Harryxun/stf_run huggingface dataset:
N = int(input())
X = list(map(int, input().strip()))

count_j = X.count(1)

def calc_table(m):
	if m == 1:
		return [0] * N
	elif m == 0:
		return None
	table = []
	x = 1
	for i in range(N):
		table.append(x)
		x = (x * 2) % m
	table.reverse()
	return table

count_m = count_j - 1
count_p = count_j + 1

mod_m = calc_table(count_m)
mod_j = calc_table(count_j)
mod_p = calc_table(count_p)

original_j = 0
original_m = 0
original_p = 0
for i, b in enumerate(X):
	if b == 1:
		original_j = (original_j + mod_j[i]) % count_j
		original_m = (original_m + mod_m[i]) % count_m
		original_p = (original_p + mod_p[i]) % count_p

#print(mod_p)
#print(original_m, original_j, original_p)

f_cache = [None] * N
def calc_f(x):
	if x == 0:
		return 0
	f = f_cache[x]
	if f != None:
		return f
	count = 0
	i = x
	while i > 0:
		if i % 2 == 1:
			count += 1
		i //= 2
	f = calc_f(x % count) + 1
	f_cache[x] = f
	return f

for i, b in enumerate(X):
	if b == 0:
		x = (original_p + mod_p[i]) % count_p
	else:
		x = (original_m - mod_m[i]) % count_m
	print(calc_f(x) + 1)


### FIXED CODE ###

N = int(input())
X = list(map(int, input().strip()))

count_j = X.count(1)

def calc_table(m):
	if m == 1:
		return [0] * N
	elif m == 0:
		return None
	table = []
	x = 1
	for i in range(N):
		table.append(x)
		x = (x * 2) % m
	table.reverse()
	return table

count_m = count_j - 1
count_p = count_j + 1

mod_m = calc_table(count_m)
mod_j = calc_table(count_j)
mod_p = calc_table(count_p)

original_j = 0
original_m = 0
original_p = 0
if count_m > 0:
	for i, b in enumerate(X):
		if b == 1:
			original_j = (original_j + mod_j[i]) % count_j
			original_m = (original_m + mod_m[i]) % count_m
			original_p = (original_p + mod_p[i]) % count_p
else:
	for i, b in enumerate(X):
		if b == 1:
			original_j = (original_j + mod_j[i]) % count_j
			original_p = (original_p + mod_p[i]) % count_p
#print(mod_p)
#print(original_m, original_j, original_p)

f_cache = [None] * N
def calc_f(x):
	if x == 0:
		return 0
	f = f_cache[x]
	if f != None:
		return f
	count = 0
	i = x
	while i > 0:
		if i % 2 == 1:
			count += 1
		i //= 2
	f = calc_f(x % count) + 1
	f_cache[x] = f
	return f

for i, b in enumerate(X):
	if b == 0:
		x = (original_p + mod_p[i]) % count_p
		print(calc_f(x) + 1)
	else:
		if count_m > 0:
			x = (original_m - mod_m[i]) % count_m
			print(calc_f(x) + 1)
		else:
			print(0)
def gcd(a,b):
    if b>a:
        a,b=b,a
    while b:
        a,b=b, a%b
    return a

def f(a,b,N):
    l=[]
    for i in range(3):
        if a[i]<b[i]: l.append(i)

    if len(l)==0: return N
    if len(l)==1:
        l=l[0]
        return (N//a[l])*b[l]+N%a[l]
    elif len(l)==2:
        x,y=l[0],l[1]
        p,q=a[x],a[y]
        lcm=p*q//gcd(p,q)

        n1,n2=N-N%lcm,N%lcm
        ans1=max(n1*b[x]//p,n1*b[y]//q)
        i=0
        ans2=0
        while i*p<=n2:
            ans2=max(ans2,i*b[x]+((n2-i*p)//q)*b[y])
            i+=1
        return ans1+ans2
        
    else:
        p,q,r=a[0]
        lcm=a[0]*a[1]//gcd(a[0],a[1])
        lcm=lcm*a[2]//gcd(a[2],lcm)
        n1,n2=N-N%lcm,N%lcm
        ans1=max(n1*b[i]//a[i] for i in range(3))
        i=0
        ans2=0
        while i*a[0]<=n2:
            n3=n2-i*a[0]
            j=0
            while  j*a[1]<=n3:
                ans2=max(ans2,i*b[0]+j*b[1]+(n3-j*a[1])*b[2])
                j+=1
            i+=1
        return ans1+ans2

import sys
N=int(input())

a=list(map(int,input().split()))
b=list(map(int,input().split()))

