CodeEff/ECCO huggingface dataset:
# Original solution
#ALDS1_5-B Merge Sort
from collections import deque

def merge(A,B):
    ans = deque()
    count = 0
    while(True):
        if len(A)==0:
            if len(B)==0:
                break
            ans.append(B.popleft())
        elif len(B) == 0:
            ans.append(A.popleft())
        elif A[0] > B[0]:
            ans.append(B.popleft())
        else:
            ans.append(A.popleft())
        count+=1
    return (ans.copy(),count)

n = int(eval(input()))
S = [int(i) for i in input().split()]
div = deque([S])
mer = deque()
count = 0
while(len(div)>0):
    d = div.pop()
    if(len(d)>2):
        mid = len(d)//2
        div.appendleft(d[:mid])
        div.appendleft(d[mid:])
    elif(len(d)==2):
        if d[0] > d[1]:
            mer.appendleft(d[::-1])
        else:
            mer.appendleft(d)
        count+=2
    else:
        mer.appendleft(d)
        
while(len(mer)>1):
    A = deque(mer.popleft())
    B = deque(mer.popleft())
    ret = merge(A,B)
    mer.append(ret[0])
    count+=ret[1]
    
ans = ""
for i in ret[0]:
    ans += str(i) + " "
print((ans[:-1]))
print(count)


# Optimized solution
#ALDS1_5-B Merge Sort
from collections import deque

def merge(A,B):
    ans = deque()
    count = 0
    while(True):
        if len(A)==0:
            if len(B)==0:
                break
            ans.append(B.popleft())
        elif len(B) == 0:
            ans.append(A.popleft())
        elif A[0] > B[0]:
            ans.append(B.popleft())
        else:
            ans.append(A.popleft())
        count+=1
    return (ans,count)

n = int(eval(input()))
S = [int(i) for i in input().split()]
div = deque([S])
mer = deque()
count = 0
while(len(div)>0):
    d = div.pop()
    if(len(d)>2):
        mid = len(d)//2
        div.appendleft(d[:mid])
        div.appendleft(d[mid:])
    elif(len(d)==2):
        if d[0] > d[1]:
            mer.appendleft(d[::-1])
        else:
            mer.appendleft(d)
        count+=2
    else:
        mer.appendleft(d)
        
while(len(mer)>1):
    A = deque(mer.popleft())
    B = deque(mer.popleft())
    ret = merge(A,B)
    mer.append(ret[0])
    count+=ret[1]
    
ans = ""
for i in ret[0]:
    ans += str(i) + " "
print((ans[:-1]))
print(count)
# Original solution
def merge(A, l, m, r):
    n1, n2 = m - l, r - m
    L = [A[l + i] for i in range(n1)] + [10 ** 10]
    R = [A[m + i] for i in range(n2)] + [10 ** 10]
    i, j = 0, 0
    for k in range(l, r):
        if L[i] <= R[j]:
            A[k] = L[i]
            i += 1
        else:
            A[k] = R[j]
            j += 1
    global cnt
    cnt += r - l

def mergeSort(A, l, r):
    if r - l > 1:
        m = (l + r) // 2
        mergeSort(A, l, m)
        mergeSort(A, m, r)
        merge(A, l, m, r)

n = int(eval(input()))
A = list(map(int, input().split()))
cnt = 0
mergeSort(A, 0, n)
print((" ".join(list(map(str, A)))))
print(cnt)

# Optimized solution
def merge(A, l, m, r):
    L = A[l:m] + [10 ** 9 + 1]
    R = A[m:r] + [10 ** 9 + 1]
    i, j = 0, 0
    for k in range(l, r):
        if L[i] <= R[j]:
            A[k] = L[i]
            i += 1
        else:
            A[k] = R[j]
            j += 1
    global cnt
    cnt += r - l

def mergeSort(A, l, r):
    if r - l > 1:
        m = (l + r) // 2
        mergeSort(A, l, m)
        mergeSort(A, m, r)
        merge(A, l, m, r)

