#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
#include<vector>
#include<queue>
#include<map>
#include<bitset>
#include<set>
#define N (410)
#define P (998244353)
#define M (10010)
#define inf (0x7f7f7f7f)
#define rg register int
#define Label puts("NAIVE")
#define spa print(' ')
#define ent print('\n')
#define rand() (((rand())<<(15))^(rand()))
#define file(s) freopen(s".in","r",stdin),freopen(s".out","w",stdout)
typedef long double ld;
typedef long long LL;
typedef unsigned long long ull;
using namespace std;
namespace fastIO1{
	inline char read(){
		static const int IN_LEN=1000000;
		static char buf[IN_LEN],*s,*t;
		return (s==t?t=(s=buf)+fread(buf,1,IN_LEN,stdin),(s==t?-1:*s++):*s++);
	}
	template<class T>
	inline void read(T &x){
		static bool iosig;
		static char c;
		for(iosig=false,c=read();!isdigit(c);c=read()){
			if(c=='-')iosig=true;
			if(c==-1)return;
		}
		for(x=0;isdigit(c);c=read())x=((x+(x<<2))<<1)+(c^'0');
		if(iosig)x=-x;
	}
	inline char readc(char &c){
		for(c=read();!isalpha(c)&&!isdigit(c);c=read())
		if(c==-1)return 0;
	}
	const int OUT_LEN = 10000000;
	char obuf[OUT_LEN],*ooh=obuf;
	inline void print(char c){
		if(ooh==obuf+OUT_LEN)fwrite(obuf,1,OUT_LEN,stdout),ooh=obuf;
		*ooh++=c;
	}
	template<class T>
	inline void print(T x){
		static int buf[30],cnt;
		if(x==0)print('0');
		else{
			if(x<0)print('-'),x=-x;
			for(cnt=0;x;x/=10)buf[++cnt]=x%10+48;
			while(cnt)print((char)buf[cnt--]);
		}
	}
	inline void flush(){fwrite(obuf,1,ooh-obuf,stdout);}
}
namespace fastIO2{
	template<class T>
	inline void read(T &x){
		static bool iosig;
		static char c;
		for(iosig=false,c=getchar();!isdigit(c);c=getchar()){
			if(c=='-')iosig=true;
			if(c==-1)return;
		}
		for(x=0;isdigit(c);c=getchar())x=((x+(x<<2))<<1)+(c^'0');
		if(iosig)x=-x;
	}
}
using namespace fastIO1;
int n,id,H[N],f[M][N],g[M][N],len[M];
int tf[N],tg[N],C[N][N],pw[N];
void add(int &x,int y){
	x=x+y>P?x+y-P:x+y;
}
void init(){
	pw[0]=C[0][0]=1;
	for(int i=1;i<=400;i++)add(pw[i]=pw[i-1],pw[i-1]);
	for(int i=1;i<=400;i++){
		C[i][0]=1;
		for(int j=1;j<=i;j++)
		C[i][j]=(C[i-1][j]+C[i-1][j-1])%P;
	}
}
void update(int t,int x){
	for(int i=0;i<=len[t]+len[x];i++)tf[i]=tg[i]=0;
	for(int i=0;i<=len[t];i++)
	for(int j=0;j<=len[x];j++){
		add(tf[i+j],1ll*f[t][i]*f[x][j]%P);
		add(tg[i+j],1ll*g[t][i]*g[x][j]%P);
	}
	len[t]+=len[x];
	for(int i=0;i<=len[t];i++)f[t][i]=tf[i],g[t][i]=tg[i];
}
int solve(int L,int R,int lst){
	if(L>R)return 0; int mid=L,nw=++id;
	for(int i=L;i<=R;i++)if(H[i]<H[mid])mid=i;
	int lc=solve(L,mid-1,H[mid]),rc=solve(mid+1,R,H[mid]);
	len[nw]=f[nw][0]=g[nw][0]=1; 
	if(lc)update(nw,lc); if(rc)update(nw,rc);
	int l=len[nw];
	for(int i=1;i<=H[mid]-lst;i++){
		for(int j=0;j<=l;j++)tf[j]=tg[j]=0;
		if(i==1){
			int p=0;
			for(int j=L;j<=R;j++)if(H[j]==H[mid])p++;
			for(int j=0;j<=l-p;j++){
				add(tf[j+p],1ll*(pw[j]-1)*f[nw][j]%P);
				add(tg[j],1ll*(pw[j]-1)*g[nw][j]%P);
				add(tf[j],g[nw][j]),add(tg[j],g[nw][j]);
				for(int a=0;a+j<=l-p;a++)
				for(int b=0;b<=p;b++)
				if(a|b){
					int tmp=1ll*C[l-j-p][a]*C[p][b]%P*pw[j]%P;
					add(tf[j+a+p],1ll*tmp*f[nw][j]%P);
					add(tg[j+a+b],1ll*tmp*g[nw][j]%P);
				}
			}
		}
		else{
			for(int j=0;j<=l;j++){
				add(tf[j],1ll*(pw[j]-1)*f[nw][j]%P);
				add(tg[j],1ll*(pw[j]-1)*g[nw][j]%P);
				add(tf[j],g[nw][j]),add(tg[j],g[nw][j]);
				for(int k=1;j+k<=l;k++){
					int tmp=1ll*C[l-j][k]*pw[j]%P;
					add(tf[j+k],1ll*tmp*f[nw][j]%P);
					add(tg[j+k],1ll*tmp*g[nw][j]%P);
				}
			}
		}
		for(int j=0;j<=l;j++)f[nw][j]=tf[j],g[nw][j]=tg[j];
	}
	return nw;
}
int main(){
	read(n);
	for(int i=1;i<=n;i++)read(H[i]);
	init(); int rt=solve(1,n,0); printf("%d\n",f[rt][n]);
} 
### Prompt