N=f(a,b,N)
N=f(b,a,N)
print(int(N))

### FIXED CODE ###

def f(a,b,N):

    tmpa,tmpb=[],[]
    for i in range(3):
        if a[i]<b[i]:
            tmpa.append(a[i])
            tmpb.append(b[i])
    a,b=tmpa,tmpb

    if len(a)==0: return N
    elif len(a)==1: return (N//a[0])*b[0]+N%a[0]

    elif len(a)==2:
        if a[0]<a[1]: a,b=a[::-1],b[::-1]

        i,ans=0,N
        while i*a[0]<=N:
            j=(N-i*a[0])//a[1]
            ans=max(ans,i*b[0]+j*b[1]+(N-i*a[0]-j*a[1]))
            i+=1
        return ans

    else:
        memo=[i for i in range(N+1)]

        for i in range(1,N+1):
            tmp=[]
            for j in range(len(a)):
                if i-a[j]>=0: tmp.append(memo[i-a[j]]+b[j])
            if tmp!=[]: memo[i]=max(tmp)
        return memo[N]

import sys
N=int(input())

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

N=f(A,B,N)
N=f(B,A,N)
print(N)
S = list(input())
T = list(input())

for i in range(len(S)):
	tmp = S[i:] + [:i]
	if T == tmp:
		print('Yes')
		break
print('No') 

### FIXED CODE ###

S = list(input())
T = list(input())

for i in range(len(S)):
	tmp = S[i:] + S[:i]
	if T == tmp:
		print('Yes')
		exit()
print('No')
if 3200 <= a:
  print(s)
else:
  print('red')

### FIXED CODE ###

a = int(input())
s = input()
if 3200 <= a:
  print(s)
else:
  print('red')
S,W=map(int, input().split())
 
if S>W:
	print("safe")
if S<W:
	print("unsafe")
if S=W:
	print("unsafe")

### FIXED CODE ###

S,W=map(int, input().split())
 
if S>W:
	print("safe")
if S<W:
	print("unsafe")
if S==W:
	print("unsafe")
A = int(input()).split()
if A.count.("5") == 2 and A.count("7")==1:
	print("YSE")
else:
	print("NO")

### FIXED CODE ###

A = input().split()
if A.count('5') == 2 and A.count('7')==1:
	print("YES")
else:
	print("NO")
A=int(input())
B=int(input())
C=int(input())
D=int(input())

if A>B:
	if C>D:
		print(B+D)
	else:
		print(B+C)
else:
	if C>D:
		print(A+D)
	else:

print(A+C)

### FIXED CODE ###


A=int(input())
B=int(input())
C=int(input())
D=int(input())

if A>B:
	if C>D:
		print(B+D)
	else:
		print(B+C)
else:
	if C>D:
		print(A+D)
	else:
		print(A+C)
def palindrome(s):
  for i in range(len(s) // 2):
    if s[i] != s[-i -1]:
      return False
  return True

def main():
  s = input()
  t = ''
  for ch in s:
    if ch != 'x':
      t += ch

  if (palindrome(t) == False):
    print(-1)
    return

  cnt = 0
  odd = len(t) & 1
  mid = len(t) // 2

  if odd == 1:  # ax[b]a

    for i in range(len(s)):
      if s[i] != 'x':
        cnt += 1
        if cnt == mid + 1:
          s1 = s[      : i]
          s2 = s[i + 1 :  ]
          break    

  else: # a[x]a

    for i in range(len(s)):
      if s[i] != 'x':
        cnt += 1
        if cnt == mid:
          s1 = s[  : i + 1]
        if cnt == mid + 1:
          s2 = s[i :  ]
          break

  st = ''
  for ch in s2:
    st = ch + st

  # print(s1, st)
  ans = 0
  i = 0
  j = 0
  while (i < len(s1) and j < len(st)):
    c1 = s1[i]
    c2 = st[j]
    if c1 == c2:
      i += 1
      j += 1
      continue

    ans += 1
    if c1 == 'x':
      i += 1
    else:
      j += 1

  ans += (len(s1) - i) + (len(st) - j)
  print(ans)






if __name__ == '__main__':
  main()

