## Character Encoding

#include<bits/stdc++.h>
#define mul(a,b,c) ((a)*(b)%(c))
#define inv(a,b) pow(a,(b)-2,b)
using namespace std;
typedef long long ll;
const ll N=1e5+7,M=998244353;
ll pow(ll a,ll b,ll m)
{
ll r=1;
for(a%=m; b; b>>=1,a=mul(a,a,m))
if(b&1)r=mul(r,a,m);
return r;
}
struct Factorial
{
vector<ll> fac,ifac;
ll M;
Factorial(int N,ll M):fac(N,1),ifac(N,1),M(M)
{
for(int i=1; i<N; ++i)fac[i]=mul(fac[i-1],i,M);
ifac[N-1]=inv(fac[N-1],M);
for(int i=N-1; i; --i)ifac[i-1]=mul(ifac[i],i,M);
}
ll c(int n,int m)
{
return mul(mul(fac[n],ifac[m],M),ifac[n-m],M);
}
} f(2*N,M);
int main()
{
int t,n,m,k,ans;
for(scanf("%d",&t); t--; printf("%d\n",ans))
{
scanf("%d%d%d",&n,&m,&k);
for(int i=ans=0; k+m-1-i*n>=m-1&&i<=m; ++i)
{
if(i%2)ans=(ans-mul(f.c(m,i),f.c(k+m-1-i*n,m-1),M)+M)%M;
else ans=(ans+mul(f.c(m,i),f.c(k+m-1-i*n,m-1),M))%M;
}
}
}


## Parentheses Matrix

#include<bits/stdc++.h>
using namespace std;
void printH(int h,int w)
{
for(int i=0; i<h; ++i,printf("\n"))
for(int j=0; j<w; ++j)
printf(i%2?")":"(");
}
void printW(int h,int w)
{
for(int i=0; i<h; ++i,printf("\n"))
for(int j=0; j<w; ++j)
printf(j%2?")":"(");
}
char s[255][255];
void PH(int h,int w)
{
for(int i=0; i<h; ++i)
for(int j=0; j<w; ++j)
s[i][j]=i%2?')':'(';
for(int i=1; i<h-2; i+=2)
for (int j=0; j<w/2; ++j)swap(s[i][j],s[i+1][j]);
for(int i=0; i<h; ++i,printf("\n"))
for (int j=0; j<w; ++j)printf("%c",s[i][j]);
}
void PW(int h,int w)
{
for(int i=0; i<h; ++i)
for(int j=0; j<w; ++j)
s[i][j]=j%2?')':'(';
for(int j=1; j<w-2; j+=2)
for (int i=0; i<h/2; ++i)swap(s[i][j],s[i][j+1]);
for(int i=0; i<h; ++i,printf("\n"))
for (int j=0; j<w; ++j)printf("%c",s[i][j]);
}
void cal1(int h,int w)
{
if(h>w)PW(h,w);
else PH(h,w);
}
void cal(int h,int w)
{
for(int i=0; i<h; ++i,printf("\n"))
for(int j=0; j<w; ++j)
printf(!i?"(":
i==h-1?")":
!j?"(":
j==w-1?")":
(i+j)%2?"(":")");
}
int main()
{
int t,h,w;
for(scanf("%d",&t); t--;)
{
scanf("%d%d",&h,&w);
if(h%2&&w%2)printW(h,w);
else if(h%2)printW(h,w);
else if(w%2)printH(h,w);
else if(h+w-min(h,w)/2-1>h+w-4)cal1(h,w);
else cal(h,w);
}
}


## Magic Square

#include<bits/stdc++.h>
using namespace std;
struct Matrix
{
char a[9][9];
void spin(int x,int y)
{
swap(a[x][y],a[x+1][y]),swap(a[x+1][y],a[x+1][y+1]),swap(a[x+1][y+1],a[x][y+1]);
}
} m;
int t,n;
int main()
{
for(scanf("%d",&t); t--;)
{
scanf("%d",&n);
for(int i=0; i<3; ++i)scanf("%s",&m.a[i]);
for(char s[9]; n--;)
{
scanf("%s",s);
for(int i=s[1]=='C'?1:3; i; --i)
m.spin(s[0]=='3'||s[0]=='4',s[0]=='2'||s[0]=='4');
}
for(int i=0; i<3; ++i)printf("%s\n",m.a[i]);
}
}


## Taotao Picks Apples

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;

const int maxn=200000+10;

struct query
{
int id,p,q;
}q[maxn];

bool cmp(query x,query y) {return x.p>y.p;}

int t,n,m,tr,br,cur;
int h[maxn],a[maxn],b[maxn],f[maxn],ans[maxn];
vector <int> k[maxn];
bool inans[maxn];

int getpos(int v)
{
int l=0,r=br,mid;
while (r-l>1)
{
mid=(l+r)/2;
if (h[b[mid]]>v) l=mid;
else r=mid;
}
return l;
}

int main()
{
scanf("%d",&t);
while (t--)
{
scanf("%d%d",&n,&m);
for (int i=1;i<=n;i++) scanf("%d",&h[i]);
for (int i=1;i<=m;i++)
{
scanf("%d%d",&q[i].p,&q[i].q);
q[i].id=i;
}
sort(q+1,q+m+1,cmp);
tr=1; cur=1; h[0]=1e9*2;
for (int i=n;i>=1;i--)
{
while ((tr>1)&&(h[a[tr-1]]<=h[i])) k[i].push_back(h[a[tr-1]]),tr--;
a[tr++]=i;
}
memset(inans,false,sizeof(inans));
for (int i=1;i<tr;i++) inans[a[i]]=true;
cur=0;
for (int i=1;i<=n;i++)
{
f[i]=cur;
if (i==a[tr-cur-1]) cur++;
}
br=1; cur=1;
for (int i=n;i>=1;i--)
{
while ((cur<=m)&&(q[cur].p==i))
{
if (q[cur].q>h[i])
{
if ((h[a[tr-f[i]]]>=q[cur].q)&&(i!=1)) ans[q[cur].id]=tr-1;
else
{
int g=getpos(q[cur].q);
//printf("??%d ",g);
ans[q[cur].id]=f[i]+g+1;
}
}
else if (q[cur].q<h[i])
{
if (!inans[i]) ans[q[cur].id]=tr-1;
else
{
int g1=upper_bound(k[i].begin(),k[i].end(),q[cur].q)-k[i].begin();
int g2=upper_bound(k[i].begin(),k[i].end(),h[a[tr-f[i]]])-k[i].begin();
if (i==1) g2=-1;
ans[q[cur].id]=tr-1+k[i].size()-max(g1,g2);
//  printf("? %d %d\n",g1,g2);
if ((q[cur].q<=h[a[tr-f[i]]])&&(i!=1)) ans[q[cur].id]--;
}
}
else ans[q[cur].id]=tr-1;
//  printf("! %d %d %d %d\n",q[cur].id,q[cur].p,q[cur].q,ans[q[cur].id]);
cur++;
}
while ((br>1)&&(h[b[br-1]]<=h[i])) br--;
b[br++]=i;
}
for (int i=1;i<=m;i++) printf("%d\n",ans[i]);
for (int i=1;i<=n;i++)
{
vector <int> x;
swap(k[i],x);
}
memset(ans,0,sizeof(ans));
}
return 0;
}