Construct a Cpp code solution to the problem outlined:

Let us consider a grid of squares with N rows and N columns. Arbok has cut out some part of the grid so that, for each i = 1, 2, \ldots, N, the bottommost h_i squares are remaining in the i-th column from the left. Now, he wants to place rooks into some of the remaining squares.

A rook is a chess piece that occupies one square and can move horizontally or vertically, through any number of unoccupied squares. A rook can not move through squares that have been cut out by Arbok.

Let's say that a square is covered if it either contains a rook, or a rook can be moved to this square in one move.

Find the number of ways to place rooks into some of the remaining squares so that every remaining square is covered, modulo 998244353.

Constraints

* 1 \leq N \leq 400
* 1 \leq h_i \leq N
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N
h_1 h_2 ... h_N


Output

Print the number of ways to place rooks into some of the remaining squares so that every remaining square is covered, modulo 998244353.

Examples

Input

2
2 2


Output

11


Input

3
2 1 2


Output

17


Input

4
1 2 4 1


Output

201


Input

10
4 7 4 8 4 6 8 2 3 6


Output

263244071

### Response

```cpp
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
#include<vector>
#include<queue>
#include<map>
#include<bitset>
#include<set>
#define N (410)
#define P (998244353)
#define M (10010)
#define inf (0x7f7f7f7f)
#define rg register int
#define Label puts("NAIVE")
#define spa print(' ')
#define ent print('\n')
#define rand() (((rand())<<(15))^(rand()))
#define file(s) freopen(s".in","r",stdin),freopen(s".out","w",stdout)
typedef long double ld;
typedef long long LL;
typedef unsigned long long ull;
using namespace std;
namespace fastIO1{
	inline char read(){
		static const int IN_LEN=1000000;
		static char buf[IN_LEN],*s,*t;
		return (s==t?t=(s=buf)+fread(buf,1,IN_LEN,stdin),(s==t?-1:*s++):*s++);
	}
	template<class T>
	inline void read(T &x){
		static bool iosig;
		static char c;
		for(iosig=false,c=read();!isdigit(c);c=read()){
			if(c=='-')iosig=true;
			if(c==-1)return;
		}
		for(x=0;isdigit(c);c=read())x=((x+(x<<2))<<1)+(c^'0');
		if(iosig)x=-x;
	}
	inline char readc(char &c){
		for(c=read();!isalpha(c)&&!isdigit(c);c=read())
		if(c==-1)return 0;
	}
	const int OUT_LEN = 10000000;
	char obuf[OUT_LEN],*ooh=obuf;
	inline void print(char c){
		if(ooh==obuf+OUT_LEN)fwrite(obuf,1,OUT_LEN,stdout),ooh=obuf;
