#pragma GCC optimize("O3") #pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize("Ofast") #pragma GCC optimize("inline") #pragma GCC optimize("-fgcse") #pragma GCC optimize("-fgcse-lm") #pragma GCC optimize("-fipa-sra") #pragma GCC optimize("-ftree-pre") #pragma GCC optimize("-ftree-vrp") #pragma GCC optimize("-fpeephole2") #pragma GCC optimize("-ffast-math") #pragma GCC optimize("-fsched-spec") #pragma GCC optimize("unroll-loops") #pragma GCC optimize("-falign-jumps") #pragma GCC optimize("-falign-loops") #pragma GCC optimize("-falign-labels") #pragma GCC optimize("-fdevirtualize") #pragma GCC optimize("-fcaller-saves") #pragma GCC optimize("-fcrossjumping") #pragma GCC optimize("-fthread-jumps") #pragma GCC optimize("-funroll-loops") #pragma GCC optimize("-freorder-blocks") #pragma GCC optimize("-fschedule-insns") #pragma GCC optimize("inline-functions") #pragma GCC optimize("-ftree-tail-merge") #pragma GCC optimize("-fschedule-insns2") #pragma GCC optimize("-fstrict-aliasing") #pragma GCC optimize("-falign-functions") #pragma GCC optimize("-fcse-follow-jumps") #pragma GCC optimize("-fsched-interblock") #pragma GCC optimize("-fpartial-inlining") #pragma GCC optimize("no-stack-protector") #pragma GCC optimize("-freorder-functions") #pragma GCC optimize("-findirect-inlining") #pragma GCC optimize("-fhoist-adjacent-loads") #pragma GCC optimize("-frerun-cse-after-loop") #pragma GCC optimize("inline-small-functions") #pragma GCC optimize("-finline-small-functions") #pragma GCC optimize("-ftree-switch-conversion") #pragma GCC optimize("-foptimize-sibling-calls") #pragma GCC optimize("-fexpensive-optimizations") #pragma GCC optimize("inline-functions-called-once") #pragma GCC optimize("-fdelete-null-pointer-checks") #pragma GCC optimize("Ofast") //#pragma GCC target("avx,avx2,fma") //#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") //#pragma GCC optimization ("unroll-loops") #include using namespace std; long double dp[101][101][101]; bool check[101][101][101]; int n,t; long double solve(int a,int b,int c) { if(check[a][b][c]) { return dp[a][b][c]; } check[a][b][c] = true; if(a==0 && b==0 && c==0) { dp[a][b][c] = 0; return dp[a][b][c]; } int d = n - (a+b+c); long double value = 1; if(a-1 >= 0) { value += ((a*solve(a-1,b+1,c))/n); } if(b-1 >= 0) { value += ((b*solve(a,b-1,c+1))/n); } if(c-1 >= 0) { value += ((c*solve(a,b,c-1))/n); } value*=n; value/=(n-d); dp[a][b][c] = value; return dp[a][b][c]; } int main(void) { cin.tie(0); ios::sync_with_stdio(false); cin >> n; int cnt[3]; memset(cnt,0,sizeof(cnt)); for(int i=0;i> t; if(t < 3) { cnt[t] += 1; } } memset(check,false,sizeof(check)); cout << fixed; cout.precision(16); cout << solve(cnt[0],cnt[1],cnt[2]) << '\n'; return 0; }