#include <cstdio>
#include <vector>
#include <iostream>
#include <deque>
#include <queue>
#include <tuple>
#include <map>
#include <set>
#include <algorithm>
#include <string>

/**
 * ACLibrary-segtree
 * Ref : https://atcoder.github.io/ac-library/master/document_ja/
 */

#include <cassert>
#include <functional>

/**
 * ACLibrary-internalbit
 * Ref : https://atcoder.github.io/ac-library/master/document_ja/
 */

#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



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


#include <boost/rational.hpp>
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>

using namespace std;
using namespace atcoder;
using namespace boost;
namespace mp = boost::multiprecision;



//Integer-Related

typedef long long i64;
typedef unsigned long long ui64;
typedef mp::int128_t i128;
typedef mp::uint128_t ui128;



//Float-Related

typedef mp::cpp_dec_float_100 float100;
typedef mp::cpp_dec_float_50 float50;



//vector-Related

template<typename T>
using vv = vector<vector<T>>;
template<typename T>
using vvv = vector<vector<vector<T>>>;
typedef vector<i64> vi64;
typedef vector<bool> vbool;
typedef vv<i64> vvi64;
typedef vv<bool> vvbool;
typedef vvv<i64> vvvi64;
typedef vvv<bool> vvvbool;
typedef pair<i64, i64> pi64;

typedef vector<string> vstr;

//これで最大値優先
template<typename Val_T, typename Pred = less<Val_T>>
using prque = priority_queue<Val_T, vector<Val_T>, Pred>;



//set-Related

#include <unordered_set>
typedef set<i64> si64;
typedef multiset<i64> msi64;
typedef unordered_set<i64> usi64;



//Calculation-Related

inline i64 rm(const i64 l, const i64 r) {
    i64 val = l % r;
    if (val >= 0) {
        return val;
    }
    else {
        return val + r;
    }
}

template<typename T>
T r_accumulate(const vector<T>& vec) {
    return std::accumulate(vec.begin(), vec.end(), T{});
}

template <typename T>
void r_insert(vector<T>& to, vector<T>& from) {
    ranges::copy(from, back_inserter(to));
}

constexpr std::string repeater3030(const std::string& s, int number) {
    std::string cur = "";
    for (i64 i = 0; i < number; i++)
    {
        cur += s;
    }
    return cur;
}

constexpr std::string repeater3030(const char& c, int number) {
    string s(1, c);
    return repeater3030(s, number);
}

constexpr i64 pow_i64(i64 base, i64 exp) {
    i64 res = 1LL;
    while (exp > 0LL)
    {
        if (exp & 1) {
            res *= base;
        }
        exp >>= 1LL;
        base *= base;
    }
    return res;
}

template<typename T>
T eqmin(T& a, T b) {
    a = min(a, b);
    return a;
}

template<typename T>
T eqmax(T& a, T b) {
    a = max(a, b);
    return a;
}



//Output-Related

template <typename T, typename U>
std::ostream& operator<<(std::ostream& os, const std::pair<T, U>& p) {
    os << "(" << p.first << ", " << p.second << ")";
    return os;
}

template<typename T>
inline void output(const T elem) {
    std::cout << elem << std::endl;
}

#ifndef __INTELLISENSE__
template<typename T1, typename T2>
inline void output(const pair<T1, T2> elem) {
    std::cout << "(" << elem.first << "," << elem.second << ")" << std::endl;
}

template<typename T>
inline void output(const vector<T>& vec) {
    for (T elem : vec) {
        std::cout << elem << " ";
    }
    std::cout << std::endl;
}

template<typename T>
inline void output(const vector<vector<T>>& vvec) {
    for (vector<T> vec : vvec) {
        std::cout << "(";
        for (T elem : vec) {
            std::cout << elem << " ";
        }
        std::cout << ")";
    }
    std::cout << std::endl;
}

template<typename T>
inline void output(const vector<vector<vector<T>>>& vvvec) {
    for (vector<vector<T>> vvec : vvvec)
    {
        std::cout << "[";
        for (vector<T> vec : vvec) {
            std::cout << "(";
            for (T elem : vec) {
                std::cout << elem << " ";
            }
            std::cout << ")";
        }
        std::cout << "]" << std::endl;
    }
}
#endif

template<typename T>
inline void output_iter(const T& iter) {
    for (auto&& elem : iter)
    {
        std::cout << elem << " ";
    }
    std::cout << std::endl;
}

