#include<bits/stdc++.h>
using namespace std;
#define I inline int
#define V inline void
#define ll long long int
#define LL long long int
#define isnum(ch) ('0'<=ch&&ch<='9')
#define FOR(i,a,b) for(int i=a;i<=b;i++)
#define ROF(i,a,b) for(int i=a;i>=b;i--)
#define gc (_op==_ed&&(_ed=(_op=_buf)+fread(_buf,1,100000,stdin),_op==_ed)?EOF:*_op++)
char _buf[100000],*_op(_buf),*_ed(_buf);
const int N=1<<18|1,mod=998244353;
V check(int&x){x-=mod,x+=x>>31&mod;}
I getint(){
	int _s=0;char _ch=gc;
	while(!isnum(_ch))_ch=gc;
	while(isnum(_ch))_s=_s*10+_ch-48,_ch=gc;
	return _s;
}
I Pow(ll t,int x){
	ll s=1;
	for(;x;x>>=1,t=t*t%mod)if(x&1)s=s*t%mod;
	return s;
}
int A[N], B[N], C[N];
LL fastpo(LL x, LL n, LL mod) {
	x %= mod;
	LL res = 1;
	while(n) {
		if(n % 2 == 1) {
			res = (res * x) % mod;
		}
		x = x * x % mod;
		n /= 2;
	}
	return res;
}
namespace poly{
	int lmt,w[N],r[N];
	V init(int n){
		int l=-1,wn;
		for(lmt=1;lmt<=n;)lmt<<=1,l++;
		FOR(i,0,lmt-1)r[i]=(r[i>>1]>>1)|((i&1)<<l);
		wn=Pow(3,mod>>++l),w[lmt>>1]=1;
		FOR(i,(lmt>>1)+1,lmt-1)w[i]=1ll*w[i-1]*wn%mod;
		ROF(i,(lmt>>1)-1,1)w[i]=w[i<<1];
	}
	V cl(int*a,int n){memset(a,0,n<<2);}
	I getLen(int n){return 1<<32-__builtin_clz(n);}
	V mul(int*a,int x,int n,int*b){while(n--)*b++=1ll**a++*x%mod;}
	V dot(int*a,int*b,int n,int*c){while(n--)*c++=1ll**a++**b++%mod;}
	V DFT(int*a,int l){
		static unsigned ll tmp[N];
		int u=__builtin_ctz(lmt/l),t;
		FOR(i,0,l-1)tmp[i]=a[r[i]>>u];
		for(int i=1;i^l;i<<=1)for(int j=0,d=i<<1;j^l;j+=d)FOR(k,0,i-1)
			t=tmp[i|j|k]*w[i|k]%mod,tmp[i|j|k]=tmp[j|k]+mod-t,tmp[j|k]+=t;
		FOR(i,0,l-1)a[i]=tmp[i]%mod;
	}
	V IDFT(int*a,int l){reverse(a+1,a+l),DFT(a,l),mul(a,mod-mod/l,l,a);}
	V Inv(const int*a,int n,int*b){
		static int A[N],B[N],tmp[N],d,l;
		tmp[0]=Pow(a[0],mod-2),cl(A,d),cl(B,d);
		for(d=1,l=2;d<n;d<<=1,l<<=1){
			copy(a,a+min(l,n),A),copy(tmp,tmp+d,B);
			DFT(A,l),DFT(B,l),dot(A,B,l,A),IDFT(A,l);
			cl(A,d),DFT(A,l),dot(A,B,l,A),IDFT(A,l);
			copy(A+d,A+l,tmp+d),mul(tmp+d,mod-1,d,tmp+d);
		}
		copy(tmp,tmp+n,b);
	}
	int*f[N],*g[N],bin[N<<5],*np(bin);
	V Mul(int*a,int*b,int n,int m,int*c){
		static int A[N],B[N],l;
		l=getLen(n+m-1),copy(a,a+n,A),copy(b,b+m,B);
		DFT(A,l),DFT(B,l),dot(A,B,l,A),IDFT(A,l);
		copy(A,A+n+m-1,c),cl(A,l),cl(B,l);
	}
	V eva_init(int p,int l,int r,int*a){
		g[p]=np,np+=r-l+2,f[p]=np,np+=r-l+2;
		if(l==r)return g[p][0]=1,check(g[p][1]=mod-a[l]);
		int lc=p<<1,rc=lc|1,mid=l+r>>1,len1=mid-l+2,len2=r-mid+1;
		eva_init(lc,l,mid,a),eva_init(rc,mid+1,r,a);
		Mul(g[lc],g[rc],len1,len2,g[p]);
	}
	V Mult(int*a,int*b,int n,int m,int*c){
		static int A[N],B[N],l;
		l=getLen(n),copy(a,a+n,A),reverse_copy(b,b+m,B);
		DFT(A,l),DFT(B,l),dot(A,B,l,A),IDFT(A,l);
		copy(A+m-1,A+n,c);
		cl(A,l),cl(B,l);
	}
	V eva_work(int p,int l,int r,int*a){
		if(l==r)return void(a[l]=f[p][0]);
		int lc=p<<1,rc=lc|1,mid=l+r>>1,len1=mid-l+2,len2=r-mid+1;
		Mult(f[p],g[rc],r-l+1,len2,f[lc]);
		eva_work(lc,l,mid,a);
		Mult(f[p],g[lc],r-l+1,len1,f[rc]);
		eva_work(rc,mid+1,r,a);
	}
	V eva(int*a,int*b,int n,int m,int*c){
		static int X[N],Y[N],l;
		eva_init(1,1,m,b),Inv(g[1],m+1,X);
		reverse(X,X+m+1),Mul(a,X,n,m+1,Y);
		copy(Y+n,Y+n+m,f[1]),eva_work(1,1,m,c);
		FOR(i,1,m)check(c[i]=1ll*c[i]*b[i]%mod+a[0]);
	}
	void dvcq(int * a, int le, int ri) {
		if(le == ri) {
		}else {
			int mid = (le + ri) / 2;
			dvcq(a, le, mid);
			dvcq(a, mid + 1, ri);
			memcpy(A, a + le, sizeof(int) * (mid - le + 1));
			A[mid - le + 1] = 1;
			memcpy(B, a + mid + 1, sizeof(int) * (ri - mid));
			B[ri - mid] = 1;
			Mul(A, B, mid - le + 2, ri - mid + 1, C);
			memcpy(a + le, C, sizeof(int) * (ri - le + 1));
		}
	}
}

