#line 1 "/home/maspy/compro/library/my_template.hpp" #if defined(LOCAL) #include #else #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #include using namespace std; using ll = long long; using u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template constexpr T infty = 0; template <> constexpr int infty = 1'000'000'000; template <> constexpr ll infty = ll(infty) * infty * 2; template <> constexpr u32 infty = infty; template <> constexpr u64 infty = infty; template <> constexpr i128 infty = i128(infty) * infty; template <> constexpr double infty = infty; template <> constexpr long double infty = infty; using pi = pair; using vi = vector; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) \ for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } int popcnt_mod_2(int x) { return __builtin_parity(x); } int popcnt_mod_2(u32 x) { return __builtin_parity(x); } int popcnt_mod_2(ll x) { return __builtin_parityll(x); } int popcnt_mod_2(u64 x) { return __builtin_parityll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template T floor(T a, T b) { return a / b - (a % b && (a ^ b) < 0); } template T ceil(T x, T y) { return floor(x + y - 1, y); } template T bmod(T x, T y) { return x - y * floor(x, y); } template pair divmod(T x, T y) { T q = floor(x, y); return {q, x - q * y}; } template T SUM(const vector &A) { T sm = 0; for (auto &&a: A) sm += a; return sm; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) \ sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit() template T POP(deque &que) { T a = que.front(); que.pop_front(); return a; } template T POP(pq &que) { T a = que.top(); que.pop(); return a; } template T POP(pqg &que) { T a = que.top(); que.pop(); return a; } template T POP(vc &que) { T a = que.back(); que.pop_back(); return a; } template ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; (check(x) ? ok : ng) = x; } return ok; } template double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; (check(x) ? ok : ng) = x; } return (ok + ng) / 2; } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } // ? は -1 vc s_to_vi(const string &S, char first_char) { vc A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template vector cumsum(vector &A, int off = 1) { int N = A.size(); vector B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } // stable sort template vector argsort(const vector &A) { vector ids(len(A)); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); }); return ids; } // A[I[0]], A[I[1]], ... template vc rearrange(const vc &A, const vc &I) { vc B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } #endif #line 1 "/home/maspy/compro/library/other/io.hpp" #define FASTIO #include // https://judge.yosupo.jp/submission/21623 namespace fastio { static constexpr uint32_t SZ = 1 << 17; char ibuf[SZ]; char obuf[SZ]; char out[100]; // pointer of ibuf, obuf uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memcpy(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; if (pir < SZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } void rd(char &c) { do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); } void rd(string &x) { x.clear(); char c; do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); do { x += c; if (pil == pir) load(); c = ibuf[pil++]; } while (!isspace(c)); } template void rd_real(T &x) { string s; rd(s); x = stod(s); } template void rd_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed::value || is_same_v) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed::value || is_same_v) { if (minus) x = -x; } } void rd(int &x) { rd_integer(x); } void rd(ll &x) { rd_integer(x); } void rd(i128 &x) { rd_integer(x); } void rd(u32 &x) { rd_integer(x); } void rd(u64 &x) { rd_integer(x); } void rd(u128 &x) { rd_integer(x); } void rd(double &x) { rd_real(x); } void rd(long double &x) { rd_real(x); } void rd(f128 &x) { rd_real(x); } template void rd(pair &p) { return rd(p.first), rd(p.second); } template void rd_tuple(T &t) { if constexpr (N < std::tuple_size::value) { auto &x = std::get(t); rd(x); rd_tuple(t); } } template void rd(tuple &tpl) { rd_tuple(tpl); } template