n = int(eval(input()))
A = list(map(int, input().split()))
cnt = 0
mergeSort(A, 0, n)
print((" ".join(list(map(str, A)))))
print(cnt)
# Original solution
#http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_5_B&lang=jp
def merge(target_list, left_index, mid_index,right_index):
    global count
    l = target_list[left_index:mid_index] + [pow(10,9) + 1]
    r = target_list[mid_index:right_index] + [pow(10,9) + 1]
    l_target = 0
    r_target = 0
    #print(left_index, right_index, mid_index, l,r)
    for k in range(left_index, right_index):
        count += 1
        if l[l_target] < r[r_target]:
            target_list[k] = l[l_target]
            l_target += 1
        else:
            target_list[k] = r[r_target]
            r_target += 1
    #print(target_list)
            
def merge_sort(target_list, left_index, right_index):
    if left_index + 1 < right_index:
        mid_index = (left_index + right_index) // 2

        merge_sort(target_list, left_index, mid_index)
        merge_sort(target_list, mid_index, right_index)
        merge(target_list, left_index, mid_index,right_index)
    
if __name__ == "__main__":
    l = eval(input())
    target_list = [int(a) for a in input().split()]
    global count
    count = 0
    merge_sort(target_list, 0, len(target_list))
    print((" ".join([str(n) for n in target_list])))
    print(count)

# Optimized solution
#http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_5_B&lang=jp
def merge(target_list, left_index, mid_index,right_index):
    l = target_list[left_index:mid_index] + [pow(10,9) + 1]
    r = target_list[mid_index:right_index] + [pow(10,9) + 1]
    l_target = 0
    r_target = 0
    count = 0
    #print(left_index, right_index, mid_index, l,r)
    for k in range(left_index, right_index):
        count += 1
        if l[l_target] < r[r_target]:
            target_list[k] = l[l_target]
            l_target += 1
        else:
            target_list[k] = r[r_target]
            r_target += 1

    return count
    #print(target_list)
            
def merge_sort(target_list, left_index, right_index):
    count = 0
    if left_index + 1 < right_index:
        mid_index = (left_index + right_index) // 2

        count += merge_sort(target_list, left_index, mid_index)
        count += merge_sort(target_list, mid_index, right_index)
        count += merge(target_list, left_index, mid_index,right_index)
    return count
if __name__ == "__main__":
    l = eval(input())
    target_list = [int(a) for a in input().split()]
    count = 0
    count = merge_sort(target_list, 0, len(target_list))
    print((" ".join([str(n) for n in target_list])))
    print(count)
# Original solution
#http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_5_B&lang=jp
def merge(target_list, left_index, mid_index,right_index):
    sentinel = pow(10,9) + 1
    l = target_list[left_index:mid_index] + [sentinel]
    r = target_list[mid_index:right_index] + [sentinel]
    l_target = 0
    r_target = 0
    count = 0
    #print(left_index, right_index, mid_index, l,r)
    for k in range(left_index, right_index):
        count += 1
        if l[l_target] < r[r_target]:
            target_list[k] = l[l_target]
            l_target += 1
        else:
            target_list[k] = r[r_target]
            r_target += 1

    return count
    #print(target_list)
            
def merge_sort(target_list, left_index, right_index):
    count = 0
    if left_index + 1 < right_index:
        mid_index = (left_index + right_index) // 2

        count += merge_sort(target_list, left_index, mid_index)
        count += merge_sort(target_list, mid_index, right_index)
        count += merge(target_list, left_index, mid_index,right_index)
        
    return count
if __name__ == "__main__":
    l = eval(input())
    target_list = [int(a) for a in input().split()]
    count = merge_sort(target_list, 0, len(target_list))
    print((" ".join([str(n) for n in target_list])))
    print(count)

# Optimized solution
#http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_5_B&lang=jp
sentinel = pow(10,9) + 1
def merge(target_list, left_index, mid_index,right_index):
    l = target_list[left_index:mid_index] + [sentinel]
    r = target_list[mid_index:right_index] + [sentinel]
    l_target = 0
    r_target = 0
    count = 0
    #print(left_index, right_index, mid_index, l,r)
    for k in range(left_index, right_index):
        count += 1
        if l[l_target] < r[r_target]:
            target_list[k] = l[l_target]
            l_target += 1
        else:
            target_list[k] = r[r_target]
            r_target += 1

    return count
    #print(target_list)
            
