Buggy python submission (verdict: Runtime Error):
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

N = ii()
N_f = float(N)
A = li()

cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1

#dp = dp3(-1.0, cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp = dp3(0.0, N+1, N+1, N+1)
dp = dp3(0.0, 301, 301, 301)
dp[0][0][0] = 0

for k in range(cnt[2]+1):
#for i in range(N+1):
    for j in range(cnt[1]+cnt[2]+1):
    #for j in range(N+1):
        #for k in range(cnt[2]+1):
        #for k in range(N+1):
        for i in range(N+1):
            #print(i, j, k)
            if i+j+k == 0:
                continue
            num = i+j+k
            dp[i][j][k] = N_f
            if i > 0:
                dp[i][j][k] += dp[i-1][j][k] * i
            if j > 0:
                dp[i][j][k] += dp[i+1][j-1][k] * j
            if k > 0:
                dp[i][j][k] += dp[i][j+1][k-1] * k
            dp[i][j][k] /= num

print(dp[cnt[0]][cnt[1]][cnt[2]])

Fixed submission:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

N = ii()
N_f = float(N)
A = li()

cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1

#dp = dp3(-1.0, cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp = dp3(0.0, N+1, N+1, N+1)
#dp = dp3(0.0, 301, 301, 301)
dp[0][0][0] = 0

for k in range(cnt[2]+1):
#for i in range(N+1):
    for j in range(cnt[1]+cnt[2]+1-k):
    #for j in range(N+1):
        #for k in range(cnt[2]+1):
        #for k in range(N+1):
        for i in range(N+1-j-k):
            #print(i, j, k)
            if i+j+k == 0:
                continue
            num = i+j+k
            dp[i][j][k] = N_f
            if i > 0:
                dp[i][j][k] += dp[i-1][j][k] * i
            if j > 0:
                dp[i][j][k] += dp[i+1][j-1][k] * j
            if k > 0:
                dp[i][j][k] += dp[i][j+1][k-1] * k
            dp[i][j][k] /= num

print(dp[cnt[0]][cnt[1]][cnt[2]])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value
 
def rec(i, j, k):
    global dp
    if dp[i][j][k] != -1.0:
        return dp[i][j][k]
    if i+j+k == 0:
        return 0.0
 
    num = i+j+k
    ans = N_f
    if i > 0:
        ans += (rec(i-1, j, k) * i)
    if j > 0:
        ans += (rec(i+1, j-1, k) * j)
    if k > 0:
        ans += (rec(i, j+1, k-1) * k)
    ans /= num
    dp[i][j][k] = ans
    return ans
 
N = ii()
N_f = float(N)
A = li()
 
cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1
 
dp = dp3(-1.0, cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp[0][0][0] = 0
 
print(rec(cnt[0], cnt[1], cnt[2]))

Fixed submission:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

N = ii()
N_f = float(N)
A = li()

cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1

#dp = dp3(-1.0, cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp = dp3(0.0, N+1, N+1, N+1)
#dp = dp3(0.0, 301, 301, 301)
dp[0][0][0] = 0

for k in range(cnt[2]+1):
#for i in range(N+1):
    for j in range(cnt[1]+cnt[2]+1-k):
    #for j in range(N+1):
        #for k in range(cnt[2]+1):
        #for k in range(N+1):
        for i in range(N+1-j-k):
            #print(i, j, k)
            if i+j+k == 0:
                continue
            num = i+j+k
            dp[i][j][k] = N_f
            if i > 0:
                dp[i][j][k] += dp[i-1][j][k] * i
            if j > 0:
                dp[i][j][k] += dp[i+1][j-1][k] * j
            if k > 0:
                dp[i][j][k] += dp[i][j+1][k-1] * k
            dp[i][j][k] /= num

print(dp[cnt[0]][cnt[1]][cnt[2]])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value
 
def rec(i, j, k):
    global dp
    if dp[i][j][k] != -1.0:
        return dp[i][j][k]
    if i+j+k == 0:
        return 0.0
 
    num = i+j+k
    ans = N_f
    if i > 0:
        ans += (rec(i-1, j, k) * i)
    if j > 0:
        ans += (rec(i+1, j-1, k) * j)
    if k > 0:
        ans += (rec(i, j+1, k-1) * k)
    ans /= num
    dp[i][j][k] = ans
    return ans
 
