#include <iostream>#include <cstdio>#include <cstring>#include <cmath>#include <cstdlib>#include <algorithm>#include <vector>#include <map>#include <queue>#include <set>using namespace std;#define SZ(v) ((int)(v).size())#define REP(i, n) for (int i = 0; i < (n); ++i)#define REPF(i, a, b) for (int i = (a); i <= (b); ++i)#define REPD(i, a, b) for (int i = (a); i >= (b); --i)const int maxint = -1u>>1;double f[1000010], g[1000010];int sum, n, req;char ss[100];int main() { n = 0; scanf("%s", ss); if (ss[0] == 's') n ++; scanf("%s", ss); if (ss[0] == 's') n ++; scanf("%s", ss); if (ss[0] == 's') n ++; scanf("%s", ss); if (ss[1] == 'a') req = 1; else req = 0; scanf("%d", ∑); f[2] = cos((double)0.0); g[2] = cos((double)0.0); double z, y; for (int i = 4; i <= sum; i += 2) { y = ((double)i / 2) - 1; z = cos(y); f[i] = max(f[i - 2], z); g[i] = min(g[i - 2], z); } f[3] = cos((double)0.5); g[3] = cos((double)0.5); for (int i = 5; i <= sum; i += 2) { y = ((double)i / 2) - 1; z = cos(y); f[i] = max(f[i - 2], z); g[i] = min(g[i - 2], z); } double ans, tmp, t, tt; for (int i = 1; i <= sum - 2; i ++) { if (n == 0 || n == 2) tmp = cos((double)i); else tmp = sin((double)i); y = (double) (sum - i) / 2; if (n == 0 || n == 1) t = 2 * cos(y); else t = 2 * sin(y); if (req) tt = max(t * f[sum - i], t * g[sum - i]); else tt = min(t * f[sum - i], t * g[sum - i]); if (i == 1) ans = tt + tmp; if (req) ans = max(ans, tt + tmp); else ans = min(ans, tt + tmp); } printf("%.12fn", ans); return 0;}