int a[N], b[N], c[N], d[N], o[N], fac[N], invfac[N];
LL choose(int a, int b) {
	return fac[a] * (LL)invfac[a - b] % mod * invfac[b] % mod;
}
int main(){
	int n;
	poly::init(131072);
	scanf("%d", &n);
	for(int  i= 0; i <= n; i++) {
		fac[i] = i == 0 ? 1 : fac[i - 1] * (LL) i % mod;
	}
	invfac[n] = fastpo(fac[n], mod - 2, mod);
	for(int i = n - 1; i >= 0; i--) {
		invfac[i] = invfac[i + 1] * (LL)(i + 1) % mod;
	}
	int ans = 0;
	a[0] = 0;
	for(int i = 1; i <= n; i++){
		scanf("%d", &a[i]);
		ans = max(ans, min(a[i], n - i + 1));
		for(int j = a[i - 1] + 1; j <= a[i]; j++) {
			b[j] = n - i + 1;
		}
	}
	printf("%d ", ans);

		
	int ri = 0, le = 0;
	for(int i = 1; i <= n; i++) {
		if(a[i] > ans) {
			ri++;
		}
	}
	//printf("before\n");
	for(int i = 1; i <= ans; i++) {
		c[i] = b[i];
		//printf("%d ", c[i]);
	}
	poly::dvcq(c, 1, ans);
	//printf("\nAfter\n");
	//for(int i = 1; i <= ans; i++) {
	//	printf("%d ", c[i]);
	//}
	//printf("\n");
	c[ans + 1] = 1;

	for(int i = 1; i <= ri + 1; i++) {
		o[i] = (mod - i + 1) % mod;
	}
	poly::eva(c + 1, o, ans + 1, max(ans, ri + 1), d);
	LL res = 0;
	for(int i = 0; i <= ri; i++) {
		//printf("val[%d] = %d\n", i, d[i + 1]);
		res = res + d[i + 1] * (i % 2 ? -1 : 1) * choose(ri, i) % mod;
		res = (res + mod) % mod;
	}

	for(int i = 1; i <= n; i++) {
		if(b[i] > ans) {
			le++;
		}
	}
	//printf("before\n");
	for(int i = 1; i <= ans; i++) {
		c[i] = a[n - i + 1];
		//printf("%d ", c[i]);
	}
	//printf("\nAfter\n");
	poly::dvcq(c, 1, ans);
	//for(int i = 1; i <= ans; i++) {
	//	printf("%d ", c[i]);
	//}
	//printf("\n");
	c[ans + 1] = 1;
	for(int i = 1; i <= le + 1; i++) {
		o[i] = (mod - i + 1) % mod;
	}
	poly::eva(c + 1, o, ans + 1, max(ans, le + 1), d);
	for(int i = 0; i <= le; i++) {
		//printf("val[%d] = %d\n", i, d[i + 1]);
		res = res + d[i + 1] * (i % 2 ? -1 : 1) * choose(le, i) % mod;
		res = (res + mod) % mod;
	}
	res = (res - fac[ans] + mod) % mod;
	cout << res << endl;

}