//Let's join Kaede Takagaki Fan Club !! #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include //#include //#include #include #include #include #include #include #include #include #include //#include //#include //#include //#include //#include //#include using namespace std; //using namespace atcoder; #define int long long //#define L __int128 typedef long long ll; typedef pair P; typedef pair P1; typedef pair P2; #define pu push #define pb push_back #define eb emplace_back #define mp make_pair #define eps 1e-7 #define INF 1000000000 #define a first #define b second #define fi first #define sc second #define rng(i,a,b) for(int i=(int)(a);i<(int)(b);i++) #define rep(i,x) for(int i=0;i=(int)(a);i--) #define per(i,b) gnr(i,0,b) #define repn(i,x) for(int i=1;i<=x;i++) #define SORT(x) sort(x.begin(),x.end()) #define ERASE(x) x.erase(unique(x.begin(),x.end()),x.end()) #define POSL(x,v) (lower_bound(x.begin(),x.end(),v)-x.begin()) #define POSU(x,v) (upper_bound(x.begin(),x.end(),v)-x.begin()) #define all(x) x.begin(),x.end() #define si(x) (int)(x.size()) #define pcnt(x) __builtin_popcountll(x) #define all(x) x.begin(),x.end() #ifdef LOCAL #define dmp(x) cerr<<__LINE__<<" "<<#x<<" "< bool chmax(t&a,u b){if(a bool chmin(t&a,u b){if(b using vc=vector; template ostream& operator<<(ostream& os,const pair& p){ return os<<"{"< ostream& operator<<(ostream& os,const vc& v){ os<<"{"; for(auto e:v)os<> 30)) * 0xbf58476d1ce4e5b9; x = (x ^ (x >> 27)) * 0x94d049bb133111eb; return x ^ (x >> 31); } size_t operator()(uint64_t x) const { static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count(); return splitmix64(x + FIXED_RANDOM); } //don't make x negative! size_t operator()(pair x)const{ return operator()(uint64_t(x.first)<<32|x.second); } }; //unordered_set -> dtype, null_type //unordered_map -> dtype(key), dtype(value) using namespace __gnu_pbds; template using hash_table=gp_hash_table; template void o(const T &a,bool space=false){ cout << a << (space?' ':'\n'); } //ios::sync_with_stdio(false); const ll mod = 998244353; //const ll mod = 1000000007; mt19937_64 mt(chrono::steady_clock::now().time_since_epoch().count()); struct mint{ ll v; mint(ll vv=0){s(vv%mod+mod);} mint& s(ll vv){ v=vv>=1; } return res; } mint inv()const{return pow(mod-2);} friend mint operator+(ll x,const mint&y){ return mint(x)+y; } friend mint operator-(ll x,const mint&y){ return mint(x)-y; } friend mint operator*(ll x,const mint&y){ return mint(x)*y; } friend mint operator/(ll x,const mint&y){ return mint(x)/y; } friend ostream& operator<<(ostream&os,const mint&m){ return os<>(istream&is,mint&m){ ll x;is>>x; m=mint(x); return is; } bool operator<(const mint&r)const{return v0){ if(n&1) res=res*x%_md; x=x*x%_md; n>>=1; } return res; } #define _sz 1 mint F[_sz],R[_sz]; void make(){ F[0] = 1; for(int i=1;i<_sz;i++) F[i] = F[i-1] * i; R[_sz-1] = F[_sz-1].pow(mod-2); for(int i=_sz-2;i>=0;i--) R[i] = R[i+1] * (i+1); } mint C(int a,int b){ if(b < 0 || a < b) return mint(); return F[a]*R[b]*R[a-b]; } using ld=long double; using vi=vc; using ull=unsigned long long; /*int dst(P p, P q){ return (p.a-q.a)*(p.a-q.a)+(p.b-q.b)*(p.b-q.b); }*/ /*template void add_inplace(t &a, t b){ if(a.size() < b.size()) swap(a, b); for(int i=0;i= mod) a[i] -= mod; } return ; }*/ template void ov(const vc&a){ if(a.empty()) return; rep(i, si(a)) cout << a[i] << (i+1==si(a)?'