#include using namespace std; const long double pi = acos(-1.0); alignas(64) complex pw[263168]; void fft(int d, vector > &v) { // d = dimensions (i.e. size(v) = 2^d) if(d == 0) return; int n = (1 << d); for(int i = 0, j = 1; j < n - 1; ++j) { for(int k = n >> 1; k > (i ^= k); k >>= 1); if(i < j) swap(v[i], v[j]); } complex t; for(int i = 0; i < d; ++i) { for(int j = 0; j < n; j += 2 << i) { for(int k = j; k < (j | (1 << i)); ++k) { t = v[k | (1 << i)] * pw[(k - j) | (1 << i)]; v[k | (1 << i)] = v[k] - t; v[k] += t; } } } } void fft_inverse(int d, vector > &v) { // d = dimensions (i.e. size(v) = 2^d) if(d == 0) return; int n = (1 << d); for(int i = 0, j = 1; j < n - 1; ++j) { for(int k = n >> 1; k > (i ^= k); k >>= 1); if(i < j) swap(v[i], v[j]); } complex t; for(int i = 0; i < d; ++i) { for(int j = 0; j < n; j += 2 << i) { t = v[j | (1 << i)]; v[j | (1 << i)] = v[j] - t; v[j] += t; for(int k = j + 1; k < (j | (1 << i)); ++k) { t = v[k | (1 << i)] * pw[(2 << i) - (k - j)]; v[k | (1 << i)] = v[k] + t; v[k] -= t; } } } for(int i = 0; i < n; ++i) { v[i] /= n; } } vector convolve(int n, const vector& va, const vector& vb) { int d = 0; while((1 << d) < 2 * n) ++d; for(int i = 0; i < d; ++i) { complex r = polar(1.0L, pi / (1 << i)); pw[1 << i] = 1.0; for(int j = (1 << i) + 1; j < 2 << i; ++j) { pw[j] = pw[j - 1] * r; } } vector > a(1 << d), b(1 << d); for(int i = 0; i < n; ++i) { a[i] = va[i]; b[i] = vb[i]; } fft(d, a); fft(d, b); for(int i = 0; i < 1 << d; ++i) { a[i] *= b[i]; } fft_inverse(d, a); vector res(2 * n - 1); for (int i = 0; i <= 2 * n - 2; i++) { res[i] = a[i].real(); } return res; } int main() { cin.tie(0); ios_base::sync_with_stdio(false); int N; cin >> N; vector A(2 * N); for (int i = 0; i < 2 * N; i++) { cin >> A[i]; if (A[i] != -1) { A[i] -= 1; } } mt19937_64 mt(1); uniform_real_distribution p(1.0, 2.0); vector g(2 * N); for (int i = 0; i < 2 * N; i++) { g[i] = p(mt); } vector sa(2 * N), sb(2 * N); for (int i = 0; i < 2 * N; i++) { if (A[i] != -1) { sa[i] = g[A[i]]; sb[i] = 1.0L / g[A[i]]; } } vector res = convolve(2 * N, sa, sb); res.resize(4 * N); bool ans = false; for (int i = 0; i < 2 * N; i++) { long double z = res[i] + res[i + 2 * N]; long double f = round(z); if (abs(z - f) < 1.0e-8L) { ans = true; } } cout << (ans ? "Yes" : "No") << endl; return 0; }