### FIXED CODE ###

def palindrome(s):
  for i in range(len(s) // 2):
    if s[i] != s[-i -1]:
      return False
  return True

def main():
  s = input()
  t = ''
  for ch in s:
    if ch != 'x':
      t += ch

  if len(t) == 0:
    print(0)
    return

  if (palindrome(t) == False):
    print(-1)
    return

  cnt = 0
  odd = len(t) & 1
  mid = len(t) // 2

  if odd == 1:  # ax[b]a

    for i in range(len(s)):
      if s[i] != 'x':
        cnt += 1
        if cnt == mid + 1:
          s1 = s[      : i]
          s2 = s[i + 1 :  ]
          break    

  else: # a[x]a

    for i in range(len(s)):
      if s[i] != 'x':
        cnt += 1
        if cnt == mid:
          s1 = s[  : i + 1]
        if cnt == mid + 1:
          s2 = s[i :  ]
          break

  # print(s1, s2)
  ans = 0
  i = 0
  j = 0
  while (i < len(s1) and j < len(s2)):
    c1 = s1[i]
    c2 = s2[-j-1]
    if c1 == c2:
      i += 1
      j += 1
      continue

    ans += 1
    if c1 == 'x':
      i += 1
    else:
      j += 1

  ans += (len(s1) - i) + (len(s2) - j)
  print(ans)






if __name__ == '__main__':
  main()
S = int(input())
K = int(input())
l = [int(x) for x in list(str(S))]
length = len(l)
flag=0
i=0
ans = 0
while flag ==0:
    if l[i] == 1 or l[i]==0:
        i = i + 1
    else:
        flag=1
        ans = l[i]
if len(l)>=K:
    ans = S[K-1]
print(ans)


### FIXED CODE ###

S = int(input())
K = int(input())
l = [int(x) for x in list(str(S))]
flag=0
flag2=0
i=0
j=0
ans = 0
if K<=len(l):
    while j<K and flag2 == 0:
        if l[j] == 1 or l[j]==0:
            ans = l[j]
            j = j + 1
        else:
            flag2 =1
            ans = l[j]
else:
    while flag ==0:
        if l[i] == 1 or l[i]==0:
            i = i + 1
        else:
            flag=1
            ans = l[i]
print(ans)
import sys
from collections import Counter
from heapq import heapify, heappop, heappush
read = sys.stdin.read

N, K, *td = map(int, read().split())
dt = sorted(zip(td[1::2], td[::2]), reverse=True)

candidates = []
neta_group = Counter([j for i, j in dt[:K]])
number = len(neta_group)
points = sum([i for i, j in dt[:K]]) + number ** 2
candidates.append(points)

heap = [(-i, j) for i, j in dt[K:]]
heapify(heap)
manzoku = dt[:K]
heapify(manzoku)

while heap:
    oishisa, neta = heappop(heap)
    oishisa = -oishisa
    if not neta_group.get(neta):
        oishisa2, neta2 = heappop(manzoku)
        if neta_group[neta2] == 1:
            heappush(heap, (-oishisa2, neta2))
        else:
            neta_group[neta2] -= 1
            neta_group[neta] = 1
            heappush(heap, (-oishisa, neta))
            points = points - oishisa2 + oishisa - number ** 2 + (number + 1) ** 2

            number += 1
            candidates.append(points)

print(max(candidates))

### FIXED CODE ###

import sys
from operator import itemgetter
read = sys.stdin.read

N, K, *td = map(int, read().split())
td = sorted(zip(*[iter(td)] * 2), key=itemgetter(1), reverse=True)

stack = []
taste = 0
neta_group = set()
for t, d in td[:K]:
    taste += d
    if t in neta_group:
        stack.append(d)
    else:
        neta_group.add(t)

variety = len(neta_group)
candidates = [taste + variety ** 2]

if N == K:
    print(candidates[0])
    exit()

rest = list(reversed(td[K::]))

while rest and stack:
    t1, d1 = rest.pop()
    if t1 not in neta_group:
        neta_group.add(t1)
        d2 = stack.pop()
        variety += 1
        taste = taste - d2 + d1

        candidates.append(taste + variety ** 2)

print(max(candidates))
sunuke=[]
for i in range(16):
    for j in range(1,10):
        sunuke.append(j*10**i+(10**i-1))

for i in range(int(input())):
    print(sunuke[i])

