#define _CRT_SECURE_NO_WARNINGS #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) #if defined(_MSC_VER) || __cplusplus > 199711L #define aut(r,v) auto r = (v) #else #define aut(r,v) typeof(v) r = (v) #endif #define each(it,o) for(aut(it, (o).begin()); it != (o).end(); ++ it) #define all(o) (o).begin(), (o).end() #define pb(x) push_back(x) #define mp(x,y) make_pair((x),(y)) #define mset(m,v) memset(m,v,sizeof(m)) #define INF 0x3f3f3f3f #define INFL 0x3f3f3f3f3f3f3f3fLL using namespace std; typedef vector vi; typedef pair pii; typedef vector > vpii; typedef long long ll; typedef vector vl; typedef pair pll; typedef vector > vpll; typedef vector vs; typedef long double ld; template inline void amin(T &x, U y) { if(y < x) x = y; } template inline void amax(T &x, U y) { if(x < y) x = y; } int N; double memo[101][101][101]; double rec(int n0, int n1, int n2) { if(n0 < 0 || n1 < 0 || n2 < 0) return 0; double &r = memo[n0][n1][n2]; if(r == r) return r; int sum = n0 + n1 + n2; if(sum == 0) return r = 0; double p0 = n0 * 1. / sum; double p1 = n1 * 1. / sum; double p2 = n2 * 1. / sum; double q = sum * 1. / N; r = 1 / q + p0 * rec(n0-1, n1+1, n2) + p1 * rec(n0, n1-1, n2+1) + p2 * rec(n0, n1, n2-1); return r; } int main() { scanf("%d", &N); vector A(N); rep(i, N) scanf("%d", &A[i]); int cnt0 = 0, cnt1 = 0, cnt2 = 0; rep(i, N) { if(A[i] == 0) ++ cnt0; else if(A[i] == 1) ++ cnt1; else if(A[i] == 2) ++ cnt2; } mset(memo, -1); double ans = rec(cnt0, cnt1, cnt2); printf("%.10f\n", ans); return 0; }