/*
* Mod I64 (Fork)
* Ref : https://noshi91.hatenablog.com/entry/2019/03/31/174006
* Submit : https://atcoder.jp/contests/abc414/tasks/abc414_e
* Note : Modulusはsqrt(long long の最大値)以下である必要がある
*/

#include <cstdint>
/**
 * ACLibrary-math
 * Ref : https://atcoder.github.io/ac-library/master/document_ja/
 */


/**
 * ACLibrary-internalmath
 * Ref : https://atcoder.github.io/ac-library/master/document_ja/
 */

#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`
    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



namespace atcoder {

long long pow_mod(long long x, long long n, int m) {
    assert(0 <= n && 1 <= m);
    if (m == 1) return 0;
    internal::barrett bt((unsigned int)(m));
    unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
    while (n) {
        if (n & 1) r = bt.mul(r, y);
        y = bt.mul(y, y);
        n >>= 1;
    }
    return r;
}

long long inv_mod(long long x, long long m) {
    assert(1 <= m);
    auto z = internal::inv_gcd(x, m);
    assert(z.first == 1);
    return z.second;
}

// (rem, mod)
std::pair<long long, long long> crt(const std::vector<long long>& r,
                                    const std::vector<long long>& m) {
    assert(r.size() == m.size());
    int n = int(r.size());
    // Contracts: 0 <= r0 < m0
    long long r0 = 0, m0 = 1;
    for (int i = 0; i < n; i++) {
        assert(1 <= m[i]);
        long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
        if (m0 < m1) {
            std::swap(r0, r1);
            std::swap(m0, m1);
        }
        if (m0 % m1 == 0) {
            if (r0 % m1 != r1) return {0, 0};
            continue;
        }
        // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1)

        // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1));
        // r2 % m0 = r0
        // r2 % m1 = r1
        // -> (r0 + x*m0) % m1 = r1
        // -> x*u0*g = r1-r0 (mod u1*g) (u0*g = m0, u1*g = m1)
        // -> x = (r1 - r0) / g * inv(u0) (mod u1)

        // im = inv(u0) (mod u1) (0 <= im < u1)
        long long g, im;
        std::tie(g, im) = internal::inv_gcd(m0, m1);

        long long u1 = (m1 / g);
        // |r1 - r0| < (m0 + m1) <= lcm(m0, m1)
        if ((r1 - r0) % g) return {0, 0};

        // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1)
        long long x = (r1 - r0) / g % u1 * im % u1;

        // |r0| + |m0 * x|
        // < m0 + m0 * (u1 - 1)
        // = m0 + m0 * m1 / g - m0
        // = lcm(m0, m1)
        r0 += x * m0;
        m0 *= u1;  // -> lcm(m0, m1)
        if (r0 < 0) r0 += m0;
    }
    return {r0, m0};
}

long long floor_sum(long long n, long long m, long long a, long long b) {
    assert(0 <= n && n < (1LL << 32));
    assert(1 <= m && m < (1LL << 32));
    unsigned long long ans = 0;
    if (a < 0) {
        unsigned long long a2 = internal::safe_mod(a, m);
        ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m);
        a = a2;
    }
    if (b < 0) {
        unsigned long long b2 = internal::safe_mod(b, m);
        ans -= 1ULL * n * ((b2 - b) / m);
        b = b2;
    }
    return ans + internal::floor_sum_unsigned(n, m, a, b);
}

}  // namespace atcoder



template <i64 Modulus>
class modI64 {
private:
    i64 val;
public:
    constexpr modI64(const i64 x = 0) noexcept : val(x% Modulus) {
        assert(x >= 0);
    }

    modI64 inv() const {
        return modI64(inv_mod(val, Modulus));
    }

    modI64 pow(i64 exp) const {
        modI64 res = 1LL;
        modI64 base = val;
        while (exp > 0LL)
        {
            if (exp & 1) {
                res *= base;
            }
            exp >>= 1LL;
            base *= base;
        }
        return res;
    }