\n':' '); } //o(ans?"Yes":"No"); template using mat = vc>; template mat make_e(int n, int m, T v = (int)1){ matret(n, vc(m)); rep(i, min(n, m)) ret[i][i] = v; return ret; } template mat operator+(mat a, mat b){ assert(a.size() == b.size()); if(a.size()) assert(a[0].size() == b[0].size()); rep(i, a.size()) rep(j, a[0].size()){ a[i][j] += b[i][j]; if(a[i][j] >= mod) a[i][j] -= mod; } return a; } template mat operator-(mat a, mat b){ assert(a.size() == b.size()); if(a.size()) assert(a[0].size() == b[0].size()); rep(i, a.size()) rep(j, a[0].size()){ a[i][j] += mod - b[i][j]; if(a[i][j] >= mod) a[i][j] -= mod; } return a; } template mat operator*(mat a, mat b){ if(a.empty() || b.empty()) return mat(); int n = a.size(); int m = b[0].size(); int len = a[0].size(); assert(len == b.size()); matret(n); rep(i, n) ret[i] = vc(m); rep(i, n) rep(j, len) rep(k, m){ ll add = (ll)(a[i][j]) * b[j][k]; add %= mod; ret[i][k] += add; if(ret[i][k] >= mod) ret[i][k] -= mod; } return ret; } template vc operator*(mat a, vc b){ if(a.empty() || b.empty()) return vc(); assert(si(a[0]) == si(b)); vcret(si(a)); rep(i, si(a)){ rep(j, si(b)){ ll add = (ll)a[i][j] * b[j] % mod; ret[i] += add; if(ret[i] >= mod) ret[i] -= mod; } } return ret; } template mat modpow(mat a, int n){ if(a.empty()) return mat(); matret = make_e(a.size(), a[0].size(), (T)(1)); while(n){ if(n&1) ret = ret * a; a = a * a; n /= 2; } return ret; } template ll det(matm){ int n = m.size(); assert(n > 0 && m[0].size() == n); ll ret = 1; for(int j=0;j>bs; template vcAxB(matA, vcb){ int r = A.size(), c = A[0].size(); assert(b.size() == r); int nxt = 0, free = 0; vcret(c, 0); rep(j, c){ int pivot = -1; for(int i=nxt;ifix(c, 0); vctop(nxt); rep(i, nxt){ rep(j, c){ if(A[i][j] != 0){ top[i] = j; fix[j] = 1; ret[j] = b[i]; break; } } } //error for(int i=nxt;i(); //get basis /*vc>basis(free); int id = 0; rep(j, c){ if(fix[j] == 1) continue; vctmp(c, 0); tmp[j] = 1; for(int i=0;i matinv(matA){ int r = A.size(), c = A[0].size(); if(c == r){ rep(i, r){ A[i].resize(r+r, 0); rep(j, r) A[i][r+j] = (i == j); } c += r; } assert(c == r+r); rep(j, r){ int pivot = -1; for(int i=j;i(); } if(j != pivot){ rep(k, c) swap(A[j][k],A[pivot][k]); } ll rev = modpow(A[j][j],mod-2); for(int g=j;gret = make_e(r, r, 0LL); rep(i, r) rep(j, r){ assert(A[i][j] == (i==j)); ret[i][j] = A[i][r+j]; } return ret; } //B...bitset //T...int //F2 /64 template vcAxB(vcA, vcb){ int r = A.size(), c = A[0].size(); assert(b.size() == r); int nxt = 0; vcret(c); rep(j, c){ int pivot = -1; for(int i=nxt;ifix(c, 0); vctop(nxt); rep(i, nxt){ rep(j, c){ if(A[i][j] != 0){ top[i] = j; fix[j] = 1; ret[j] = b[i]; break; } } } //error for(int i=nxt;i(); return ret; } void solve(){ matM[10]; rep(i,10){ M[i] = make_e(120, 120, 0); } rep(now,10){ rep(m3, 3){ rep(m5, 5){ rep(eq, 2){ rep(isz, 2){ int id = m3*20 + m5*4 + eq*2 + isz; //id -> count rep(nxt, 10){ if(eq == 1 and now < nxt) continue; int nid = (m3*10+nxt)%3*20 + (m5*10+nxt)%5*4 + (eq == 1 and now == nxt)*2 + (isz == 1 and nxt == 0); M[now][nid][id] ++; if(isz == 1 and nxt == 0); else M[now][nid+60][id] ++; M[now][nid+60][id+60] ++; } } } } } } vi dp(120); //0,0,1,1 dp[3] = 1; int m;cin>>m; int sum = 0; vc

vec; rep(i,m){ int v; int len; cin>>v>>len; sum += len; vec.eb(v, len); //dp = (modpow(M[v],len)*dp); } dp = modpow(M[9],sum-1)*dp; auto get=[&](int t, int add)->mint{ //10^t+add / 15 int rem = modpow(10, t, 15) + add; rem %= 15; //10^t+add-rem / 15 int up = modpow(10, t) + add - rem; up *= modpow(15, mod-2); return mint(up%mod); }; auto get2=[&](int add)->mint{ //vec+add / 15 int now = 0; for(auto [v, len]:vec){ now = now * modpow(10, len, 15) % 15; //v * (10^len-1) / 9 int up = v * (modpow(10, len, 135)-1) % 135; up /= 9; now = (now+up)%15; } int rem = (now+add)%15; //vec+add-rem / 15 mint ret; for(auto [v, len]:vec){ ret = ret*modpow(10,len); ret += v*(modpow(10,len)-1)*modpow(9,mod-2); } ret += add-rem; ret /= mint(15); return ret; }; mint ans; rep(r,15){ //[10^(sum-1), vec] //[10^(sum-1)+15-r, vec+15-r] mint now = get2(15-r) - get(sum-1, 14-r); if(r == 0){ ans += now * 8; } else if(r%3 == 0 or r%5 == 0){ ans += now * 4; } else{ ans += now * (sum%mod); } } { rep(m3, 3){ rep(m5, 5){ rep(eq, 2){ rep(isz, 2){ int id = m3*20 + m5*4 + eq*2 + isz; if(m3 == 0 and m5 == 0){ ans += dp[id] * 8 % mod; } else if(m3 == 0 or m5 == 0){ ans += dp[id] * 4 % mod; } else{ ans += dp[id+60]; } } } } } } o(ans+mod-8); } signed main(){ cin.tie(0); ios::sync_with_stdio(0); cout<> t; while(t--) solve(); }