#ifndef HIDDEN_IN_VS // 折りたたみ用 // 警告の抑制 #define _CRT_SECURE_NO_WARNINGS // ライブラリの読み込み #include using namespace std; // 型名の短縮 using ll = long long; // -2^63 ~ 2^63 = 9 * 10^18(int は -2^31 ~ 2^31 = 2 * 10^9) using pii = pair; using pll = pair; using pil = pair; using pli = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vvvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vvvvl = vector; using vb = vector; using vvb = vector; using vvvb = vector; using vc = vector; using vvc = vector; using vvvc = vector; using vd = vector; using vvd = vector; using vvvd = vector; template using priority_queue_rev = priority_queue, greater>; using Graph = vvi; using ull = unsigned long long; // 定数の定義 const double PI = acos(-1); const vi DX = { 1, 0, -1, 0 }; // 4 近傍(下,右,上,左) const vi DY = { 0, 1, 0, -1 }; int INF = 1001001001; ll INFL = 4004004003104004004LL; // (int)INFL = 1010931620; double EPS = 1e-15; // 入出力高速化 struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp; // 汎用マクロの定義 #define all(a) (a).begin(), (a).end() #define sz(x) ((int)(x).size()) #define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x)) #define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x)) #define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");} #define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順 #define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順 #define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順 #define repe(v, a) for(const auto& v : (a)) // a の全要素(変更不可能) #define repea(v, a) for(auto& v : (a)) // a の全要素(変更可能) #define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d ビット全探索(昇順) #define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て(昇順) #define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod #define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去 #define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了 #define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定 // 汎用関数の定義 template inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; } template inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら true を返す) template inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら true を返す) template inline T get(T set, int i) { return (set >> i) & T(1); } // 演算子オーバーロード template inline istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline istream& operator>>(istream& is, vector& v) { repea(x, v) is >> x; return is; } template inline vector& operator--(vector& v) { repea(x, v) --x; return v; } template inline vector& operator++(vector& v) { repea(x, v) ++x; return v; } #endif // 折りたたみ用 #if __has_include() #include using namespace atcoder; #ifdef _MSC_VER #include "localACL.hpp" #endif //using mint = modint1000000007; using mint = modint998244353; //using mint = modint; // mint::set_mod(m); namespace atcoder { inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; } inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; } } using vm = vector; using vvm = vector; using vvvm = vector; using vvvvm = vector; #endif #ifdef _MSC_VER // 手元環境(Visual Studio) #include "local.hpp" #else // 提出用(gcc) inline int popcount(int n) { return __builtin_popcount(n); } inline int popcount(ll n) { return __builtin_popcountll(n); } inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; } inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; } inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; } inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; } inline int msb(__int128 n) { return (n >> 64) != 0 ? (127 - __builtin_clzll((ll)(n >> 64))) : n != 0 ? (63 - __builtin_clzll((ll)(n))) : -1; } #define gcd __gcd #define dump(...) #define dumpel(v) #define dump_list(v) #define dump_mat(v) #define input_from_file(f) #define output_to_file(f) #define Assert(b) { if (!