### FIXED CODE ###

def f(n):
    s=str(n)
    return sum([int(s[i]) for i in range(len(s))])

sunuke=[]
for i in range(16):
    for j in range(1,500):
        sunuke.append(j*(10**i)-1)

sunuke=list(set(sunuke))
sunuke.sort()
sunuke.pop(0)
L=len(sunuke)

tmp1,tmp2=sunuke[L-1],f(sunuke[L-1])
ans=[sunuke[L-1]]
for i in range(len(sunuke)-2,-1,-1):
    x=sunuke[i]
    if x*tmp2<=tmp1*f(x):
        ans.append(x)
        tmp1,tmp2=x,f(x)

ans.sort()

    

for i in range(int(input())):
    print(ans[i])
data = input()
target = input()

start = 0
flag = "No"
for i in target:
    if(data[start:].find(i)):
        start = data[start:].find(i)
    elif(data[:start].find(i)):
        start = data.[:start:].find(i)
    else:
        print("No")
        break
    if(i == target[-1]):
        print("Yes")
        break


### FIXED CODE ###

s = input()*2
p = input()
print("Yes" if p in s else "No")
n,k=map(int,input().split())
l=soted(map(int,input().split()))
def gcd(x,y):
  if y==0:return x
  return gcd(y,x%y)
ans=""
s=0
for i in l:
  s=gcd(i,s)
  if s==1:break
else:
  if k%s!=l[-1]%s:
    ans="IM"
print(ans+"POSSIBLE")

### FIXED CODE ###

n,k=map(int,input().split())
l=sorted(map(int,input().split()))
def gcd(x,y):
  if y==0:return x
  return gcd(y,x%y)
ans=""
s=0
for i in l:
  s=gcd(i,s)
  if s==1:break
else:
  if k%s!=l[-1]%s:
    ans="IM"
if l[-1]<k:ans="IM"
print(ans+"POSSIBLE")
#! /usr/bin/env python3
 
# from fractions import gcd
from math import gcd
from collections import Counter, deque, defaultdict
from heapq import heappush, heappop, heappushpop, heapify, heapreplace, merge
from bisect import bisect_left, bisect_right, bisect, insort_left, insort_right, insort
from itertools import accumulate, product, permutations, combinations, combinations_with_replacement
 
N, K = [int(_) for _ in input().split()]
A = [int(_) for _ in input().split()]
 
root = [1]
index = 0
 
for i in range(K):
    if A[index] in root:
        ho = root.index(A[index])
        hoge = root[ho:]
        break
 
    root += [A[index]]
    index = A[index] - 1
 
nokori = (K-ho) % len(hoge)
 
print(hoge[nokori])

### FIXED CODE ###

#! /usr/bin/env python3

from fractions import gcd
# from math import gcd
from collections import Counter, deque, defaultdict
from heapq import heappush, heappop, heappushpop, heapify, heapreplace, merge
from bisect import bisect_left, bisect_right, bisect, insort_left, insort_right, insort
from itertools import accumulate, product, permutations, combinations, combinations_with_replacement

N, K = [int(_) for _ in input().split()]
A = [int(_) for _ in input().split()]

flag = 0
done = [0] * (N + 1)

root = []
ind = 0

ind = A[0]
root = [1]
done[1] = 1

while True:

    if done[ind]:
        flag = 1
        break
    done[ind] = 1

    root += [ind]
    ind = A[ind-1]

if flag:
    if len(root) <= K:
        left = root.index(ind) - 1
        loopcnt = len(root) - (root.index(ind))