def merge_sort(target_list, left_index, right_index):
    count = 0
    if left_index + 1 < right_index:
        mid_index = (left_index + right_index) // 2

        count += merge_sort(target_list, left_index, mid_index)
        count += merge_sort(target_list, mid_index, right_index)
        count += merge(target_list, left_index, mid_index,right_index)
        
    return count
if __name__ == "__main__":
    l = eval(input())
    target_list = [int(a) for a in input().split()]
    count = merge_sort(target_list, 0, len(target_list))
    print((" ".join([str(n) for n in target_list])))
    print(count)
# Original solution
from ctypes import *

def merge_sort(A, left, right):
    if left + 1 < right:
        mid = (left + right) // 2
        merge_sort(A, left, mid)
        merge_sort(A, mid, right)
        merge(A, left, mid, right)


def merge(A, left, mid, right):
    global Comp_count
    n1 = mid - left
    n2 = right - mid
    L = [A.d[left+i] for i in range(n1)]
    R = [A.d[mid+j] for j in range(n2)]
    L.append(1000000001)
    R.append(1000000001)
    i = 0  # L[]??¨?????????????????????
    j = 0  # R[]??¨?????????????????????
    for k in range(left, right):
        Comp_count += 1
        if L[i] <= R[j]:
            A.d[k] = L[i]
            i += 1
        else:
            A.d[k] = R[j]
            j += 1


class DATA(Structure):
    _fields_ = ("d", c_int * 500001),



Comp_count = 0
if __name__ == '__main__':
    # ??????????????\???
    num_of_data = int(eval(input()))
    IN = [int(x) for x in input().split(' ')]
    S = DATA()
    for i in range(num_of_data):
        S.d[i] = IN[i]
    #S = [8, 5, 9, 2, 6, 3, 7, 1, 10, 4]
    #S = []
    #with open('ALDS1_5_B_in10.txt') as f:
    #    for line in f:
    #        if ' ' not in line:
    #            pass
    #        else:
    #            S = [int(x) for x in line.split(' ')]

    # ????????????????????????
    merge_sort(S, 0, num_of_data)

    # ???????????????
    txt = ''
    for i in range(num_of_data):
        txt += str(S.d[i])
        txt += ' '
    txt = txt[:-1]
    print(('{0}'.format(txt)))
    print(Comp_count)

# Optimized solution
from array import array

def merge_sort(A, left, right):
    if left + 1 < right:
        mid = (left + right) // 2
        merge_sort(A, left, mid)
        merge_sort(A, mid, right)
        merge(A, left, mid, right)


def merge(A, left, mid, right):
    global Comp_count
    n1 = mid - left
    n2 = right - mid
    L = [A[left+i] for i in range(n1)]
    R = [A[mid+j] for j in range(n2)]
    L.append(1000000001)
    R.append(1000000001)

    i = 0  # L[]??¨?????????????????????
    j = 0  # R[]??¨?????????????????????
    for k in range(left, right):
        Comp_count += 1
        if L[i] <= R[j]:
            A[k] = L[i]
            i += 1
        else:
            A[k] = R[j]
            j += 1



Comp_count = 0
if __name__ == '__main__':
    # ??????????????\???
    num_of_data = int(eval(input()))
    S = array('I', [int(x) for x in input().split(' ')])

    #S = []
    #with open('ALDS1_5_B_in10.txt') as f:
    #    for line in f:
    #        if ' ' not in line:
    #           num_of_data = int(line)
    #       else:
    #           S = [int(x) for x in line.split(' ')]
    #S = [8, 5, 9, 2, 6, 3, 7, 1, 10, 4]


