#pragma GCC optimize ("Ofast") #include using namespace std; inline int my_getchar_unlocked(){ static char buf[1048576]; static int s = 1048576; static int e = 1048576; if(s == e && e == 1048576){ e = fread_unlocked(buf, 1, 1048576, stdin); s = 0; } if(s == e){ return EOF; } return buf[s++]; } inline void rd(int &x){ int k; int m=0; x=0; for(;;){ k = my_getchar_unlocked(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = my_getchar_unlocked(); if(k<'0'||k>'9'){ break; } x=x*10+k-'0'; } if(m){ x=-x; } } struct MY_WRITER{ char buf[1048576]; int s; int e; MY_WRITER(){ s = 0; e = 1048576; } ~MY_WRITER(){ if(s){ fwrite_unlocked(buf, 1, s, stdout); } } } ; MY_WRITER MY_WRITER_VAR; void my_putchar_unlocked(int a){ if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){ fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout); MY_WRITER_VAR.s = 0; } MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a; } inline void wt_L(char a){ my_putchar_unlocked(a); } int WRITER_DOUBLE_DIGIT = 15; inline int writerDigit_double(){ return WRITER_DOUBLE_DIGIT; } inline void writerDigit_double(int d){ WRITER_DOUBLE_DIGIT = d; } inline void wt_L(double x){ const int d = WRITER_DOUBLE_DIGIT; int k; int r; double v; if(x!=x || (x==x+1 && x==2*x)){ my_putchar_unlocked('E'); my_putchar_unlocked('r'); my_putchar_unlocked('r'); return; } if(x < 0){ my_putchar_unlocked('-'); x = -x; } x += 0.5 * pow(0.1, d); r = 0; v = 1; while(x >= 10*v){ v *= 10; r++; } while(r >= 0){ r--; k = floor(x / v); if(k >= 10){ k = 9; } if(k <= -1){ k = 0; } x -= k * v; v *= 0.1; my_putchar_unlocked(k + '0'); } if(d > 0){ my_putchar_unlocked('.'); v = 1; for(r=(0);r<(d);r++){ v *= 0.1; k = floor(x / v); if(k >= 10){ k = 9; } if(k <= -1){ k = 0; } x -= k * v; my_putchar_unlocked(k + '0'); } } } template inline void DigitF_L(T n, int sz, S res[], U b){ int i; for(i=(0);i<(sz);i++){ res[i] = n % b; n /= b; } } template inline S chmax(S &a, T b){ if(a s2){ dp[0][mask] = 1; } else{ dp[1][mask] = 1; } } for(ao_dF3pO=(0);ao_dF3pO<(400);ao_dF3pO++){ int p; for(p=(0);p<(2);p++){ for(mask=(0);mask<(pw[N]);mask++){ DigitF_L(mask, N, arr, 3); for(i=(0);i<(N);i++){ if(arr[i]==0){ break; } } if(i==N){ continue; } dp[p][mask] = 0; for(i=(0);i<(N);i++){ if(arr[i]==0){ tmp = 0; tmp += (1.0 / A[i]) * (1 - dp[p^1][mask + pw[i] * (p+1)]); tmp += (1 - 1.0 / A[i]) * (1 - dp[p^1][mask]); chmax(dp[p][mask], tmp); } } } } } wt_L(dp[0][0]); wt_L('\n'); return 0; } // cLay varsion 20200509-1 // --- original code --- // int N, A[10]; // double dp[2][59049]; // int arr[10], pw[11]; // { // int s1, s2; // double tmp; // // pw[0] = 1; // rep(i,10) pw[i+1] = pw[i] * 3; // // rd(N,A(N)); // // rep(mask,pw[N]){ // DigitF(mask, N, arr, 3); // rep(i,N) if(arr[i]==0) break; // if(i < N) continue; // // s1 = s2 = 0; // rep(i,N) if[arr[i]==1, s1, s2] += A[i]; // dp[if[s1 > s2, 0, 1]][mask] = 1; // } // // rep(400){ // rep(p,2) rep(mask,pw[N]){ // DigitF(mask, N, arr, 3); // rep(i,N) if(arr[i]==0) break; // if(i==N) continue; // // dp[p][mask] = 0; // rep(i,N) if(arr[i]==0){ // tmp = 0; // tmp += (1.0 / A[i]) * (1 - dp[p^1][mask + pw[i] * (p+1)]); // tmp += (1 - 1.0 / A[i]) * (1 - dp[p^1][mask]); // dp[p][mask] >?= tmp; // } // } // } // // wt(dp[0][0]); // }