void rd(array &x) { for (auto &d: x) rd(d); } template void rd(vc &x) { for (auto &d: x) rd(d); } void read() {} template void read(H &h, T &... t) { rd(h), read(t...); } void wt(const char c) { if (por == SZ) flush(); obuf[por++] = c; } void wt(const string s) { for (char c: s) wt(c); } void wt(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) wt(s[i]); } template void wt_integer(T x) { if (por > SZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template void wt_real(T x) { ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); wt(s); } void wt(int x) { wt_integer(x); } void wt(ll x) { wt_integer(x); } void wt(i128 x) { wt_integer(x); } void wt(u32 x) { wt_integer(x); } void wt(u64 x) { wt_integer(x); } void wt(u128 x) { wt_integer(x); } void wt(double x) { wt_real(x); } void wt(long double x) { wt_real(x); } void wt(f128 x) { wt_real(x); } template void wt(const pair val) { wt(val.first); wt(' '); wt(val.second); } template void wt_tuple(const T t) { if constexpr (N < std::tuple_size::value) { if constexpr (N > 0) { wt(' '); } const auto x = std::get(t); wt(x); wt_tuple(t); } } template void wt(tuple tpl) { wt_tuple(tpl); } template void wt(const array val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } template void wt(const vector val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } void print() { wt('\n'); } template void print(Head &&head, Tail &&... tail) { wt(head); if (sizeof...(Tail)) wt(' '); print(forward(tail)...); } // gcc expansion. called automaticall after main. void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::read; using fastio::print; using fastio::flush; #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define U32(...) \ u32 __VA_ARGS__; \ read(__VA_ARGS__) #define U64(...) \ u64 __VA_ARGS__; \ read(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ read(name) #define VV(type, name, h, w) \ vector> name(h, vector(w)); \ read(name) void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } #line 3 "main.cpp" #line 2 "/home/maspy/compro/library/ds/my_bitset.hpp" // https://codeforces.com/contest/914/problem/F // https://yukicoder.me/problems/no/142 // わずかに普通の bitset より遅いときもあるようだが, // 固定長にしたくないときや slice 操作が必要なときに使う struct My_Bitset { using T = My_Bitset; int N; vc dat; // x で埋める My_Bitset(int N = 0, int x = 0) : N(N) { assert(x == 0 || x == 1); u64 v = (x == 0 ? 0 : -1); dat.assign((N + 63) >> 6, v); if (N) dat.back() >>= (64 * len(dat) - N); } int size() { return N; } void resize(int size) { dat.resize((size + 63) >> 6); int remainingBits = size & 63; if (remainingBits != 0) { u64 mask = (u64(1) << remainingBits) - 1; dat.back() &= mask; } N = size; } // thanks to chatgpt! class Proxy { public: Proxy(vc &d, int i) : dat(d), index(i) {} operator bool() const { return (dat[index >> 6] >> (index & 63)) & 1; } Proxy &operator=(u64 value) { dat[index >> 6] &= ~(u64(1) << (index & 63)); dat[index >> 6] |= (value & 1) << (index & 63); return *this; } void flip() { dat[index >> 6] ^= (u64(1) << (index & 63)); // XOR to flip the bit } private: vc &dat; int index; }; Proxy operator[](int i) { return Proxy(dat, i); } T &operator&=(const T &p) { assert(N == p.N); FOR(i, len(dat)) dat[i] &= p.dat[i]; return *this; } T &operator|=(const T &p) { assert(N == p.N); FOR(i, len(dat)) dat[i] |= p.dat[i]; return *this; } T &operator^=(const T &p) { assert(N == p.N); FOR(i, len(dat)) dat[i] ^= p.dat[i]; return *this; } T operator&(const T &p) const { return T(*this) &= p; } T operator|(const T &p) const { return T(*this) |= p; } T operator^(const T &p) const { return T(*this) ^= p; } int count() { int ans = 0; for (u64 val: dat) ans += popcnt(val); return ans; } int next(int i) { chmax(i, 0); if (i >= N) return N; int k = i >> 6; { u64 x = dat[k]; int s = i & 63; x = (x >> s) << s; if (x) return (k << 6) | lowbit(x); } FOR(idx, k + 1, len(dat)) { if (dat[idx] == 0) continue; return (idx << 6) | lowbit(dat[idx]); } return N; } int prev(int i) { chmin(i, N - 1); if (i <= -1) return -1; int k = i >> 6; if ((i & 63) < 63) { u64 x = dat[k]; x &= (u64(1) << ((i & 63) + 1)) - 