        root2 = root[left+1:]
        print(root2[(K-(left+1)) % loopcnt])
    else:
        print(root[K])
else:
    print(root[K-1])
import numpy as np
class AdjDiGraph:
     def __init__(self,g):
          lines = g.split("\n")
          self.size = int(lines[0])+1 
          self.adjMatrix = np.zeros((self.size, self.size)) # 指定された大きさで要素が0の行列を生成する
          for s in lines[1:]:
               d1,d2 = s.split(" ")
               self.connect(int(d1),int(d2))
          self.adjMatrix=np.dot(np.dot(self.adjMatrix,self.adjMatrix),self.adjMatrix)
     def connect(self, x, y):
          self.connect1(x,y)            
     def connect1(self, x, y):
          self.adjMatrix[x][y] = 1
     def connected(self,x,y):
          return self.adjMatrix[x][y] == 1

     def traceByPower(self,start,end,rememberA=None,kaisu=None):
          if rememberA==None:
               c=self.adjMatrix
               rememberA=[self.adjMatrix]
               for i in range(2,self.size):
                    c=np.dot(c,self.adjMatrix)
                    rememberA.append(c)
        
          if kaisu==None:
               kaisu=0
               for A_i in rememberA:
                    kaisu+=1
                    if A_i[start][end]!=0:
                         return self.traceByPower(start,end,rememberA,kaisu)
          else:
               if kaisu==1:
                    return [start,end]
               else:
                    for i in range(1,kaisu):#startからi回でinterchange(中継地点)、interchangeからendをkaisu-i回で行く
                         for interchange in range(self.size):
                              if rememberA[i-1][start][interchange]!=0 and rememberA[kaisu-i-1][interchange][end]!=0:
                                   return self.traceByPower(start,interchange,rememberA,i)[:-1]+self.traceByPower(interchange,end,rememberA,kaisu-i)



n,m=map(int,input().split())
g=[str(n),"\n"]
for i in range(m):
     g.append(input())
     g.append("\n")
graph = AdjDiGraph("".join(g[:-1]))
s,t=map(int,input().split())
ans=graph.traceByPower(s,t)
if ans==None:
     print(-1)
else:
     print(len(ans)-1)

### FIXED CODE ###

import sys
input = sys.stdin.readline
 
def main():
     n,m=map(int,input().split())
     field=[[] for i in range(3*n)]
     for i in range(m):
          x,y=map(int,input().split())
          x,y=x-1,y-1
          field[3*x].append(3*y+1)
          field[3*x+1].append(3*y+2)
          field[3*x+2].append(3*y)
     
     s,t=map(int,input().split())
     s,t=s-1,t-1
     s,t=3*s,3*t
     
     d=[float('inf') for i in range(3*n)]
     d[s]=0
     
     que=[s]
     cnt=0
     while que!=[]:
          que2=[]
          cnt+=1
          for i in que:
               for j in field[i]:
                    if d[j]>cnt:
                         d[j]=cnt
                         que2.append(j)
          que=que2
     if d[t]==float('inf'):
          print(-1)
     else:
          print(d[t]//3)
     return 
 
if __name__ == '__main__':
    main()
a,b,c=input().split()

if a[0]==b[-1] anb b[0] == c[-1]:
  print('YES')
else:
  print('NO')


### FIXED CODE ###

a,b,c=input().split()
 
if a[-1]==b[0] and b[-1] == c[0]:
  print('YES')
else:
  print('NO')
import  math
lis = []

N,M = [int(i) for i in input().split()]

for i in range(1,int(math.sqrt(M))):
    if M % i == 0:
        lis.append(i)
        lis.append(M//i)


lis.sort()
for i in lis:
    if i >= N:
        break

print(M//i3 )


### FIXED CODE ###

import  math
lis = []

N,M = [int(i) for i in input().split()]

for i in range(1,int(math.sqrt(M))):
    if M % i == 0:
        lis.append(i)
        lis.append(M//i)


lis.sort()
i =1
for i in lis:
    if i >= N:
        break

print(M//i )
N, K, C = map(int, input().split())
S = list(input())
#left_greedy
countr = 0
countl = 0
switchr = 0
switchl = 0
left_greedy = [0]*len(S)
right_greedy=[0]*len(S)
#left
for l in range(len(S)):
    i = S[l]
    if switchl ==1:
        if i == 'o':
            if countl >= C:
                left_greedy[l]=1
                clist[l] = countl
                countl = 0
            else:
                countl+=1
                clist[l] = countl
        else:
            countl+=1
    else:
        if i == 'o':
            left_greedy[l]=1
            switchl+=1
#right_greedy
    r = len(S)-l-1
    i = S[r]
    if switchr ==1:
        if i == 'o':
            if countr >= C:
                right_greedy[r]=1
                
                countr = 0
            else:
                countr+=1
        else:
            countr+=1
            
    else:
        if i == 'o':
            right_greedy[r]=1
            switchr+=1
for n in range(len(S)):
    if left_greedy[n] == right_greedy[n]==1:
        print(n+1)

