#include #define FOR(i,a,b) for (int i=(a);i<(b);i++) #define FORR(i,a,b) for (int i=(a);i>=(b);i--) #define pb push_back #define pcnt __builtin_popcount #define show(x) cout<<#x<<" = "< pii; typedef vector vi; typedef vector vvi; typedef vector vpii; typedef set si; typedef pair pll; typedef vector vl; typedef vector vvl; typedef vector vpll; typedef set sl; templatestring join(vector&v) {stringstream s;FOR(i,0,sz(v))s<<' '<b)swap(a,b);for(;a>0;b%=a,swap(a,b));return b;} int modpow(ll a,ll n,int m){if(a==0)return a;ll p=1;for(;n>0;n/=2,a=a*a%m)if(n&1)p=p*a%m;return(int)p;} void dout(double d){printf("%.12f\n",d);} const int iinf = 1e9; const ll linf = 1e18; const int mod = 1e9+7; const double eps = 1e-10; typedef vector vd; typedef vector vvd; vvd V[65], EV; vd T[65], ET; void merge(vvd&va, vd&ta, vvd&vb, vd&tb, vvd&vc, vd&tc){ vvd vtmp; vd ttmp; vtmp.resize(6); FOR(i, 0, 6)vtmp[i].resize(6); ttmp.resize(6); FOR(i, 0, 6)FOR(j, 0, 6)FOR(k, 0, 6)vtmp[i][j] += va[i][k] * vb[k][j]; FOR(i, 0, 6)FOR(j, 0, 6)ttmp[i] += va[i][j] * tb[j]; FOR(i, 0, 6)tc[i] = ta[i] + ttmp[i]; FOR(i, 0, 6)FOR(j, 0, 6)vc[i][j] = vtmp[i][j]; } main(){ cin.tie(0); ios::sync_with_stdio(false); FOR(i, 0, 65){ V[i].resize(6); T[i].resize(6); FOR(j, 0, 6)V[i][j].resize(6); } EV.resize(6); FOR(i, 0, 6){ EV[i].resize(6); EV[i][i] = 1.0; } ET.resize(6); FOR(i, 0, 5)V[0][i][i+1] = 1.0; FOR(i, 0, 6)V[0][5][i] = 1.0/6; T[0][5] = 1.0; FOR(i, 1, 65)merge(V[i-1], T[i-1], V[i-1], T[i-1], V[i], T[i]); ll n, t; cin >> t; FOR(i, 0, t){ cin >> n; vvd v = EV; vd t = ET; int c = 0; while(n > 0){ if(n&1)merge(v, t, V[c], T[c], v, t); n /= 2; c++; } double dd = 1.0; FOR(i, 0, 5) dd -= v[5][i]; dout(t[5] / dd); } }