1; if (x) return (k << 6) | topbit(x); --k; } FOR_R(idx, k + 1) { if (dat[idx] == 0) continue; return (idx << 6) | topbit(dat[idx]); } return -1; } My_Bitset range(int L, int R) { assert(L <= R); My_Bitset p(R - L); int rm = (R - L) & 63; FOR(rm) { p[R - L - 1] = bool((*this)[R - 1]); --R; } int n = (R - L) >> 6; int hi = L & 63; int lo = 64 - hi; int s = L >> 6; if (hi == 0) { FOR(i, n) { p.dat[i] ^= dat[s + i]; } } else { FOR(i, n) { p.dat[i] ^= (dat[s + i] >> hi) ^ (dat[s + i + 1] << lo); } } return p; } int count_range(int L, int R) { assert(L <= R); int cnt = 0; while ((L < R) && (L & 63)) cnt += (*this)[L++]; while ((L < R) && (R & 63)) cnt += (*this)[--R]; int l = L >> 6, r = R >> 6; FOR(i, l, r) cnt += popcnt(dat[i]); return cnt; } // [L,R) に p を代入 void assign_to_range(int L, int R, My_Bitset &p) { assert(p.N == R - L); int a = 0, b = p.N; while (L < R && (L & 63)) { (*this)[L++] = bool(p[a++]); } while (L < R && (R & 63)) { (*this)[--R] = bool(p[--b]); } // p[a:b] を [L:R] に int l = L >> 6, r = R >> 6; int s = a >> 6, t = b >> t; int n = r - l; if (!(a & 63)) { FOR(i, n) dat[l + i] = p.dat[s + i]; } else { int hi = a & 63; int lo = 64 - hi; FOR(i, n) dat[l + i] = (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo); } } // [L,R) に p を xor void xor_to_range(int L, int R, My_Bitset &p) { assert(p.N == R - L); int a = 0, b = p.N; while (L < R && (L & 63)) { dat[L >> 6] ^= u64(p[a]) << (L & 63); ++a, ++L; } while (L < R && (R & 63)) { --b, --R; dat[R >> 6] ^= u64(p[b]) << (R & 63); } // p[a:b] を [L:R] に int l = L >> 6, r = R >> 6; int s = a >> 6, t = b >> t; int n = r - l; if (!(a & 63)) { FOR(i, n) dat[l + i] ^= p.dat[s + i]; } else { int hi = a & 63; int lo = 64 - hi; FOR(i, n) dat[l + i] ^= (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo); } } // [L,R) に p を and void and_to_range(int L, int R, My_Bitset &p) { assert(p.N == R - L); int a = 0, b = p.N; while (L < R && (L & 63)) { if (!p[a++]) (*this)[L++] = 0; } while (L < R && (R & 63)) { if (!p[--b]) (*this)[--R] = 0; } // p[a:b] を [L:R] に int l = L >> 6, r = R >> 6; int s = a >> 6, t = b >> t; int n = r - l; if (!(a & 63)) { FOR(i, n) dat[l + i] &= p.dat[s + i]; } else { int hi = a & 63; int lo = 64 - hi; FOR(i, n) dat[l + i] &= (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo); } } // [L,R) に p を or void or_to_range(int L, int R, My_Bitset &p) { assert(p.N == R - L); int a = 0, b = p.N; while (L < R && (L & 63)) { dat[L >> 6] |= u64(p[a]) << (L & 63); ++a, ++L; } while (L < R && (R & 63)) { --b, --R; dat[R >> 6] |= u64(p[b]) << (R & 63); } // p[a:b] を [L:R] に int l = L >> 6, r = R >> 6; int s = a >> 6, t = b >> t; int n = r - l; if (!(a & 63)) { FOR(i, n) dat[l + i] |= p.dat[s + i]; } else { int hi = a & 63; int lo = 64 - hi; FOR(i, n) dat[l + i] |= (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo); } } string to_string() const { string S; FOR(i, N) S += '0' + (dat[i >> 6] >> (i & 63) & 1); return S; } // bitset に仕様を合わせる void set(int i) { (*this)[i] = 1; } void reset(int i) { (*this)[i] = 0; } void flip(int i) { (*this)[i].flip(); } void set() { fill(all(dat), u64(-1)); resize(N); } void reset() { fill(all(dat), 0); } int _Find_first() { return next(0); } int _Find_next(int p) { return next(p + 1); } }; #line 5 "main.cpp" void solve() { INT(N); VEC(int, A, 2 * N); FOR(i, 2 * N) A.eb(A[i]); /* 長さ N 以上の回文があるか 長さ N / N + 1 の回文があるか */ /* vc ng(7 * N); FOR(i, 3 * N) { FOR(j, i + 1, i + N + 1) { if (A[i] != -1 && A[j] != -1 && A[i] != A[j]) { ng[i + j] = 1; } } } int s = N - 1, t = 5 * N - 1; FOR(i, s, t) if (!ng[i]) return Yes(); No(); */ using BS = My_Bitset; BS ng(7 * N); BS other(4 * N); vvc pos(2 * N + 1); FOR(i, len(A)) { if (A[i] == -1) continue; pos[A[i]].eb(i); other[i] = 1; } FOR(x, 1, 2 * N + 1) { auto& I = pos[x]; for (auto& i: I) { other[i] = 0; } for (auto& i: I) { BS x = other.range(i + 1, i + N + 1); ng.or_to_range(2 * i + 1, 2 * i + N + 1, x); } for (auto& i: I) { other[i] = 1; } } int s = N - 1, t = 5 * N - 1; FOR(i, s, t) if (!ng[i]) return Yes(); No(); } signed main() { int T = 1; // INT(T); FOR(T) solve(); return 0; }