    i64 value() const {
        return val;
    }

    constexpr modI64 operator+(const modI64 rhs) const noexcept {
        return modI64(*this) += rhs;
    }
    constexpr modI64 operator-(const modI64 rhs) const noexcept {
        return modI64(*this) -= rhs;
    }
    constexpr modI64 operator*(const modI64 rhs) const noexcept {
        return modI64(*this) *= rhs;
    }
    constexpr modI64 operator/(const modI64 rhs) const noexcept {
        return modI64(*this) /= rhs;
    }
    constexpr modI64& operator+=(const modI64 rhs) noexcept {
        val += rhs.val;
        if (val >= Modulus) {
            val -= Modulus;
        }
        return *this;
    }
    constexpr modI64& operator-=(const modI64 rhs) noexcept {
        if (val < rhs.val) {
            val += Modulus;
        }
        val -= rhs.val;
        return *this;
    }
    constexpr modI64& operator*=(const modI64 rhs) noexcept {
        val = val * rhs.val % Modulus;
        return *this;
    }
    constexpr modI64& operator/=(modI64 rhs) noexcept {
        i64 div = inv_mod(rhs.val, Modulus);
        val = val * div % Modulus;
        return *this;
    }
    constexpr bool operator==(const modI64& rhs) const noexcept {
        return val == rhs.val;
    }
    constexpr bool operator!=(const modI64& rhs) const noexcept {
        return val != rhs.val;
    }
    friend ostream& operator<<(ostream& os, const modI64& x) {
        return os << x.val;
    }
};

typedef modI64<998244353> mi64;
//typedef modI64<1000000007> mi64;
typedef vv<mi64> vvmi64;
typedef vector<mi64> vmi64;

/*
* Point-Related(IntegerOnly)
* Author : WhiteKnight
* Submit:https://atcoder.jp/contests/abc421/tasks/abc421_d
*/


template <typename T1 = long long, typename T2 = double>
struct Point {
private:
    void single_rect_rotate(Point<T1> min_anchor, i64 size) {
        Point<T1> res = { y - min_anchor.y + min_anchor.x, size - 1 - (x - min_anchor.x) + min_anchor.y };
        x = res.x;
        y = res.y;
    }
public:
    T1 x, y;

    Point() : x(0), y(0) {}

    Point(T1 x_val, T1 y_val) : x(x_val), y(y_val) {}

    Point& operator+=(const Point& rhs) {
        x += rhs.x;
        y += rhs.y;
        return *this;
    }

    Point& operator-=(const Point& rhs) {
        x -= rhs.x;
        y -= rhs.y;
        return *this;
    }

    Point& operator*=(T1 scalar) {
        x *= scalar;
        y *= scalar;
        return *this;
    }

    Point& operator/=(T1 scalar) {
        x /= scalar;
        y /= scalar;
        return *this;
    }

    /**
     * @brief ベクトルの大きさを計算します。
     * @return ベクトルの大きさ。
     */
    T2 magnitude() const {
        return std::sqrt(static_cast<T2>(x) * x + static_cast<T2>(y) * y);
    }

    /**
     * @brief ベクトルを五種類に大別して向きを表す。
     * @return T1型の正規化されたベクトル。
     */
    Point<T1> direction() const {
        return Point<T1>(sign(x),sign(y));
    }

    /**
     * @brief このベクトルを正規化した新しいベクトルを返します。
     * @return T2型の正規化されたベクトル。
     */
    Point<T2> normalized() const {
        T2 mag = magnitude();
        if (mag > 0) {
            return Point<T2>(x / mag, y / mag);
        }
        return Point<T2>(0.0, 0.0);
    }

    //included
    bool in(i64 min_x,i64 max_x,i64 min_y,i64 max_y) {
        return min_x <= x && x <= max_x && min_y <= y && y <= max_y;
    }

    //min_anchor : incl, clockwise
    void rect_rotate(Point<T1> min_anchor, i64 size, i64 cnt) {
        for (i64 i = 0; i < cnt % 4; i++)
        {
            single_rect_rotate(min_anchor, size);
        }
    }
};

template <typename T1, typename T2>
inline Point<T1,T2> operator+(Point<T1, T2> lhs, const Point<T1, T2>& rhs) {
    return lhs += rhs;
}

template <typename T1, typename T2>
inline Point<T1, T2> operator-(Point<T1, T2> lhs, const Point<T1, T2>& rhs) {
    return lhs -= rhs;
}

