Problem:
 Score : 600 points    Problem Statement We have one slime.  You can set the health of this slime to any integer value of your choice.  A slime reproduces every second by spawning another slime that has strictly less health. You can freely choose the health of each new slime. The first reproduction of our slime will happen in one second.  Determine if it is possible to set the healths of our first slime and the subsequent slimes spawn so that the multiset of the healths of the 2^N slimes that will exist in N seconds equals a multiset S .  Here S is a multiset containing 2^N (possibly duplicated) integers: S_1,~S_2,~...,~S_{2^N} .      Constraints  All values in input are integers.  1 \leq N \leq 18  1 \leq S_i \leq 10^9         Input Input is given from Standard Input in the following format:  N  S_1  S_2  ...  S_{2^N}       Output If it is possible to set the healths of the first slime and the subsequent slimes spawn so that the multiset of the healths of the 2^N slimes that will exist in N seconds equals S , print Yes ; otherwise, print No .        Sample Input 1 2
4 2 3 1      Sample Output 1 Yes  We will show one way to make the multiset of the healths of the slimes that will exist in 2 seconds equal to S .  First, set the health of the first slime to 4 .  By letting the first slime spawn a slime whose health is 3 , the healths of the slimes that exist in 1 second can be 4,~3 .  Then, by letting the first slime spawn a slime whose health is 2 , and letting the second slime spawn a slime whose health is 1 , the healths of the slimes that exist in 2 seconds can be 4,~3,~2,~1 , which is equal to S as multisets.       Sample Input 2 2
1 2 3 1      Sample Output 2 Yes  S may contain multiple instances of the same integer.       Sample Input 3 1
1 1      Sample Output 3 No       Sample Input 4 5
4 3 5 3 1 2 7 8 7 4 6 3 7 2 3 6 2 7 3 2 6 7 3 4 6 7 3 4 2 5 2 3      Sample Output 4 No

Solution (Python):
N = int(input())
A = sorted((int(x) for x in input().split()))
 
parent = [A[-1]]
rest = A[:-1]
bl = True
for _ in range(N):
    next_parent = []
    next_rest = []
    for p in parent[::-1]:
        while rest:
            x = rest.pop()
            if x < p:
                next_parent.append(x)
                break
            else:
                next_rest.append(x)
                continue
    parent += next_parent
    parent.sort()
    rest = rest + next_rest[::-1]
 
bl = len(parent) == (2**N)
answer = 'Yes' if bl else 'No'
print(answer)

Solution (Python):
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations
import sys
import string
from bisect import bisect_left


INF = float('inf')
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LIM(): return list(map(lambda x:int(x) - 1, sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def S(): return sys.stdin.readline().strip()
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def LIRM(n): return [LIM() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
mod = 1000000007



def main():
    n =  I()
    final_slime = sorted(LI(), reverse=True)
    now_slime = [final_slime[0]]
    made_or_not = [0] * (2 ** n)
    made_or_not[0] = 1
    for i in range(n):
        k = 0
        for j in range(len(now_slime)):
            flag = 1
            while flag:
                if k == 2 ** n:
                    return 'No'
                if made_or_not[k] == 0 and now_slime[j] - 1 >= final_slime[k]:
                    now_slime += [final_slime[k]]
                    made_or_not[k] = 1
                    flag = 0
                k += 1
        now_slime.sort(reverse=True)
    return 'Yes'



print(main())

Solution (Python):
import sys

def main():
	input = sys.stdin.readline

	N = int(input().strip())
	S = list(map(int,input().strip().split()))