    # ????????????????????????
    merge_sort(S, 0, num_of_data)

    # ???????????????
    print(('{0}'.format(' '.join(map(str, S)))))
    print(Comp_count)
# Original solution
import sys
from subprocess import Popen, PIPE
from itertools import groupby
from collections import Counter

def main():
    N, *S = sys.stdin.read().split()
    T = []
    inv_dict = {}
    for s in S:
        factors = list(map(int, Popen(["factor", s], stdout=PIPE).communicate()[0].split()[1:]))
        t = 1
        t_inv = 1
        for f, group in groupby(factors):
            n = len(list(group)) % 3
            if n == 1:
                t *= f
                t_inv *= f * f
            elif n == 2:
                t *= f * f
                t_inv *= f
        T.append(t)
        inv_dict[t] = t_inv

    counter_T = Counter(T)
    ans = 0
    for t, t_cnt in list(counter_T.items()):
        if t == 1:
            ans += 1
            continue
        t_inv = inv_dict[t]
        t_inv_cnt = counter_T[t_inv]
        if t_cnt > t_inv_cnt or (t_cnt == t_inv_cnt and t > t_inv):
            ans += t_cnt
    print(ans)

main()


# Optimized solution
import sys
from collections import Counter

def make_prime_checker(n):
    # nまでの自然数が素数かどうかを表すリストを返す  O(nloglogn)
    is_prime = [False, True, False, False, False, True] * (n//6+1)
    del is_prime[n+1:]
    is_prime[1:4] = False, True, True
    for i in range(5, int(n**0.5)+1):
        if is_prime[i]:
            is_prime[i*i::i] = [False] * (n//i-i+1)
    return is_prime

def main():
    Primes = [p for p, is_p in enumerate(make_prime_checker(2200)) if is_p]
    def decomp(n):
        res1 = res2 = 1
        for p in Primes:
            cnt = 0
            while n % p == 0:
                n //= p
                cnt += 1
            cnt %= 3
            if cnt == 1:
                res1 *= p
            elif cnt == 2:
                res2 *= p
        if int(n**0.5)**2 == n:
            res2 *= int(n**0.5)
        else:
            res1 *= n
        return res1 * res2 * res2, res1 * res1 * res2

    N, *S = list(map(int, sys.stdin.buffer.read().split()))
    T = []
    inv_dict = {}
    for s in S:
        t, t_inv = decomp(s)
        T.append(t)
        inv_dict[t] = t_inv

    counter_T = Counter(T)
    ans = 0
    for t, t_cnt in list(counter_T.items()):
        if t == 1:
            ans += 1
            continue
        t_inv = inv_dict[t]
        t_inv_cnt = counter_T[t_inv]
        if t_cnt > t_inv_cnt or (t_cnt == t_inv_cnt and t > t_inv):
            ans += t_cnt
    print(ans)

main()
# Original solution
a,b,c,d = list(map(int,input().split()))
if a + b > c + d:
    print("Left")
elif a + b < c + d:
    print("Right")
else:
    print("Balanced")

# Optimized solution
a,b,c,d = list(map(int,input().split()))
e = a+b
f = c+d
if e < f:
    print("Right")
elif e > f:
    print("Left")
else:
    print("Balanced")
# Original solution
a, b, c, d = list(map(int, input().split()))
if a + b > c + d:
    print('Left')
elif a + b < c + d:
    print('Right')
else:
    print('Balanced')

# Optimized solution
a, b, c, d = list(map(int, input().split()))

print(('Left' if a + b > c + d else ('Balanced' if a + b == c + d else 'Right')))
# Original solution
N = int(eval(input()))

goods = ["2", "8"]
for i in range(9):
    goods += ["2" + g for g in goods] + ["8" + g for g in goods]
goods = list(map(int, goods))


def isgood(n):
    for c in str(n):
        if(c != '2' and c != '8'):
            return False
    return True


def ma(n, mi, nowma):
    if(n == 1):
        return 0
    if(n % 2 != 0):
        return -1
    mama = int(n**(1 / nowma))
    g = 2
    i = mi
    mamama = -1
    if(isgood(n)):
        mamama = 1
    while(g < mama + 3):
        if(n % g == 0):
            k = n // g
            newnowma = 2
            if(mamama > 2):
                newnowma = mamama
            if(newnowma < nowma - 1):
                newnowma = nowma - 1
            tma = ma(k, i, newnowma)
            t = tma + 1 if tma != -1 else -1
            if(t > mamama):
                mamama = t
        i += 1
        g = goods[i]
    return mamama
if(N == 1):
    print((-1))
else:
    print((ma(N, 0, 2)))

