#define ATCODER #define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ld = long double; using pll = pair; using pdd = pair; //template using pq = priority_queue, greater>; #define FOR(i, a, b) for(ll i=(a); i<(b);i++) #define REP(i, n) for(ll i=0; i<(n);i++) #define ROF(i, a, b) for(ll i=(b-1); i>=(a);i--) #define PER(i, n) for(ll i=n-1; i>=0;i--) #define REPREP(i,j,a,b) for(ll i=0;i > #define VV2(type,n,m,val) vector< vector > val;val.resize(n);for(ll i;i #define VEC(type,n,val) vector val;val.resize(n) #define VL vector #define VVL vector< vector > #define VP vector< pair > #define SZ size() #define all(i) begin(i),end(i) #define SORT(i) sort(all(i)) #define BITI(i) (1<>i) & 1) != 0) #define ALLBIT(n) (ll(1)<v?v:n #define MP(a,b) make_pair(a,b) #define DET2(x1,y1,x2,y2) x1*y2-x2*y1 #define DET3(x1,y1,z1,x2,y2,z2,x3,y3,z3) x1*y2*z3+x2*y3*z1+x3*y1*z2-z1*y2*x3-z2*y3*x1-z3*y1*x2 #define INC(a) for(auto& v:a)v++; #define DEC(a) for(auto& v:a)v--; #define SQU(x) (x)*(x) #define L0 ll(0) #ifdef ATCODER #include using namespace atcoder; using mint = modint1000000007; using mint2 = modint998244353; #endif template vector read(size_t n) { vector ts(n); for (size_t i = 0; i < n; i++) cin >> ts[i]; return ts; } template void read_tuple_impl(TV&) {} template void read_tuple_impl(TV& ts) { get(ts).emplace_back(*(istream_iterator(cin))); read_tuple_impl(ts); } template decltype(auto) read_tuple(size_t n) { tuple...> ts; for (size_t i = 0; i < n; i++) read_tuple_impl(ts); return ts; } using val = ll; using func = ll; val op(val a, val b) { return a + b; } val e() { return 0; } val mp(func f, val a) { if (f == -1) return a; return f; } func comp(func f, func g) { if (f == -1) return g; return f; } func id() { return -1; } ll di[4] = { 1,0,-1,0 }; ll dj[4] = { 0,1,0,-1 }; //ll di[4] = { -1,-1,1,1 }; //ll dj[4] = { -1,1,-1,1 }; ll di8[8] = { 0,-1,-1,-1,0,1,1,1 }; ll dj8[8] = { -1,-1,0,1,1,1,0,-1 }; ll n; VL a; vector rev(vector& f, ll mod) { vector res = { mint2(1) / f[0] }; ll t = 1; vector ff; while (t < mod) { t *= 2; while (ff.size() < t && ff.size() < f.size()) { ff.push_back(f[ff.size()]); } auto m = convolution(res, res); m = convolution(m, ff); vector nres(t); REP(i, t) { if (i < res.size()) nres[i] += 2 * res[i]; if (i < m.size()) nres[i] += -m[i]; } res = nres; } return res; } vector div(vector& f, vector& g) { auto rf = f; auto rg = g; reverse(all(rf)); reverse(all(rg)); auto rv = rev(rg, f.size() - g.size() + 1); while (rf.size() > f.size() - g.size() + 1) rf.pop_back(); while (rv.size() > f.size() - g.size() + 1) rv.pop_back(); auto q = convolution(rf, rv); while (q.size() > f.size() - g.size() + 1) q.pop_back(); reverse(all(q)); auto gq = convolution(g, q); auto res = f; REP(i, res.size()) { if (i < gq.size()) { res[i] -= gq[i]; } } while (res.back() == 0 && res.size() > 1) { res.pop_back(); } return res; } mint2 solve3(ll l1, ll l2, ll d) { if (d <= 60) { mint2 res = 1; REP(i, d) { REP(j, d) { res *= a[l1 + i] - a[l2 + j]; } } return res; } ll c = 1; while (c < d) { c *= 2; } VL a1(d), a2(d); REP(i, d) { a1[i] = a[l1 + i]; a2[i] = a[l2 + i]; } vector> f1(c * 2); vector> f2(c * 2); FOR(i, c, c * 2) { if (i < c + d) { f1[i].assign(2, -1); f1[i][0] = a1[i - c]; f2[i].assign(2, -1); f2[i][0] = a2[i - c]; } else { f1[i].assign(1, 1); f2[i].assign(1, 1); } } PER(i, c) { f1[i] = convolution(f1[i * 2], f1[i * 2 + 1]); f2[i] = convolution(f2[i * 2], f2[i * 2 + 1]); } f1[1] = div(f1[1], f2[1]); FOR(i, 2, 2 * c) { auto& p = f1[i / 2]; if (f2[i].size() != 1) f1[i] = div(p, f2[i]); } mint2 res = 1; FOR(i, c, 2 * c) { res *= f1[i][0]; } return res; } mint2 solve2(ll l, ll r) { if (l >= r - 1) return 1; mint2 res = 1; ll d = (r - l) / 2; res *= solve3(l, r - d, d); res *= solve2(l, r - d); res *= solve2(l + d, r); return res; } void solve() { //ifstream file("case.txt"); // ファイルを開く //streambuf* cinbuf = cin.rdbuf(); //cin.rdbuf(file.rdbuf()); cin >> n; a = read(n); mint2 ans = 1; cout << solve2(0, n).val(); } int main() { ll t = 1; //cin >> t; while (t--) { solve(); } return 0; }