#include using namespace std; typedef signed long long ll; #define _P(...) (void)printf(__VA_ARGS__) #define FOR(x,to) for(x=0;x<(to);x++) #define FORR(x,arr) for(auto& x:arr) #define FORR2(x,y,arr) for(auto& [x,y]:arr) #define ALL(a) (a.begin()),(a.end()) #define ZERO(a) memset(a,0,sizeof(a)) #define MINUS(a) memset(a,0xff,sizeof(a)) template bool chmax(T &a, const T &b) { if(a bool chmin(T &a, const T &b) { if(a>b){a=b;return 1;}return 0;} //------------------------------------------------------- ll N; const ll mo=998244353; ll p10[20]; const int MAT=3; struct Mat { ll v[MAT][MAT]; Mat(){ZERO(v);};}; Mat mulmat(Mat& a,Mat& b,int n=MAT) { ll mo2=4*mo*mo; int x,y,z; Mat r; FOR(x,n) FOR(y,n) r.v[x][y]=0; FOR(x,n) FOR(z,n) FOR(y,n) { r.v[x][y] += a.v[x][z]*b.v[z][y]; if(r.v[x][y]>mo2) r.v[x][y] -= mo2; } FOR(x,n) FOR(y,n) r.v[x][y]%=mo; return r; } Mat powmat(ll p,Mat a,int n=MAT) { int i,x,y; Mat r; FOR(x,n) FOR(y,n) r.v[x][y]=0; FOR(i,n) r.v[i][i]=1; while(p) { if(p%2) r=mulmat(r,a,n); a=mulmat(a,a,n); p>>=1; } return r; } void solve() { int i,j,k,l,r,x,y; string s; cin>>N; p10[0]=1; FOR(i,19) p10[i+1]=p10[i]*10; ll ret=0; ll dig=1; for(int d=1;p10[d-1]<=N;d++) { ll p=p10[d]%mo; //桁数 ll L=p10[d-1]; ll R=min(p10[d],N+1); FOR(i,50) { if(L==R) break; if(i>=24&&(R-L)%24==0) break; ret=(ret*dig%mo*p%mo+L%mo*dig+ret)%mo; dig=dig*p%mo*dig%mo; L++; } if(L==R) continue; Mat A; A.v[0][0]=A.v[1][1]=A.v[2][2]=1; ll v=dig; FOR(i,24) { Mat B; B.v[0][0]=(dig*p+1)%mo; B.v[0][1]=dig; B.v[1][1]=B.v[1][2]=B.v[2][2]=1; A=mulmat(B,A); dig=dig*p%mo*dig%mo; } A=powmat((R-L)/24,A); ret=(ret*A.v[0][0]+L%mo*A.v[0][1]+A.v[0][2])%mo; } cout<