template <typename T1, typename T2>
inline Point<T1, T2> operator*(Point<T1, T2> lhs, T1 scalar) {
    return lhs *= scalar;
}

template <typename T1, typename T2>
inline Point<T1, T2> operator*(T1 scalar, Point<T1, T2> rhs) {
    return rhs *= scalar;
}

template <typename T1, typename T2>
inline Point<T1, T2> operator/(Point<T1, T2> lhs, T1 scalar) {
    return lhs /= scalar;
}

template <typename T1, typename T2>
inline bool operator==(const Point<T1, T2>& lhs, const Point<T1, T2>& rhs) {
    return lhs.x == rhs.x && lhs.y == rhs.y;
}

template <typename T1, typename T2>
inline bool operator!=(const Point<T1, T2>& lhs, const Point<T1, T2>& rhs) {
    return !(lhs == rhs);
}

/**
 * @brief 2点間のユークリッド距離（直線距離）を計算します。
 * @param p1 始点
 * @param p2 終点
 * @return double型の距離
 */
template <typename T1, typename T2>
inline T2 distance_euclidean(const Point<T1,T2>& p1, const Point<T1,T2>& p2) {
    T2 dx = static_cast<T2>(p1.x) - p2.x;
    T2 dy = static_cast<T2>(p1.y) - p2.y;
    return std::sqrt(dx * dx + dy * dy);
}

/**
 * @brief 2点間のマンハッタン距離を計算します。
 * @param p1 始点
 * @param p2 終点
 * @return 座標と同じ型の距離
 */
template <typename T1, typename T2>
inline T1 distance_manhattan(const Point<T1, T2>& p1, const Point<T1, T2>& p2) {
    return std::abs(p1.x - p2.x) + std::abs(p1.y - p2.y);
}

template <typename T1, typename T2>
std::ostream& operator<<(std::ostream& os, const Point<T1, T2>& p) {
    os << "(" << p.x << ", " << p.y << ")";
    return os;
}

using point = Point<long long,double>;

using q64 = rational<i64>;

/*
* Submit : https://atcoder.jp/contests/abc297/tasks/abc297_c
*/
void replace(string& S, string from, string to) {
    assert(from.size() == to.size());
    size_t start_pos = 0;
    while ((start_pos = S.find(from, start_pos)) != std::string::npos) {
        S.replace(start_pos, from.length(), to);
        start_pos += to.length();
    }
}

vi64 get_digits(i64 val) {
    assert(val >= 0);
    if (val == 0) {
        return { 0 };
    }
    vi64 res;
    while (val > 0)
    {
        res.push_back(val % 10);
        val /= 10;
    }
    return res;
}

//0-indexedで処理していたものから0部分をはねる
template<typename T>
vv<T> cut_false(vv<T>& base) {
    vv<T> res = base;
    res.erase(res.begin());
    for (auto&& e : res)
    {
        e.erase(e.begin());
    }
    return res;
}

std::array<point, 4> gridOn = {
    point(1,0),point(0,1),point(-1,0),point(0,-1)
};


/**
 * Graph一式
 * Author : WhiteKnight
 */

struct Dest {
    i64 to;
    i64 cost;
};

typedef vector<vector<Dest>> wgraphList;//Weighted,List
typedef vector<vector<i64>> sgraphList;//Simple,List
typedef vector<Dest> vedge;
typedef vvi64 wgraphMat;//Weighted,Matrix

wgraphList translate_simple_weight(sgraphList graph) {
    i64 N = graph.size();
    wgraphList res(N);
    for (i64 i = 0; i < N; i++)
    {
        for (auto&& e : graph[i])
        {
            res[i].push_back({e,1});
        }
    }
    return res;
}

template<i64 INF>
wgraphList translate_mat_list(wgraphMat graph){
    i64 N = graph.size();
    wgraphList res(N);
    for (i64 i = 0; i < N; i++)
    {
        for (i64 j = 0; j < N; j++)
        {
            if(graph[i][j] >= INF){
                continue;
            }
            res[i].push_back({ j,graph[i][j] });
        }
    }
    return res;
}

//Main Flow

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << setprecision(15);
    i64 N;
    cin >> N;
    string ans = repeater3030('1',N/2);
    N %= 2;
    if(N){
        ans[0] = '7';
    }
    output(ans);
    return 0;
}