### FIXED CODE ###

X, Y, Z = map(int, input().split())
print("{} {} {}".format(Z,X,Y))
from collections import defaultdict
from operator import itemgetter

n, a, b, c, *L = map(int, open(0).read().split())
L.sort()
A = [a, b, c]
dicts = [defaultdict(lambda: 10**5) for _ in range(3)]
for i in range(n-2):
    for x in combinations(enumerate(L), i+1):
        k = tuple(i for i, l in x)
        v = sum(l for i, l in x)
        for d, x in zip(dicts, A):
            d[k] = min(d[k], abs(x-v) + 10*i)
scores = [sorted(d.items(), key=itemgetter(1)) for d in dicts]

ans = 10**5
for p1, p2, p3 in permutations(range(3)):
    k1, v1 = scores[p1][0]
    k1 = set(k1)
    for k2, v2 in scores[p2]:
        k2 = set(k2)
        if len(k1 & k2) == 0:
            break
    for k3, v3 in scores[p3]:
        k3 = set(k3)
        if len(k1 & k3) + len(k2 & k3) == 0:
            break
    ans = min(ans, sum([v1, v2, v3]))
print(ans)

### FIXED CODE ###

from collections import defaultdict
from itertools import combinations, permutations
from operator import itemgetter
n, a, b, c, *L = map(int, open(0).read().split())
L.sort()
A = [a, b, c]
dicts = [defaultdict(lambda: 10**5) for _ in range(3)]
for i in range(n-2):
    for x in combinations(enumerate(L), i+1):
        k = tuple(i for i, l in x)
        v = sum(l for i, l in x)
        for d, x in zip(dicts, A):
            d[k] = min(d[k], abs(x-v) + 10*i)
scores = [sorted(d.items(), key=itemgetter(1)) for d in dicts]

ans = 10**5
for p1, p2, p3 in permutations(range(3)):
    k1, v1 = scores[p1][0]
    k1 = set(k1)
    for k2, v2 in scores[p2]:
        k2 = set(k2)
        if len(k1 & k2) == 0:
            break
    for k3, v3 in scores[p3]:
        k3 = set(k3)
        if len(k1 & k3) + len(k2 & k3) == 0:
            break
    ans = min(ans, sum([v1, v2, v3]))
print(ans)
import math
N = int(input())
ps = []
minx = float('inf')
miny = float('inf')
mini = None
for i in range(N):
  x, y = map(int, input().split())
  if x < minx or (x == minx and y < miny):
    minx = x
    miny = y
    mini = i
  ps.append((x, y))

if len(ps) == 2:
  print(0.5)
  print(0.5)
  exit()

# 2点の2等分線の単位ベクトルを返す
# i -> j に対して右方向
def divvector(xi, yi, xj, yj):
  if xi == xj:
    if yj > yi: return (1, 0)
    else: return (-1, 0)
  elif yi == yj:
    if xj > xi: return (0, -1)
    else: return (0, 1)

  a = (yi - yj) / (xi - xj) # 傾き
  b = (1/a**2)
  x = math.sqrt(1/(1+b))
  y = math.sqrt(b/(1+b))
  if xj > xi:
    if yj > yi: return (x, -y)
    else: return (-x, -y)
  else:
    if yj > yi: return (x, y)
    else: return (-x, y)

# p1 -> p0 -> p2 が時計回りかどうか
def clockwise(x0, y0, x1, y1, x2, y2):
  return (x1 - x0) * (y2 - y0) - (x2 - x0) * (y1 - y0) <= 0

