#include #include using namespace std; using namespace atcoder; //using mint = modint1000000007; //const int mod = 1000000007; using mint = modint998244353; const int mod = 998244353; //const int INF = 1e9; //const long long LINF = 1e18; #define rep(i, n) for (int i = 0; i < (n); ++i) #define rep2(i,l,r)for(int i=(l);i<(r);++i) #define rrep(i, n) for (int i = (n-1); i >= 0; --i) #define rrep2(i,l,r)for(int i=(r-1);i>=(l);--i) #define all(x) (x).begin(),(x).end() #define allR(x) (x).rbegin(),(x).rend() #define endl "\n" #define P pair template inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; } // combination mod prime // https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619 struct combination { std::vector fact, ifact; combination(int n) :fact(n + 1), ifact(n + 1) { assert(n < mod); fact[0] = 1; for (int i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i; ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) ifact[i - 1] = ifact[i] * i; } mint operator()(int n, int k) { return com(n, k); } mint com(int n, int k) { //負の二項係数を考慮する場合にコメントアウトを外す //if (n < 0) return com(-n, k) * (k % 2 ? -1 : 1); if (k < 0 || k > n) return 0; return fact[n] * ifact[k] * ifact[n - k]; } mint comsub(long long n, long long k) { if (n - k < k) k = n - k; assert(k < (int)fact.size()); mint val = ifact[k]; for (int i = 0; i < k; ++i) val *= n - i; return val; } template ...>, std::nullptr_t> = nullptr> mint polynom(const int n, const Ms & ...ms) { mint res = fact[n]; int sum = 0; for (int m : { ms... }) { if (m < 0 or m > n) return 0; res *= ifact[m]; sum += m; } if (sum > n)return 0; res *= ifact[n - sum]; return res; } mint div(int x) { if (x >= (int)fact.size())return mint(x).inv(); return fact[x - 1] * ifact[x]; } mint inv(int n, int k) { //if (n < 0) return inv(-n, k) * (k % 2 ? -1 : 1); if (k < 0 || k > n) return 0; return ifact[n] * fact[k] * fact[n - k]; } mint p(int n, int k) { return fact[n] * ifact[n - k]; } }c(2000006); int f(const vector &v) { int now = 0; int ret = 0; for (auto e : v) { if (0 == e)ret += now; else now++; } return ret; } // 01文字列(数列から単調増加列に変換する) // 0:x++,1:y++ // ex:10100->[1,2,2] std::vector exchange01(const std::vector&v) { int now = 0; std::vectorret; for (auto e : v) { if (0 == e)ret.push_back(now); else now++; } return ret; } // 単調増加列に対して標準盤を数える // O(n^2) mint hookLengthFormula(const std::vector&v) { if (v.empty())return 1; int sum = 0; for (auto e : v)sum += e; mint p = 1; for (int i = 1; i <= sum; ++i)p *= i; mint q = 1; std::vectorcnt(v.back() + 1); for (int i = 0; i < (int)v.size(); ++i) { for (int j = 1; j <= v[i]; ++j) { int tmp = cnt[j] + v[i] - j + 1; q *= tmp; cnt[j]++; } } return p * q.inv(); } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int n; cin >> n; vectora(n); rep(i, n)cin >> a[i]; int sum = 0; rep(i, n)sum += a[i]; vectorstr01; rep(i, n) { int x = 0 == i ? a[i] : a[i] - a[i - 1]; rep(j, x)str01.push_back(1); str01.push_back(0); } vectorstr01A, str01B; rep(i, str01.size()) { if (i % 2 == 0)str01A.push_back(str01[i]); else str01B.push_back(str01[i]); } int sumA = f(str01A), sumB = f(str01B); if ((sumA + sumB) * 2 != sum) { cout << 0 << endl; return 0; } mint ans = c(sumA + sumB, sumA); ans *= hookLengthFormula(exchange01(str01A)); ans *= hookLengthFormula(exchange01(str01B)); cout << ans.val() << endl; return 0; }