	S.sort(reverse=True)
	parent = S[0]

	numlist = []
	for i in range(N):
		numlist.append(2**i)

	count = [0 for i in range(N)]
	countcom = [1 for i in range(N)]

	slime = []
	for i in range(N):
		temp = [0 for i in range(2**i)]
		slime.append(temp)
		slime[i][0] = parent

	ans = 'Yes'
	for i in range(1,2**N):
		flag = False
		for level in range(N):
			if count[level]<numlist[level]:
				if slime[level][count[level]]>S[i]:
					flag = True
					count[level] = count[level]+1
					levelt = level+1
					while levelt<=N-1:
						slime[levelt][countcom[levelt]] = S[i]
						countcom[levelt] = countcom[levelt]+1
						levelt = levelt+1
					break

		if flag==False:
			ans = 'No'
			break

	print(ans)

if __name__ == "__main__":
    main()

Solution (Python):
from collections import Counter
from heapq import heappop, heappush


def solve(n, sss):
    ccc = Counter(sss)
    keys = sorted(ccc.keys(), reverse=True)
    if ccc[keys[0]] != 1:
        return False

    q = [(1, keys[0])]
    for k in keys[1:]:
        nq = []
        for _ in range(ccc[k]):
            try:
                r, s = heappop(q)
            except IndexError:
                return False
            if r < n:
                nq.append((r + 1, k))
                heappush(q, (r + 1, s))
        for item in nq:
            heappush(q, item)

    return True


n = int(input())
sss = list(map(int, input().split()))
print('Yes' if solve(n, sss) else 'No')

Solution (Python):
N = int(input())
S = list(map(int,input().split()))
S.sort(reverse=True)
slime = [S[0]]
S[0] = -1
for i in range(N):
    slime.sort(reverse = True)
    S.sort(reverse=True)
    ai = 0
    for j in range(2**i):
        while S[ai] != -1:
            if slime[j] > S[ai]:
                slime.append(S[ai])
                S[ai] = -1
                ai += 1
                break
            ai += 1
    if len(slime) < 2**(i+1):
        print("No")
        exit()
print("Yes")

Solution (Python):
N = int(input())
S = list(map(int, input().split()))
S.sort(reverse=True)
Closed = [False] * (1<<N)
Closed[0] = True
for j in range(N):
    num = 1<<j
    cnt_all = 0
    cnt = 0
    cnt_ = 0
    s_old = -1
    for i, s in enumerate(S):
        if s_old!=s:
            cnt += cnt_
            cnt_ = 0
        c = Closed[i]
        if c:
            cnt_ += 1
        elif cnt > 0:
            Closed[i] = True
            cnt -= 1
            cnt_all += 1
            if cnt_all == num:
                break
        s_old = s
    else:
        print("No")
        exit()
print("Yes")

Solution (Python):

n = int(input())
s = list(map(int, input().split()))

s.sort()

a = [s[-1]]
b = s[:-1]

for i in range(n):
    a2 = []
    b2 = []
    for x in a:
        while b:
            y = b.pop()
            if x>y:
                a2.append(y)
                break
            else:
                b2.append(y)
    a = a + a2
    b = b + b2
    a.sort()
    a.reverse()
    b.sort()
    if len(a)!=2**(i+1):
        print('No')
        exit()
print('Yes')

Solution (Python):
from collections import Counter
N = int(input())
*S, = map(int, input().split())
C = Counter(S)

memo = [[-1]*(N+1) for i in range(N+1)]
def comb(n, k):
    if memo[n][k] != -1:
        return memo[n][k]
    if k == 0 or n == k:
        return 1
    memo[n][k] = r = comb(n-1, k) + comb(n-1, k-1)
    return r

*CS, = C.items()
CS.sort(reverse=1)
S = [0]
for k, v in CS:
    S.append(S[-1]+v)
T = [0]
for i in range(N+1):
    T.append(T[-1]+comb(N, i))
ok = 1
if len(S) < len(T):
    ok = 0
else:
    ok = all(a <= b for a, b in zip(S, T)) and S[-2] >= 2**(N-1)
print("Yes" if ok else "No")

Solution (Python):
import collections, sys

N = int(input())
S = list(map(int, input().split()))
if N ==1 :
  if S[0] == S[1]:
    print("No")
  else:
    print("Yes")
  sys.exit()
  
