#include <iostream>
#include <algorithm>
#include <vector>
using namespace std;
const int mod=998244353,g=3;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> Poly;
int rev[600010],w[600010],maxn;
ll inv[200010];
Poly tmp[600010];
template<typename T>
void upd(int &a,T b){a=(a+b)%mod;}
ll power(ll a,int b)
{
	ll ans=1;
	for(;b;b>>=1,a=a*a%mod)
		if(b&1) ans=ans*a%mod;
	return ans;
}
void init(int len)
{
	int l=0;maxn=1;
	while(maxn<=len) maxn<<=1,l++;
	for(int i=0;i<maxn;i++) rev[i]=(rev[i>>1]>>1)|((i&1)<<(l-1));
	for(int i=1;i<maxn;i<<=1)
	{
		ll wm=power(g,(mod-1)/(i<<1));w[i]=1;
		for(int j=1;j<i;j++) w[i+j]=w[i+j-1]*wm%mod;
	}
}
void NTT(Poly &p,bool flag)
{
	static ull a[600010];
	p.resize(maxn);
	for(int i=0;i<maxn;i++) a[i]=p[rev[i]];
	for(int i=1;i<maxn;i<<=1)
		for(int j=0;j<maxn;j+=i<<1)
			for(int k=j;k<j+i;k++)
			{
				ull x=a[k],y=a[k+i]*w[i+k-j]%mod;
				a[k]=x+y;a[k+i]=x+mod-y;
			}
	if(flag) for(int i=0;i<maxn;i++) p[i]=a[i]%mod;
	else
	{
		reverse(a+1,a+maxn);
		int inv=power(maxn,mod-2);
		for(int i=0;i<maxn;i++) p[i]=a[i]%mod*inv%mod;
	}
}
Poly operator+(const Poly &a,const Poly &b)
{
	int n=a.size(),m=b.size();
	Poly ans(max(n,m));
	for(int i=0;i<n;i++) ans[i]=a[i];
	for(int i=0;i<m;i++) upd(ans[i],b[i]);
	return ans;
}
Poly operator-(const Poly &a,const Poly &b)
{
	int n=a.size(),m=b.size();
	Poly ans(max(n,m));
	for(int i=0;i<n;i++) ans[i]=a[i];
	for(int i=0;i<m;i++) upd(ans[i],mod-b[i]);
	return ans;
}
Poly operator*(Poly a,int k)
{
	for(int &i:a) i=(ll)i*k%mod;
	return a;
}
Poly mul(Poly a,Poly b,int sz=-1)
{
	int n=a.size(),m=b.size();
	if(sz<0) sz=n+m-1;
	init(n+m);
	NTT(a,1);NTT(b,1);
	for(int i=0;i<maxn;i++) a[i]=(ll)a[i]*b[i]%mod;
	NTT(a,0);a.resize(sz);
	return a;
}
Poly mulT(Poly a,Poly b,int sz=-1)
{
	int n=a.size(),m=b.size();
	if(sz<0) sz=n-m+1;
	a.resize(m+sz-1);
	reverse(b.begin(),b.end());
	init(m+sz-1);
	NTT(a,1);NTT(b,1);
	for(int i=0;i<maxn;i++) a[i]=(ll)a[i]*b[i]%mod;
	NTT(a,0);
	return Poly(a.begin()+m-1,a.begin()+m+sz-1);
}
Poly INV(const Poly &a,int n)
{
	if(n==1) return {(int)power(a[0],mod-2)};
	Poly b=INV(a,(n+1)/2),c(a.begin(),a.begin()+n),d=b;
	init(n);
	NTT(b,1);NTT(c,1);
	for(int i=0;i<maxn;i++) c[i]=(ll)b[i]*c[i]%mod;
	NTT(c,0);c.resize(n);fill(c.begin(),c.begin()+(n+1)/2,0);
	NTT(c,1);
	for(int i=0;i<maxn;i++) b[i]=(ll)b[i]*(mod-c[i])%mod;
	NTT(b,0);b.resize(n);move(d.begin(),d.end(),b.begin());
	return b;
}
Poly DER(const Poly &a,int sz=-1)
{
	int n=a.size();
	if(sz<0) sz=n-1;
	Poly ans(n-1);
	for(int i=1;i<n;i++) ans[i-1]=(ll)i*a[i]%mod;
	ans.resize(sz);
	return ans;
}
Poly INT(const Poly &a,int sz=-1)
{
	int n=a.size();
	if(sz<0) sz=n+1;
	Poly ans(n+1);
	for(int i=0;i<n;i++) ans[i+1]=inv[i+1]*a[i]%mod;
	ans.resize(sz);
	return ans;
}
Poly LN(const Poly &a,int n){return INT(mul(DER(a),INV(a,n),n),n);}
Poly EXP(const Poly &a,int n)
{
	if(n==1) return {1};
	Poly b=EXP(a,(n+1)/2),c(a.begin(),a.begin()+n),d=b;
	b.resize(n);c[0]++;c=c-LN(b,n);
	init(n);
	NTT(b,1);NTT(c,1);
	for(int i=0;i<maxn;i++) b[i]=(ll)b[i]*c[i]%mod;
	NTT(b,0);b.resize(n);move(d.begin(),d.end(),b.begin());
	return b;
}
Poly POW(const Poly &a,int k,int n)
{
	int st=0,sz=a.size();
	for(;!a[st] && st<sz;st++);
	if((ll)st*k>=n) return Poly(n);
	Poly b(a.begin()+st,a.end()),c(n);b.resize(n);
