.x + rhs.x, lhs.y + rhs.y);
    }

    friend ::tools::vector2<T> operator-(const ::tools::vector2<T>& lhs, const ::tools::vector2<T>& rhs) {
      return ::tools::vector2<T>(lhs.x - rhs.x, lhs.y - rhs.y);
    }

    template <typename OTHER, typename ::std::enable_if<!::std::is_same<OTHER, ::tools::vector2<T>>::value, ::std::nullptr_t>::type = nullptr>
    friend ::tools::vector2<T> operator*(const ::tools::vector2<T>& lhs, const OTHER& rhs) {
      return ::tools::vector2<T>(lhs.x * rhs, lhs.y * rhs);
    }
    template <typename OTHER, typename ::std::enable_if<!::std::is_same<OTHER, ::tools::vector2<T>>::value, ::std::nullptr_t>::type = nullptr>
    friend ::tools::vector2<T> operator*(const OTHER& lhs, const ::tools::vector2<T>& rhs) {
      return ::tools::vector2<T>(lhs * rhs.x, lhs * rhs.y);
    }

    template <typename OTHER, typename ::std::enable_if<!::std::is_same<OTHER, ::tools::vector2<T>>::value, ::std::nullptr_t>::type = nullptr>
    friend ::tools::vector2<T> operator/(const ::tools::vector2<T>& lhs, const OTHER& rhs) {
      return ::tools::vector2<T>(lhs.x / rhs, lhs.y / rhs);
    }

    T inner_product(const ::tools::vector2<T>& other) const {
      return this->x * other.x + this->y * other.y;
    }

    T outer_product(const ::tools::vector2<T>& other) const {
      return this->x * other.y - this->y * other.x;
    }

    ::tools::vector2<T>& operator+=(const ::tools::vector2<T>& other) {
      return *this = *this + other;
    }

    ::tools::vector2<T>& operator-=(const ::tools::vector2<T>& other) {
      return *this = *this - other;
    }

    template <typename OTHER, typename ::std::enable_if<!::std::is_same<OTHER, ::tools::vector2<T>>::value, ::std::nullptr_t>::type = nullptr>
    ::tools::vector2<T>& operator*=(const OTHER& other) {
      return *this = *this * other;
    }

    template <typename OTHER, typename ::std::enable_if<!::std::is_same<OTHER, ::tools::vector2<T>>::value, ::std::nullptr_t>::type = nullptr>
    ::tools::vector2<T>& operator/=(const OTHER& other) {
      return *this = *this / other;
    }

    friend bool operator==(const ::tools::vector2<T>& lhs, const ::tools::vector2<T>& rhs) {
      return lhs.x == rhs.x && lhs.y == rhs.y;
    }

    friend bool operator!=(const ::tools::vector2<T>& lhs, const ::tools::vector2<T>& rhs) {
      return lhs.x != rhs.x || lhs.y != rhs.y;
    }

    static ::std::array<::tools::vector2<T>, 4> four_directions() {
      return ::std::array<::tools::vector2<T>, 4>({
        ::tools::vector2<T>(static_cast<T>(-1), static_cast<T>(0)),
        ::tools::vector2<T>(static_cast<T>(1), static_cast<T>(0)),
        ::tools::vector2<T>(static_cast<T>(0), static_cast<T>(-1)),
        ::tools::vector2<T>(static_cast<T>(0), static_cast<T>(1))
      });
    }

    static ::std::array<::tools::vector2<T>, 8> eight_directions() {
      return ::std::array<::tools::vector2<T>, 8>({
        ::tools::vector2<T>(static_cast<T>(-1), static_cast<T>(-1)),
        ::tools::vector2<T>(static_cast<T>(-1), static_cast<T>(0)),
        ::tools::vector2<T>(static_cast<T>(-1), static_cast<T>(1)),
        ::tools::vector2<T>(static_cast<T>(0), static_cast<T>(-1)),
        ::tools::vector2<T>(static_cast<T>(0), static_cast<T>(1)),
        ::tools::vector2<T>(static_cast<T>(0), static_cast<T>(-1)),
        ::tools::vector2<T>(static_cast<T>(1), static_cast<T>(-1)),
        ::tools::vector2<T>(static_cast<T>(1), static_cast<T>(0)),
        ::tools::vector2<T>(static_cast<T>(1), static_cast<T>(1))
      });
    }
  };
}