N = ii()
N_f = float(N)
A = li()
 
cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1
 
dp = dp3(-1.0, cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp[0][0][0] = 0
 
print(rec(cnt[0], cnt[1], cnt[2]))

Fixed submission:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

N = ii()
N_f = float(N)
A = li()

cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1

#dp = dp3(-1.0, cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp = dp3(0.0, N+1, N+1, N+1)
#dp = dp3(0.0, 301, 301, 301)
dp[0][0][0] = 0

for k in range(cnt[2]+1):
#for i in range(N+1):
    for j in range(cnt[1]+cnt[2]+1-k):
    #for j in range(N+1):
        #for k in range(cnt[2]+1):
        #for k in range(N+1):
        for i in range(N+1-j-k):
            #print(i, j, k)
            if i+j+k == 0:
                continue
            num = i+j+k
            dp[i][j][k] = N_f
            if i > 0:
                dp[i][j][k] += dp[i-1][j][k] * i
            if j > 0:
                dp[i][j][k] += dp[i+1][j-1][k] * j
            if k > 0:
                dp[i][j][k] += dp[i][j+1][k-1] * k
            dp[i][j][k] /= num

print(dp[cnt[0]][cnt[1]][cnt[2]])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

def rec(k, j, i):
    global dp
    if dp[k][j][i] != -1.0:
        return dp[k][j][i]
    if i+j+k == 0:
        return 0.0

    num = i+j+k
    ans = N_f / num
    if i > 0:
        ans += (rec(k, j, i-1) * i) / num
    if j > 0:
        ans += (rec(k, j-1, i+1) * j) / num
    if k > 0:
        ans += (rec(k-1, j+1, i) * k) / num
    dp[k][j][i] = ans
    return ans

N = ii()
N_f = float(N)
A = li()

cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1

#dp = dp3(-1.0, cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp = dp3(-1.0, N+1, cnt[1]+cnt[2]+1, cnt[2]+1)

print(rec(cnt[2], cnt[1], cnt[0]))

Fixed submission:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

N = ii()
N_f = float(N)
A = li()

cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1

#dp = dp3(-1.0, cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp = dp3(0.0, N+1, N+1, N+1)
#dp = dp3(0.0, 301, 301, 301)
dp[0][0][0] = 0

for k in range(cnt[2]+1):
#for i in range(N+1):
    for j in range(cnt[1]+cnt[2]+1-k):
    #for j in range(N+1):
        #for k in range(cnt[2]+1):
        #for k in range(N+1):
        for i in range(N+1-j-k):
            #print(i, j, k)
            if i+j+k == 0:
                continue
            num = i+j+k
            dp[i][j][k] = N_f
            if i > 0:
                dp[i][j][k] += dp[i-1][j][k] * i
            if j > 0:
                dp[i][j][k] += dp[i+1][j-1][k] * j
            if k > 0:
                dp[i][j][k] += dp[i][j+1][k-1] * k
            dp[i][j][k] /= num

print(dp[cnt[0]][cnt[1]][cnt[2]])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

def rec(i, j, k):
    global dp
    if dp[i][j][k] != -1.0:
        return dp[i][j][k]
    if i+j+k == 0:
        return 0.0

    num = i+j+k
    ans = N_f / num
    if i > 0:
        ans += (rec(i-1, j, k) * i) / num
    if j > 0:
        ans += (rec(i+1, j-1, k) * j) / num
    if k > 0:
        ans += (rec(i, j+1, k-1) * k) / num
    dp[i][j][k] = ans
    return ans

N = ii()
N_f = float(N)
A = li()

cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1

dp = dp3(-1.0, cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp[0][0][0] = 0

print(rec(cnt[0], cnt[1], cnt[2]))