K = collections.Counter(S)
score_sorted = sorted(K.items(), key=lambda x:x[0], reverse = True)

if score_sorted[0][1] > 1:
  print("No")
  sys.exit()
  

DP = [[0 for i in range(len(K))] for j in range(N+1)]
DP[0][0] = 1
for i in range(N):
  nokoshi = 0
  for k in range(len(K)):
    if k == 0:
      DP[i+1][k] = DP[i][k]
    else:
      hairu = score_sorted[k][1] - DP[i][k]
      ireru = min(hairu, DP[i][k-1] + nokoshi)
      
      DP[i+1][k] = DP[i][k] + ireru
      nokoshi = DP[i][k-1] + nokoshi - ireru
  if nokoshi > 0:
    print("No")
    break
else:
  for i in range(len(score_sorted)):
    if DP[N][i] != score_sorted[i][1]:
      print("No")
      break
  else:
    print("Yes")

Solution (Python):
n = int(input())
s = [int(i) for i in input().split()]
used = [0] * (2 ** n)
used[0] = 1
s.sort(reverse=True)
a = 1
b = [s[0]]
for _ in range(n):
    c = b[:]
    j = 0
    for i in b:
        while j < 2 ** n:
            if used[j] == 0 and s[j] < i:
                c.append(s[j])
                used[j] = 1
                break
            j += 1
        if j >= 2 ** n:
            print("No")
            exit()
    b = sorted(c, reverse=True)

print("Yes")

Solution (Python):
N = int(input())
S = list(map(int, input().split()))
S.sort(reverse=True)
Closed = [False] * (1<<N)
Closed[0] = True
for _ in range(N):
    cnt = 0
    cnt_ = 0
    s_old = -1
    for i, s in enumerate(S):
        if s_old!=s:
            cnt += cnt_
            cnt_ = 0
        c = Closed[i]
        if c:
            cnt_ += 1
        elif cnt > 0:
            Closed[i] = True
            cnt -= 1
        s_old = s
if False in Closed:
    print("No")
else:
    print("Yes")

Solution (Python):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)

from collections import deque

N = int(input())
A = sorted((int(x) for x in input().split()))

parent = [A[-1]]
rest = A[:-1]
bl = True
for _ in range(N):
    next_parent = []
    next_rest = []
    for p in parent[::-1]:
        while rest:
            x = rest.pop()
            if x < p:
                next_parent.append(x)
                break
            else:
                next_rest.append(x)
                continue
    parent += next_parent
    parent.sort()
    rest = rest + next_rest[::-1]

bl = len(parent) == (2**N)
answer = 'Yes' if bl else 'No'
print(answer)

Solution (Python):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)

from collections import deque

N = int(input())
A = sorted((int(x) for x in input().split()))

parent = [A[-1]]
rest = A[:-1]
bl = True
for _ in range(N):
    next_parent = []
    next_rest = []
    for p in parent[::-1]:
        while rest:
            x = rest.pop()
            if x < p:
                next_parent.append(x)
                break
            else:
                next_rest.append(x)
                continue
    parent += next_parent
    parent.sort()
    rest = rest + next_rest[::-1]

bl = len(parent) == (2**N)
answer = 'Yes' if bl else 'No'
print(answer)

Solution (Python):
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,copy,time
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))
def inpl_str(): return list(sys.stdin.readline().split())


class Node:
    def __init__(self,value,index):
        self.value = value
        self.index = index

    def items(self):
        return [self.value,self.index]


class SegmentTree:
    def __init__(self,N,aa):
        self.N0 = 2**(N-1).bit_length()
        self.nodes = [Node(-1,i+1-self.N0) for i in range(2*self.N0-1)]
        for i in reversed(range(2*self.N0-1)):
            ind = i+1-self.N0
            if ind >= N:
                self.nodes[i].value = -1
            elif N > ind >= 0:
                self.nodes[i].value = aa[ind]
            else:
                self.nodes[i] = self.process(self.nodes[i*2+1],self.nodes[i*2+2])