# 反時計回りに、凸包を求める
first = now = mini
convexs = [now]
divvecs = { now: [] }
end = False
while not end:
  xnow = ps[now][0]
  ynow = ps[now][1]
  for j in range(N):
    if j == now or j != first and j in divvecs: continue
    xj = ps[j][0]
    yj = ps[j][1]
    for k in range(N):
      if k == now or k == j: continue
      if not clockwise(xj, yj, xnow, ynow, ps[k][0], ps[k][1]):
        break
    else:
      convexs.append(j)
      divv = divvector(xnow, ynow, xj, yj)
      if j not in divvecs:
        divvecs[j] = []
      divvecs[j].append(divv)
      divvecs[now].append(divv)
      now = j
      if now == first:
        end = True
      break

# 凸包を構成する各頂点について、
# 隣の頂点との二等分線のなす角を360度で割ったものが確率
# 凸包を構成しない点については、確率はほぼ0
for i in range(N):
  if i not in convexs:
    print(0)
    continue
  v1, v2 = divvecs[i]
  # すでに単位ベクトルになっているので、cos = 内積
  cos = v1[0]*v2[0] + v1[1]*v2[1]
  print(math.acos(cos) / (2*math.pi))

### FIXED CODE ###

import math
N = int(input())
ps = []
for i in range(N):
  x, y = map(int, input().split())
  ps.append((x, y, i))
ps.sort()

# i -> j のベクトル
def vec(pi, pj):
  return (pj[0] - pi[0], pj[1] - pi[1])
# i -> j 向きの外積
def det(vi, vj):
  return vi[0] * vj[1] - vi[1] * vj[0]

# 凸包を求める
cvx = []
for i in list(range(N)) + list(range(N-1))[::-1]:
  while len(cvx) >= 2 and det(vec(ps[cvx[-2]], ps[cvx[-1]]), vec(ps[cvx[-1]], ps
[i])) < 0:
    cvx.pop()
  cvx.append(i)

# 凸包の各頂点について、頂点から出る2辺のなす角を計算
ans = {}
pi = None
for i in cvx:
  x, y, j = ps[i]
  if pi is not None:
    px, py, pj = ps[pi]
    slope = math.atan2(y-py, x-px)
    if j not in ans: ans[j] = [0, 0]
    if pj not in ans: ans[pj] = [0, 0]
    ans[j][0] = slope
    ans[pj][1] = slope
  pi = i

for i in range(N):
  if i not in ans:
    print(0)
    continue
  v1, v2 = ans[i]
  if v2 < v1:
    v2 += 2*math.pi
  print(round((v2-v1) / (2*math.pi), 8))
import numpy as np

N = int(input())
A = np.array(list(map(int,input().split())))
B = np.array(list(map(int,input().split())))
Bsi = np.argsort(B)
A2 = A[Bsi]
Bs = B[Bsi]
A2si = np.argsort(A2)
As = A2[A2si]
C = Bs-As
if any(C[C<0]):
    ans = 'No'
else:
    D = A2-As
    if any(D == 0):
        ans = 'Yes'
    elif all(As[1::]-Bs[:-1:] > 0):
        psum = A2si[0]
        for i,pi in enumerate(A2si[1:-1],1):
            psum += pi
            if psum == int(i*(i+1)/2):
                ans = 'Yes'
                break
        else:
            ans = 'No'
    else:
        ans = 'Yes'
        
print(ans)

### FIXED CODE ###

N = int(input())

if N%2 == 0:
    print(int(N//2-1))
else:
    print(int((N+1)//2-1))
n, k = map(int, input().split())
a = list(map(int, input().split()))
l = [1]
for i in range(n):
    if a[l[i] - 1] in l:
        res = l[:l.index(a[l[i] - 1])]
        cyc = l[l.index(a[l[i] - 1]):]
        break
    else:
        l += [a[l[i] - 1]]
print(cyc[(k - len(res)) % len(cyc)] if k > len(res) else res[k])

### FIXED CODE ###

n, k = map(int, input().split())
a = list(map(lambda x: int(x) - 1, input().split()))
visited = [-1 for _ in range(n)]
visited[0] = 0
l = [0]
for i in range(k):
    nex = a[l[i]]
    if visited[nex] != -1:
        res = visited[nex]
        cyc = i + 1 - visited[nex]
        break
    else:
        l += [nex]
        visited[nex] = i + 1
else:
    res = k + 1
print(l[res + (k - res) % cyc] + 1 if k > res else l[k] + 1)