	int b0=b[0],iv=power(b0,mod-2),pw=power(b0,k);
	for(int i=0;i<n;i++) b[i]=(ll)b[i]*iv%mod;
	b=LN(b,n);
	for(int i=0;i<n;i++) b[i]=(ll)b[i]*k%mod;
	b=EXP(b,n);
	for(int i=0;i+st*k<n;i++) c[i+st*k]=(ll)b[i]*pw%mod;
	return c;
}
void Multi_prework(int rt,int l,int r,const Poly &x)
{
	if(l==r) return tmp[rt]=(Poly){1,mod-x[l]},void();
	int mid=(l+r)/2;
	Multi_prework(rt*2,l,mid,x);
	Multi_prework(rt*2+1,mid+1,r,x);
	tmp[rt]=mul(tmp[rt*2],tmp[rt*2+1]);
}
Poly MultiEval_solve(int rt,int l,int r,const Poly &P)
{
	if(l==r) return P;
	int mid=(l+r)/2;
	Poly L=MultiEval_solve(rt*2,l,mid,mulT(P,tmp[rt*2+1])),R=MultiEval_solve(rt*2+1,mid+1,r,mulT(P,tmp[rt*2]));
	return L.insert(L.end(),R.begin(),R.end()),L;
}
Poly MultiEval(const Poly &a,const Poly &x)
{
	int n=a.size(),m=x.size();
	Multi_prework(1,0,m-1,x);
	tmp[1].resize(n);
	return MultiEval_solve(1,0,m-1,mulT(a,INV(tmp[1],n),m));
}
Poly MultiInterpolation_solve(int rt,int l,int r,const Poly &y)
{
	reverse(tmp[rt].begin(),tmp[rt].end());
	if(l==r) return (Poly){y[l]};
	int mid=(l+r)/2;
	Poly L=MultiInterpolation_solve(rt*2,l,mid,y),R=MultiInterpolation_solve(rt*2+1,mid+1,r,y),M;
	init(r-l+1);M.resize(maxn);
	NTT(L,1);NTT(R,1);NTT(tmp[rt*2],1);NTT(tmp[rt*2+1],1);
	for(int i=0;i<maxn;i++) M[i]=((ll)L[i]*tmp[rt*2+1][i]+(ll)R[i]*tmp[rt*2][i])%mod;
	NTT(M,0);M.resize(r-l+1);
	return M;
}
Poly MultiInterpolation(const Poly &x,Poly y)
{
	int n=x.size();
	Multi_prework(1,0,n-1,x);
	Poly a=MultiEval_solve(1,0,n-1,mulT(DER(Poly(tmp[1].rbegin(),tmp[1].rend())),INV(tmp[1],n),n));
	for(int i=0;i<n;i++) y[i]=y[i]*power(a[i],mod-2)%mod;
	return MultiInterpolation_solve(1,0,n-1,y);
}
constexpr int N((1<<17)+10),p(998244353);
int a[N],n;
Poly solve(int c[],int l,int r)
{
	if(l==r) return {1,c[l]};
	int mid((l+r)>>1);
	return mul(solve(c,l,mid),solve(c,mid+1,r));
}
int main()
{
	std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr);
	init(N);
	std::cin>>n;int m(0);
	for(int i(1);i<=n;++i) std::cin>>a[i],m=std::max(m,std::min(a[i],n-i+1));
	std::cout<<m<<" ";
	static int fac[N],ifac[N],inv[N];
	::inv[1]=1;for(int i(2);i<200010;++i) ::inv[i]=(1ll*::inv[p%i]*(p-p/i)%p);
	inv[1]=1;for(int i(2);i<N;++i) inv[i]=1ll*(p-p/i)*inv[p%i]%p;
	ifac[0]=fac[0]=1;for(int i(1);i<N;++i) ifac[i]=1ll*ifac[i-1]*inv[i]%p,fac[i]=1ll*fac[i-1]*i%p;
	auto binom=[](int a,int b)->int{return 1ll*fac[a]*ifac[b]%p*ifac[a-b]%p;};
	auto slv=[](int m,int mx,int c[])->int
	{
		// std::cerr<<m<<" "<<mx<<std::endl;
		Poly K=solve(c,1,m);
		Poly ex(ifac,ifac+m+1);
		// for(int v:ex) std::cerr<<v<<" ";
		// std::cerr<<std::endl;
		Poly ex1(ex);ex1[0]=0;
		ex=POW(ex,m-mx,m+1);
		// for(int v:ex) std::cerr<<v<<" ";
		// std::cerr<<std::endl;
		Poly T=mul(POW(ex1,mx,m+1),ex);
		// for(int v:T) std::cerr<<v<<" ";
		// std::cerr<<std::endl;
		int ans(0);
		for(int i(0);i<=m;++i) ans=(ans+1ll*K[i]*T[m-i]%p*fac[m-i])%p;
		return ans;
	};
	int ans(0);
	{
		int mx(0);
		static int c[N];
		for(int i(1);i<=n-m;++i) mx=std::max(mx,a[i]);
		for(int i(n-m+1);i<=n;++i) c[i-(n-m)]=a[i]-m;
		ans=(ans+slv(m,mx,c))%p;
	}
	{
		int mx(0);
		static int c[N];
		for(int i(n-m+1);i<=n;++i) if(a[i]>m) mx=std::max(mx,n-i+1);
		for(int i(1);i<=n-m;++i) ++c[a[i]];
		for(int i(m);i;--i) c[i]+=c[i+1];
		ans=(ans+slv(m,mx,c))%p;
	}
	std::cout<<(ans-fac[m]+p)%p<<std::endl;
	return 0;
}