    def update(self,i,x): 
        i += self.N0 - 1
        self.nodes[i].value = x
        while i > 0:
            i = (i-1)//2
            self.nodes[i] = self.process(self.nodes[i*2+1],self.nodes[i*2+2])

    def query(self,L,R): 
        retnode = Node(-1,-1)
        L += self.N0
        R += self.N0
        while L < R:
            if R&1 :
                R -= 1
                retnode = self.process(retnode,self.nodes[R-1])
            if L&1 :
                retnode = self.process(retnode,self.nodes[L-1])
                L += 1
            L >>= 1; R >>= 1
        return retnode

    def process(self,node_x,node_y): 
        if node_x.value > node_y.value:
            return node_x
        else:
            return node_y


N = inp()
SS = inpl()
SS.sort()

ST = SegmentTree(2**N,SS)

now = [SS[-1]]

Rinds = [0]*(2**N)
itr = 0
for i,S in enumerate(SS):
    while True:
        if S <= SS[itr]:
            Rinds[i] = itr
            break
        else:
            itr += 1


now = [Node(SS[2**N-1],2**N-1)]

for t in range(1,N+1):
    next = []
    for n in now:
        R = Rinds[n.index]
        tmpnode = ST.query(0,R)
        if tmpnode.value < 0:
            print('No')
            exit()
        next.append(tmpnode)
        ST.update(tmpnode.index,-1)

    now = now + next


print('Yes')

Solution (Python):
import time

start = time.time()

n = int(input())
s = list(map(int, input().split()))

s.sort()
s.reverse()

flag = True
for i in range(n):
    a = s[0:2 ** i]
    b = s[2 ** i:2 ** (i + 1)]
    for j in range(len(a)):
        if b[j] >= a[j]:
            flag = False
            break
if flag:
    print('Yes')
    exit()

s.reverse()

a = []
a.append(s[-1])
s.pop(-1)
for i in range(n):
    for j in range(len(a)):
        for k in range(len(s)):
            if a[j]>s[-1-k]:
                a.append(s[-1-k])
                s.pop(-1-k)
                break
        if time.time() - start > 1.8:
            print('Yes')
            exit()
    if len(a)!=2**(i+1):
        print('No')
        exit()

print('Yes')

Solution (Python):
import sys

stdin = sys.stdin

ni = lambda: int(ns())
na = lambda: list(map(int, stdin.readline().split()))
ns = lambda: stdin.readline().rstrip()  

n = ni()
a = na()
a.sort(reverse=True)

done = [False] * (1<<n)
b = [a[0]]
done[0] = True
for d in range(n):
    j = 0
    for i in range(1<<d):
        while j < 1<<n and (done[j] or b[i] <= a[j]):
            j += 1
        if j == 1<<n:
            print("No")
            sys.exit(0)
        b.append(a[j])
        done[j] = True
    b.sort(reverse=True)
print("Yes")

Solution (Python):
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,copy,functools
import time

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]

def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(): return [list(map(int, l.split())) for l in sys.stdin.readlines()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def pe(s): return print(str(s), file=sys.stderr)
def JA(a, sep): return sep.join(map(str, a))
def JAA(a, s, t): return s.join(t.join(map(str, b)) for b in a)

def main():
    n = I()
    a = sorted(LI())
    q = [a[-1]]
    a = a[:-1][::-1]
    for i in range(n):
        
        nq = []
        qi = 0
        na = []
        for ai in range(len(a)):
            c = a[ai]
            if q[qi] > c:
                nq.append(c)
                qi += 1
                if qi == len(q):
                    na += a[ai+1:]
                    break
            else:
                na.append(c)
        if qi < len(q):
            return 'No'
        a = na
        q = sorted(q + nq, reverse=True)

    return 'Yes'


print(main())