		*ooh++=c;
	}
	template<class T>
	inline void print(T x){
		static int buf[30],cnt;
		if(x==0)print('0');
		else{
			if(x<0)print('-'),x=-x;
			for(cnt=0;x;x/=10)buf[++cnt]=x%10+48;
			while(cnt)print((char)buf[cnt--]);
		}
	}
	inline void flush(){fwrite(obuf,1,ooh-obuf,stdout);}
}
namespace fastIO2{
	template<class T>
	inline void read(T &x){
		static bool iosig;
		static char c;
		for(iosig=false,c=getchar();!isdigit(c);c=getchar()){
			if(c=='-')iosig=true;
			if(c==-1)return;
		}
		for(x=0;isdigit(c);c=getchar())x=((x+(x<<2))<<1)+(c^'0');
		if(iosig)x=-x;
	}
}
using namespace fastIO1;
int n,id,H[N],f[M][N],g[M][N],len[M];
int tf[N],tg[N],C[N][N],pw[N];
void add(int &x,int y){
	x=x+y>P?x+y-P:x+y;
}
void init(){
	pw[0]=C[0][0]=1;
	for(int i=1;i<=400;i++)add(pw[i]=pw[i-1],pw[i-1]);
	for(int i=1;i<=400;i++){
		C[i][0]=1;
		for(int j=1;j<=i;j++)
		C[i][j]=(C[i-1][j]+C[i-1][j-1])%P;
	}
}
void update(int t,int x){
	for(int i=0;i<=len[t]+len[x];i++)tf[i]=tg[i]=0;
	for(int i=0;i<=len[t];i++)
	for(int j=0;j<=len[x];j++){
		add(tf[i+j],1ll*f[t][i]*f[x][j]%P);
		add(tg[i+j],1ll*g[t][i]*g[x][j]%P);
	}
	len[t]+=len[x];
	for(int i=0;i<=len[t];i++)f[t][i]=tf[i],g[t][i]=tg[i];
}
int solve(int L,int R,int lst){
	if(L>R)return 0; int mid=L,nw=++id;
	for(int i=L;i<=R;i++)if(H[i]<H[mid])mid=i;
	int lc=solve(L,mid-1,H[mid]),rc=solve(mid+1,R,H[mid]);
	len[nw]=f[nw][0]=g[nw][0]=1; 
	if(lc)update(nw,lc); if(rc)update(nw,rc);
	int l=len[nw];
	for(int i=1;i<=H[mid]-lst;i++){
		for(int j=0;j<=l;j++)tf[j]=tg[j]=0;
		if(i==1){
			int p=0;
			for(int j=L;j<=R;j++)if(H[j]==H[mid])p++;
			for(int j=0;j<=l-p;j++){
				add(tf[j+p],1ll*(pw[j]-1)*f[nw][j]%P);
				add(tg[j],1ll*(pw[j]-1)*g[nw][j]%P);
				add(tf[j],g[nw][j]),add(tg[j],g[nw][j]);
				for(int a=0;a+j<=l-p;a++)
				for(int b=0;b<=p;b++)
				if(a|b){
					int tmp=1ll*C[l-j-p][a]*C[p][b]%P*pw[j]%P;
					add(tf[j+a+p],1ll*tmp*f[nw][j]%P);
					add(tg[j+a+b],1ll*tmp*g[nw][j]%P);
				}
			}
		}
		else{
			for(int j=0;j<=l;j++){
				add(tf[j],1ll*(pw[j]-1)*f[nw][j]%P);
				add(tg[j],1ll*(pw[j]-1)*g[nw][j]%P);
				add(tf[j],g[nw][j]),add(tg[j],g[nw][j]);
				for(int k=1;j+k<=l;k++){
					int tmp=1ll*C[l-j][k]*pw[j]%P;
					add(tf[j+k],1ll*tmp*f[nw][j]%P);
					add(tg[j+k],1ll*tmp*g[nw][j]%P);
				}
			}
		}
		for(int j=0;j<=l;j++)f[nw][j]=tf[j],g[nw][j]=tg[j];
	}
	return nw;
}
int main(){
	read(n);
	for(int i=1;i<=n;i++)read(H[i]);
	init(); int rt=solve(1,n,0); printf("%d\n",f[rt][n]);
} 
```