Fixed submission:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

N = ii()
N_f = float(N)
A = li()

cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1

#dp = dp3(-1.0, cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp = dp3(0.0, N+1, N+1, N+1)
#dp = dp3(0.0, 301, 301, 301)
dp[0][0][0] = 0

for k in range(cnt[2]+1):
#for i in range(N+1):
    for j in range(cnt[1]+cnt[2]+1-k):
    #for j in range(N+1):
        #for k in range(cnt[2]+1):
        #for k in range(N+1):
        for i in range(N+1-j-k):
            #print(i, j, k)
            if i+j+k == 0:
                continue
            num = i+j+k
            dp[i][j][k] = N_f
            if i > 0:
                dp[i][j][k] += dp[i-1][j][k] * i
            if j > 0:
                dp[i][j][k] += dp[i+1][j-1][k] * j
            if k > 0:
                dp[i][j][k] += dp[i][j+1][k-1] * k
            dp[i][j][k] /= num

print(dp[cnt[0]][cnt[1]][cnt[2]])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

def rec(i, j, k):
    global dp
    if dp[i][j][k] < float("inf"):
        return dp[i][j][k]
    if i+j+k == 0:
        return 0

    num = float(i+j+k)
    ans = float(N) / num
    if i > 0:
        ans += (rec(i-1, j, k) * i) / num
    if j > 0:
        ans += (rec(i+1, j-1, k) * j) / num
    if k > 0:
        ans += (rec(i, j+1, k-1) * k) / num
    dp[i][j][k] = ans
    return ans

N = ii()
A = li()

cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1

dp = dp3(float("inf"), cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp[0][0][0] = 0

print(rec(cnt[0], cnt[1], cnt[2]))

Fixed submission:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

N = ii()
N_f = float(N)
A = li()

cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1

#dp = dp3(-1.0, cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp = dp3(0.0, N+1, N+1, N+1)
#dp = dp3(0.0, 301, 301, 301)
dp[0][0][0] = 0

for k in range(cnt[2]+1):
#for i in range(N+1):
    for j in range(cnt[1]+cnt[2]+1-k):
    #for j in range(N+1):
        #for k in range(cnt[2]+1):
        #for k in range(N+1):
        for i in range(N+1-j-k):
            #print(i, j, k)
            if i+j+k == 0:
                continue
            num = i+j+k
            dp[i][j][k] = N_f
            if i > 0:
                dp[i][j][k] += dp[i-1][j][k] * i
            if j > 0:
                dp[i][j][k] += dp[i+1][j-1][k] * j
            if k > 0:
                dp[i][j][k] += dp[i][j+1][k-1] * k
            dp[i][j][k] /= num

print(dp[cnt[0]][cnt[1]][cnt[2]])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

def rec(i, j, k):
    global dp
    if dp[i][j][k] < float("inf"):
        return dp[i][j][k]
    if i+j+k == 0:
        return 0

    num = float(i+j+k)
    ans = float(N) / num
    if i > 0:
        ans += (rec(i-1, j, k) * i) / num
    if j > 0:
        ans += (rec(i+1, j-1, k) * j) / num
    if k > 0:
        ans += (rec(i, j+1, k-1) * k) / num
    dp[i][j][k] = ans
    return ans

N = ii()
A = li()

cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1

dp = dp3(float("inf"), cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp[0][0][0] = 0

print(rec(cnt[0], cnt[1], cnt[2]))

Fixed submission:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

N = ii()
N_f = float(N)
A = li()

cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1

#dp = dp3(-1.0, cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp = dp3(0.0, N+1, N+1, N+1)
#dp = dp3(0.0, 301, 301, 301)
dp[0][0][0] = 0

for k in range(cnt[2]+1):
#for i in range(N+1):
    for j in range(cnt[1]+cnt[2]+1-k):
    #for j in range(N+1):
        #for k in range(cnt[2]+1):
        #for k in range(N+1):
        for i in range(N+1-j-k):
            #print(i, j, k)
            if i+j+k == 0:
                continue
            num = i+j+k
            dp[i][j][k] = N_f
            if i > 0:
                dp[i][j][k] += dp[i-1][j][k] * i
            if j > 0:
                dp[i][j][k] += dp[i+1][j-1][k] * j
            if k > 0:
                dp[i][j][k] += dp[i][j+1][k-1] * k
            dp[i][j][k] /= num

print(dp[cnt[0]][cnt[1]][cnt[2]])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

def rec(i, j, k):
    global dp
    #print(i, j, k)
    if dp[i][j][k] < float("inf"):
        return dp[i][j][k]
    if i+j+k == 0:
        return 0

    num = float(i+j+k)
    ans = float(N) / num
    if i > 0:
        ans += (rec(i-1, j, k) * i) / num
    if j > 0:
        ans += (rec(i+1, j-1, k) * j) / num
    if k > 0:
        ans += (rec(i, j+1, k-1) * k) / num
    dp[i][j][k] = ans
    return ans