# Optimized solution
N = int(eval(input()))

goods = ["2", "8"]
for i in range(9):
    goods += ["2" + g for g in goods] + ["8" + g for g in goods]
goods = list(map(int, goods))
del goods[1]


def isgood(n):
    for c in str(n):
        if(c != '2' and c != '8'):
            return False
    return True


def ma(n, mi, nowma):
    if(n == 1):
        return 0
    if(n % 2 != 0):
        return -1
    mama = int(n**(1 / nowma))
    g = 2
    i = mi
    mamama = -1
    if(isgood(n)):
        mamama = 1
    while(g < mama + 3):
        if(n % g == 0):
            k = n // g
            newnowma = 2
            if(mamama > 2):
                newnowma = mamama
            if(newnowma < nowma - 1):
                newnowma = nowma - 1
            tma = ma(k, i, newnowma)
            t = tma + 1 if tma != -1 else -1
            if(t > mamama):
                mamama = t
        i += 1
        g = goods[i]
        # print(g)
    return mamama
if(N == 1):
    print((-1))
else:
    print((ma(N, 0, 2)))
# Original solution
a,b = (int(i) for i in input().split())
print(("Yes" if (a*b)&1 or (a*b*2)&1 or (a*b*3)&1 else "No"))

# Optimized solution
def main():
    a, b = (int(i) for i in input().split())
    ans = a*b
    if any(a*b*c % 2 == 1 for c in range(1, 4)):
        print("Yes")
    else:
        print("No")


if __name__ == '__main__':
    main()
# Original solution
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())

A,B = inpl()

if (A*B)%2 == 0:
	print('No')
else:
	print('Yes')


# Optimized solution
A,B = list(map(int,input().split()))
if (A*B)%2 == 0:
  print('No')
else:
  print('Yes')
# Original solution
A, B = list(map(int, input().split()))

if (A == 2) or (B == 2):
  print("No")
  
else:
  print("Yes")

# Optimized solution
A, B = list(map(int, input().split()))

if A == 2 or B == 2:
  print("No")
  
else: 
  print("Yes")
# Original solution
from bisect import bisect_left
from collections import defaultdict
from itertools import accumulate

n = int(eval(input()))
arr = list(map(int, input().split()))
arr.sort()
sa = sum(arr)
lim = sa // 2
dp = defaultdict(int)
dp[0] = 1

for a in arr:
    # print(a, dp)
    ndp = dp.copy()
    for i, v in list(dp.items()):
        if i + a <= lim:
            ndp[i + a] += v
    dp = ndp
    # print(a, dp)

dpk = list(dp.keys())
dpk.sort()
dpv = [dp[k] for k in dpk]
adp = list(accumulate(dpv))
k = 2 ** (n - 1)
j = bisect_left(adp, k)

# print(adp)
# print(k)

print((sa - dpk[j]))


# Optimized solution
n, arr, dp = int(eval(input())), list(map(int, input().split())), 1
for a in arr:
    dp |= dp << a
ofs = (sum(arr) + 1) // 2
dp >>= ofs
print(((dp & -dp).bit_length() + ofs - 1))
# Original solution
import sys

sys.setrecursionlimit(10**7)

N=int(eval(input()))
A=list(map(int,input().split()))

def condition(val):
    memo={}
    def dfs(num,count):
        if count>=val:
            return 0

        if (num,count) in memo:
            return memo[(num,count)]

        if num==N:
            memo[(num,count)]=int(val>count)
            return memo[(num,count)]

        ans=dfs(num+1,count+A[num])+dfs(num+1,count)
        memo[(num,count)]=ans
        return memo[(num,count)]

    return 2**(N-1)>dfs(0,0)-1

start=0
end=2000**2
while end-start>1:
    test=(start+end)//2
    if condition(test):
        start=test
    else:
        end=test

if condition(end):
    print(end)
else:
    print(start)

# Optimized solution
N=int(eval(input()))
A=list(map(int,input().split()))
S=sum(A)
if S%2==1:
    check=1
    for i in range(N):
        check=check|check<<A[i]
    for i in range(S//2+1,S+1):
        if check>>i &1==1:
            print(i)
            break
else:
    check=1
    for i in range(N):
        check=check|check<<A[i]

    for i in range(S//2,S+1):
        if check>>i &1==1:
            print(i)
            break