#include using namespace std; #if __has_include() #include using namespace atcoder; #endif using ll = long long; using ld = long double; using ull = unsigned long long; #define endl "\n" typedef pair Pii; #define REP(i, n) for (int i = 0; i < (n); ++i) #define REP3(i, m, n) for (int i = (m); (i) < int(n); ++ (i)) #define FOR(i,a,b) for(ll i=a;i<=(ll)(b);i++) #define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++) #define ALL(x) begin(x), end(x) #define PB push_back #define rrep(i,a,b) for(int i=a;i>=b;i--) #define fore(i,a) for(auto &i:a) #define all(s) (s).begin(),(s).end() #define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i) #define drep(i, n) drep2(i, n, 0) #define rever(vec) reverse(vec.begin(), vec.end()) #define sor(vec) sort(vec.begin(), vec.end()) #define fi first #define se second #define pb push_back #define P pair #define PQminll priority_queue, greater> #define PQmaxll priority_queue,less> #define PQminP priority_queue, greater

> #define PQmaxP priority_queue,less

> #define NP next_permutation typedef string::const_iterator State; class ParseError {}; //const ll mod = 1000000009; const ll mod = 998244353; //const ll mod = 1000000007; const ll inf = 4100000000000000000ll; const ld eps = ld(0.00000000000001); const long double pi = 3.141592653589793; templatevoid vcin(vector &n){for(int i=0;i>n[i];} templatevoid vcin(vector &n,vector &m){for(int i=0;i>n[i]>>m[i];} templatevoid vcout(vector &n){for(int i=0;ivoid vcin(vector> &n){for(int i=0;i>n[i][j];}}} templatevoid vcout(vector> &n){for(int i=0;ivoid print(T a){cout<auto min(const T& a){ return *min_element(all(a)); } templateauto max(const T& a){ return *max_element(all(a)); } templatevoid print(pair a){cout<bool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b void ifmin(T t,T u){if(t>u){cout<<-1< void ifmax(T t,T u){if(t>u){cout<<-1<>=1;v>>=1;}else if(eu&&!ev){u>>=1;}else if(!eu&&ev){v>>=1;}else if(u>=v){u=(u-v)>>1;}else{ll tmp=u;u=(v-u)>>1;v=tmp;}}return !u?v<>= 1; } return ret; } vector divisor(ll x){ vector ans; for(ll i = 1; i * i <= x; i++){ if(x % i == 0) {ans.push_back(i); if(i*i!=x){ ans.push_back(x / ans[i]);}}}sor(ans); return ans; } ll pop(ll x){return __builtin_popcountll(x);} ll poplong(ll x){ll y=-1;while(x){x/=2;y++;}return y;} void cincout() { ios::sync_with_stdio(false); std::cin.tie(nullptr); cout<< fixed << setprecision(20); } using mint = modint998244353; mint dp[105][105][105]; int main() { cincout(); ll n; cin>>n; vector a(105); assert(1<=n&&n<=100); for(int i=0;i>x; assert(0<=x&&x<=100); a[x]++; } ll mi=inf; for(int i=0;i<105;i++) if(a[i]) chmin(mi,ll(i)); dp[104][0][0]++; mint ans=0; //dp[i][j][k] -> i 以上確定 i-1 以下が j 個ずつ S のうち i 以上が k 個 for(int i=103;i>=0;i--){ //dp[i+1] -> dp[i] vector d(n); d[max(i-1,0)]=1; ll sum=0; for(int j=i-1;j>=1;j--){ d[j-1]=d[j]+(d[j]-min(a[j],d[j])); chmin(d[j-1],10000ll); sum+=a[j]-min(a[j],d[j]); } for(ll j=103;j>=0;j--){ for(int k=103;k>=0;k--){ if(dp[i+1][j][k].val()==0) continue; for(int l=103;l>=0;l--){ //l 個 T に i があるとする //min(j+l,a[i]) 個消える if(0<=j+j+l-min(j+l,a[i])&&j+j+l-min(j+l,a[i])<=103&&0<=k+a[i]-min(j+l,a[i])&&k+a[i]-min(j+l,a[i])<=103) dp[i][j+j+l-min(j+l,a[i])][k+a[i]-min(j+l,a[i])]+=dp[i+1][j][k]; if(i==0&&j+j+l-min(j+l,a[i])>0&&j+l<=a[0]+k) ans+=dp[i+1][j][k]; if((mi!=i||k+a[i]-min(j+l,a[i])>0)&&j+j+l-min(j+l,a[i])==0&&l>0&&k+a[i]-min(j+l,a[i])+1+sum>=d[0]-a[0]) ans+=dp[i+1][j][k]; } } } } cout<<(ans+1).val()<