N = ii()
A = li()

dp = dp3(float("inf"), N+1, N+1, N+1)
dp[0][0][0] = 0
cnt = [0, 0, 0]

for a in A:
    cnt[a-1] += 1

print(rec(cnt[0], cnt[1], cnt[2]))

Fixed submission:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

N = ii()
N_f = float(N)
A = li()

cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1

#dp = dp3(-1.0, cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp = dp3(0.0, N+1, N+1, N+1)
#dp = dp3(0.0, 301, 301, 301)
dp[0][0][0] = 0

for k in range(cnt[2]+1):
#for i in range(N+1):
    for j in range(cnt[1]+cnt[2]+1-k):
    #for j in range(N+1):
        #for k in range(cnt[2]+1):
        #for k in range(N+1):
        for i in range(N+1-j-k):
            #print(i, j, k)
            if i+j+k == 0:
                continue
            num = i+j+k
            dp[i][j][k] = N_f
            if i > 0:
                dp[i][j][k] += dp[i-1][j][k] * i
            if j > 0:
                dp[i][j][k] += dp[i+1][j-1][k] * j
            if k > 0:
                dp[i][j][k] += dp[i][j+1][k-1] * k
            dp[i][j][k] /= num

print(dp[cnt[0]][cnt[1]][cnt[2]])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

def rec(i, j, k):
    global dp
    #print(i, j, k)
    if dp[i][j][k] < float("inf"):
        return dp[i][j][k]
    if i+j+k == 0:
        return 0

    num = float(i+j+k)
    ans = float(N) / num
    if i > 0:
        ans += (rec(i-1, j, k) * i) / num
    if j > 0:
        ans += (rec(i+1, j-1, k) * j) / num
    if k > 0:
        ans += (rec(i, j+1, k-1) * k) / num
    dp[i][j][k] = ans
    return ans

N = ii()
A = li()

dp = dp3(float("inf"), N+1, N+1, N+1)
dp[0][0][0] = 0
cnt = [0, 0, 0]

for a in A:
    cnt[a-1] += 1

print(rec(cnt[0], cnt[1], cnt[2]))

Fixed submission:
import sys
sys.setrecursionlimit(10**8)
def ii(): return int(sys.stdin.readline())
def mi(): return map(int, sys.stdin.readline().split())
def li(): return list(map(int, sys.stdin.readline().split()))
def li2(N): return [list(map(int, sys.stdin.readline().split())) for i in range(N)]
def dp2(ini, i, j): return [[ini]*i for i2 in range(j)]
def dp3(ini, i, j, k): return [[[ini]*i for i2 in range(j)] for i3 in range(k)]
#import bisect #bisect.bisect_left(B, a)
#from collections import defaultdict #d = defaultdict(int) d[key] += value

N = ii()
N_f = float(N)
A = li()

cnt = [0, 0, 0]
for a in A:
    cnt[a-1] += 1

#dp = dp3(-1.0, cnt[2]+1, cnt[1]+cnt[2]+1, N+1)
dp = dp3(0.0, N+1, N+1, N+1)
#dp = dp3(0.0, 301, 301, 301)
dp[0][0][0] = 0

for k in range(cnt[2]+1):
#for i in range(N+1):
    for j in range(cnt[1]+cnt[2]+1-k):
    #for j in range(N+1):
        #for k in range(cnt[2]+1):
        #for k in range(N+1):
        for i in range(N+1-j-k):
            #print(i, j, k)
            if i+j+k == 0:
                continue
            num = i+j+k
            dp[i][j][k] = N_f
            if i > 0:
                dp[i][j][k] += dp[i-1][j][k] * i
            if j > 0:
                dp[i][j][k] += dp[i+1][j-1][k] * j
            if k > 0:
                dp[i][j][k] += dp[i][j+1][k-1] * k
            dp[i][j][k] /= num

print(dp[cnt[0]][cnt[1]][cnt[2]])