(b)) while (1) cout << "OLE"; } #endif //【任意数列の列挙(要素ごと上限指定)】O(Πub[0..n)) /* * 数列 a[0..n) で,∀i, a[i] ∈ [0..ub[i]) を満たすもの全てを格納したリストを返す. */ vvi enumerate_all_sequences(const vi& ub) { // verify : https://atcoder.jp/contests/arc104/tasks/arc104_e int n = sz(ub); vvi seqs; vi seq; // 作成途中の列 int i = 0; // 列の長さ function rf = [&]() { // 完成していれば記録する. if (i == n) { seqs.push_back(seq); return; } rep(x, ub[i]) { seq.push_back(x); i++; rf(); seq.pop_back(); i--; } }; rf(); return seqs; } mint naive(ll m) { mint res = 0; int n_max = 1 << (msb(m - 1) + 1); dump(n_max); repi(n, 1, n_max) { vi ub(n, (int)m); auto seqs = enumerate_all_sequences(ub); repe(a, seqs) { vi b(n); b[0] = a[0]; repi(i, 1, n - 1) b[i] = b[i - 1] ^ a[i]; bool ok = true; rep(i, n - 1) if (b[i] >= b[i + 1]) { ok = false; break; } if (ok) res++; } } return res; } void zikken() { repi(m, 1, 8) { dump(m, naive(m)); } exit(0); } /* 1 1 = 2^1 - 1 2 3 = 2^2 - 1 3 9 4 15 = 2^4 - 1 5 55 6 99 7 169 8 255 = 2^8 - 1 */ void zikken2() { repi(m, 1, 8) { vm cnt(m); int n_max = 1 << (msb(m - 1) + 1); // dump(n_max); repi(n, 1, n_max) { vi ub(n, (int)m); auto seqs = enumerate_all_sequences(ub); repe(a, seqs) { vi b(n); b[0] = a[0]; repi(i, 1, n - 1) b[i] = b[i - 1] ^ a[i]; bool ok = true; rep(i, n - 1) if (b[i] >= b[i + 1]) { ok = false; break; } if (ok) cnt[*max_element(all(a))]++; } } dump(m, ":", cnt); } exit(0); } /* 1 : 1 2 : 1 2 3 : 1 2 6 4 : 1 2 6 6 5 : 1 2 6 6 40 6 : 1 2 6 6 40 44 7 : 1 2 6 6 40 44 70 8 : 1 2 6 6 40 44 70 86 */ //【狭義単調増加列の列挙】O(bin(m, n)) /* * 0 ≦ a[0] < a[1] < ... < a[n-1] < m なる列 a[0..n) を格納したリストを返す. */ vvi enumerate_strongly_increase_sequences(int n, int m) { // verify : https://atcoder.jp/contests/abc263/tasks/abc263_c vi a(n); vvi seqs; // len : 列の長さ function rf = [&](int len) { // 列の長さが n の場合 if (len == n) { // 完成しているので記録 seqs.push_back(a); return; } // i0 : 直前の数の大きさ int i0 = (len > 0 ? a[len - 1] : -1); // 直前の数 i0 より大きい数が選べる. repi(i, i0 + 1, m - 1) { a[len++] = i; rf(len); len--; } }; rf(0); return seqs; } void zikken3() { int m = 16; vm cnt(m); int n_max = 1 << (msb(m - 1) + 1); repi(n, 1, n_max) { vi ub(n, (int)m); auto seqs = enumerate_strongly_increase_sequences(n, n_max); repe(b, seqs) { vi a(n); a[0] = b[0]; repi(i, 1, n - 1) a[i] = b[i - 1] ^ b[i]; int a_max = *max_element(all(a)); if (a_max < m) cnt[a_max]++; } } dump_list(cnt); exit(0); } /* {1, 2, 6, 6, 40, 44, 70, 86, 1152, 1344, 2208, 2736, 8232, 10284, 17478, 21846} */ void zikken4() { int m = 16; vvm cnt(m, vm(m)); int n_max = 1 << (msb(m - 1) + 1); repi(n, 1, n_max) { vi ub(n, (int)m); auto seqs = enumerate_strongly_increase_sequences(n, n_max); repe(b, seqs) { vi a(n); a[0] = b[0]; repi(i, 1, n - 1) a[i] = b[i - 1] ^ b[i]; int a_max = *max_element(all(a)); int a_min = *min_element(all(a)); if (a_max < m) cnt[a_min][a_max]++; } } dump_mat(cnt); exit(0); } /* {{1,1,3,3,20,22,35,43,576,672,1104,1368,4116,5142,8739,10923}, {0,1,2,2,15,17,28,36,495,591,981,1245,3787,4813,8192,10376}, {0,0,1,0,2,2,4,4,44,44,82,82,214,214,404,404}, {0,0,0,1,2,2,2,2,28,28,32,32,94,94,122,122}, {0,0,0,0,1,0,0,0,2,2,2,2,8,8,8,8}, {0,0,0,0,0,1,0,0,2,2,2,2,6,6,6,6}, {0,0,0,0,0,0,1,0,2,2,2,2,4,4,4,4}, {0,0,0,0,0,0,0,1,2,2,2,2,2,2,2,2}, {0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1}} */ //【上から桁 DP,未満フラグ,数え上げ】O(n b)(の改変) /* * b=10 進数で n 桁の数 num 以下の非負の整数の個数を返す. */ mint count_digit(int B, ll s) { dump(B, s); // dp[i][f] : 以下の条件を満たす数の個数: // i : 上からの桁 d[0..i) まで決まっている. // f : d[0..i) < num[0..i) なら 1,さもなくば 0(未満フラグ) vvm dp(B + 1, vm(1LL << 1)); dp[0][0] = 1; mint inv2 = mint(2).inv(); // 上の桁から順に配る DP rep(b, B) { // x : num の上から i 桁目の数 int x = (int)get(s, B - 1 - b); repb(f, 1) { int smaller = (f >> 0) & 1; // d_max : d[i] のとれる値の最大値 int k_max = (smaller ? 1 : x); // d : d[i] repi(k, 0, k_max) { repi(i, 0, 1) { int n_smaller = (int)(smaller || (k < k_max)); int nf = (n_smaller << 0); int e = i - (i ^ k); mint mul = 1; if (e == 1) mul = mint(2).pow(1LL << (B - 1 - b)); else if (e == -1) mul = inv2.pow(1LL << (B - 1 - b)); dp[b + 1][nf] += dp[b][f] * mul; } } } //dump("----", i + 1, "----"); //repb(f, 1) dump("(smaller) =", bitset<1>(f), ":", dp[i + 1][f]); } mint res = 0; repb(f, 1) res += dp[B][f]; return res; } mint solve(ll m) { if (m == 1) return 1; int B = msb(m - 1); dump(B); ll k_max = m - 1 - (1LL << B); auto res = count_digit(B, k_max); res *= mint(2).pow((1LL << B) - 1); res += mint(2).pow((1LL << B) + 1); res -= mint(2).pow((1LL << (B + 1)) - m); res--; return res; } int main() { // input_from_file("input.txt"); // output_to_file("output.txt"); // zikken4(); ll m; cin >> m; // dump(naive(m)); dump("----"); cout << solve(m) << endl; }