#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(double &x){ int k; int m=0; int p=0; double r = 1; x = 0; for(;;){ k = my_getchar_unlocked(); if(k=='-'){ m = 1; break; } if(k=='.'){ p = 1; break; } if('0'<=k&&k<='9'){ x = k - '0'; break; } } for(;;){ k = my_getchar_unlocked(); if(k=='.'){ p = 1; continue; } if(k<'0'||k>'9'){ break; } if(p){ r *= 0.1; x += r * (k - '0'); } else{ 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'); } } } double X; double solve(double X){ int j; double res = 0; double tmp; if(X==0){ res += 1; } else{ res += sin(X) * sin(X) / X / X; } for(j=(1);j<(1000000);j++){ tmp = sin(X+j) / (X+j); res += tmp * tmp; } return res; } int main(){ double res = 0; double add = 0; double tmp; rd(X); while(X >= 1){ X--; if(X==0){ tmp = 1; } else{ tmp = sin(X) / X; } add -= tmp * tmp; } res = 2.07079632677096370230; res -= solve(0); res += solve(X); wt_L(res+add); wt_L('\n'); return 0; } // cLay varsion 20200509-1 // --- original code --- // double X; // // double solve(double X){ // double res = 0, tmp; // if(X==0) res += 1; else res += sin(X) * sin(X) / X / X; // rep(j,1,1d6){ // tmp = sin(X+j) / (X+j); // res += tmp * tmp; // } // return res; // } // // { // double res = 0, add = 0, tmp; // rd(X); // // while(X >= 1){ // X--; // if(X==0) tmp = 1; else tmp = sin(X) / X; // add -= tmp * tmp; // } // // res = 2.07079632677096370230; // res -= solve(0); // res += solve(X); // // wt(res+add); // }