namespace std {
  template <typename T>
  ::std::string to_string(const ::tools::vector2<T>& f) {
    return '(' + ::std::to_string(f.x) + ", " + ::std::to_string(f.y) + ')';
  }

  template <typename T>
  struct hash<::tools::vector2<T>> {
    using result_type = ::std::size_t;
    using argument_type = ::tools::vector2<T>;
    ::std::size_t operator()(const ::tools::vector2<T>& key) const {
      static const ::tools::pair_hash<T, T> hasher = ::tools::pair_hash<T, T>();
      return hasher(key.x, key.y);
    }
  };

  template <typename T>
  ::std::ostream& operator<<(::std::ostream& os, const ::tools::vector2<T>& self) {
    return os << ::std::to_string(self);
  }

  template <typename T>
  ::std::istream& operator>>(::std::istream& is, ::tools::vector2<T>& self) {
    return is >> self.x >> self.y;
  }
}


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



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



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

namespace tools {
  template <typename T>
  ::std::int_fast64_t ccw(const ::tools::vector2<T>& a, ::tools::vector2<T> b, ::tools::vector2<T> c) {
    b -= a;
    c -= a;
    if (b.outer_product(c) > 0) return +1;
    if (b.outer_product(c) < 0) return -1;
    if (b.inner_product(c) < 0) return +2;
    if (b.squared_norm() < c.squared_norm()) return -2;
    return 0;
  }
}


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

namespace tools {

  template <bool DEFAULT, typename T>
  class less_by_arg {
  private:
    ::tools::vector2<T> d;

    template <typename U>
    int where(const ::tools::vector2<U>& p) const {
      if constexpr (DEFAULT) {
        return p.y > 0 || (p.y == 0 && p.x >= 0) ? 0 : 1;
      } else {
        if (this->d == p) return 0;
        const int ccw = ::tools::ccw(::tools::vector2<U>(0, 0), this->d, p);
        if (ccw == -2) return 0;
        if (ccw == +1) return 1;
        if (ccw == +2) return 2;
        if (ccw == -1) return 3;
        return 4;
      }
    }

  public:
    less_by_arg() = default;

    template <typename U>
    explicit less_by_arg(const ::tools::vector2<U>& d) : d(d) {
    }

    template <typename U>
    bool operator()(const ::tools::vector2<U>& a, const ::tools::vector2<U>& b) const {
      const int wa = this->where(a);
      const int wb = this->where(b);
      return wa == wb ? a.outer_product(b) > 0 || (a.outer_product(b) == 0 && a.squared_norm() < b.squared_norm()) : wa < wb;
    }
  };

  less_by_arg() -> less_by_arg<true, int>;

  template <typename U>
  less_by_arg(const ::tools::vector2<U>&) -> less_by_arg<false, U>;
}


#line 8 "main.cpp"

using mint = atcoder::modint1000000007;
using i64 = std::int_fast64_t;

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

  i64 n;
  std::cin >> n;
  std::vector<tools::vector2<i64>> orig_p(n);
  for (auto& orig_p_i : orig_p) std::cin >> orig_p_i;

  mint answer(0);
  for (auto it = orig_p.begin(); it != orig_p.end(); ++it) {
    std::vector<tools::vector2<i64>> p(std::next(it), orig_p.end());
    for (auto& p_i : p) p_i -= *it;
    std::sort(p.begin(), p.end(), tools::less_by_arg());

    auto whole = std::accumulate(p.begin(), p.end(), tools::vector2<i64>(0, 0));
    i64 r = 0;
    tools::vector2<i64> sum(0, 0);
    for (i64 l = 0; l < i64(p.size()); ++l) {
      for (; r < i64(p.size()) && tools::less_by_arg(p[l])(p[r], -p[l]); ++r) {
        sum += p[r];
      }

      answer += mint(p[l].outer_product(sum));
      answer -= mint(p[l].outer_product(whole - sum));

      if (l == r) {
        ++r;
      } else {
        sum -= p[l];
      }
      whole -= p[l];
    }
  }

  std::cout << answer.val() << '\n';
}