text stringlengths 198 433k | conversation_id int64 0 109k |
|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vus the [Cossack](https://en.wikipedia.org/wiki/Cossacks) holds a programming competition, in which n people participate. He decided to award them all with pens and notebooks. It is known that Vus has exactly m pens and k notebooks.
Determine whether the Cossack can reward all participants, giving each of them at least one pen and at least one notebook.
Input
The first line contains three integers n, m, and k (1 ≤ n, m, k ≤ 100) — the number of participants, the number of pens, and the number of notebooks respectively.
Output
Print "Yes" if it possible to reward all the participants. Otherwise, print "No".
You can print each letter in any case (upper or lower).
Examples
Input
5 8 6
Output
Yes
Input
3 9 3
Output
Yes
Input
8 5 20
Output
No
Note
In the first example, there are 5 participants. The Cossack has 8 pens and 6 notebooks. Therefore, he has enough pens and notebooks.
In the second example, there are 3 participants. The Cossack has 9 pens and 3 notebooks. He has more than enough pens but only the minimum needed number of notebooks.
In the third example, there are 8 participants but only 5 pens. Since the Cossack does not have enough pens, the answer is "No".
Submitted Solution:
```
string = input()
li = string.split(" ")
n = int(li[0])
m = int(li[1])
k = int(li[2])
#print(n,m,k)
if (k>=n) and (m>=n):
print("Yes")
else:
print("No")
```
Yes
| 106,200 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vus the [Cossack](https://en.wikipedia.org/wiki/Cossacks) holds a programming competition, in which n people participate. He decided to award them all with pens and notebooks. It is known that Vus has exactly m pens and k notebooks.
Determine whether the Cossack can reward all participants, giving each of them at least one pen and at least one notebook.
Input
The first line contains three integers n, m, and k (1 ≤ n, m, k ≤ 100) — the number of participants, the number of pens, and the number of notebooks respectively.
Output
Print "Yes" if it possible to reward all the participants. Otherwise, print "No".
You can print each letter in any case (upper or lower).
Examples
Input
5 8 6
Output
Yes
Input
3 9 3
Output
Yes
Input
8 5 20
Output
No
Note
In the first example, there are 5 participants. The Cossack has 8 pens and 6 notebooks. Therefore, he has enough pens and notebooks.
In the second example, there are 3 participants. The Cossack has 9 pens and 3 notebooks. He has more than enough pens but only the minimum needed number of notebooks.
In the third example, there are 8 participants but only 5 pens. Since the Cossack does not have enough pens, the answer is "No".
Submitted Solution:
```
n,p,m=map(int,input().split())
if p>=n and m>=p:
print('Yes')
else:
print('No')
```
No
| 106,201 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vus the [Cossack](https://en.wikipedia.org/wiki/Cossacks) holds a programming competition, in which n people participate. He decided to award them all with pens and notebooks. It is known that Vus has exactly m pens and k notebooks.
Determine whether the Cossack can reward all participants, giving each of them at least one pen and at least one notebook.
Input
The first line contains three integers n, m, and k (1 ≤ n, m, k ≤ 100) — the number of participants, the number of pens, and the number of notebooks respectively.
Output
Print "Yes" if it possible to reward all the participants. Otherwise, print "No".
You can print each letter in any case (upper or lower).
Examples
Input
5 8 6
Output
Yes
Input
3 9 3
Output
Yes
Input
8 5 20
Output
No
Note
In the first example, there are 5 participants. The Cossack has 8 pens and 6 notebooks. Therefore, he has enough pens and notebooks.
In the second example, there are 3 participants. The Cossack has 9 pens and 3 notebooks. He has more than enough pens but only the minimum needed number of notebooks.
In the third example, there are 8 participants but only 5 pens. Since the Cossack does not have enough pens, the answer is "No".
Submitted Solution:
```
string = input()
li = string.split(" ")
n = li[0]
m = li[1]
k = li[2]
if (k>=n) and (m>=n):
print("Yes")
else:
print("No")
```
No
| 106,202 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vus the [Cossack](https://en.wikipedia.org/wiki/Cossacks) holds a programming competition, in which n people participate. He decided to award them all with pens and notebooks. It is known that Vus has exactly m pens and k notebooks.
Determine whether the Cossack can reward all participants, giving each of them at least one pen and at least one notebook.
Input
The first line contains three integers n, m, and k (1 ≤ n, m, k ≤ 100) — the number of participants, the number of pens, and the number of notebooks respectively.
Output
Print "Yes" if it possible to reward all the participants. Otherwise, print "No".
You can print each letter in any case (upper or lower).
Examples
Input
5 8 6
Output
Yes
Input
3 9 3
Output
Yes
Input
8 5 20
Output
No
Note
In the first example, there are 5 participants. The Cossack has 8 pens and 6 notebooks. Therefore, he has enough pens and notebooks.
In the second example, there are 3 participants. The Cossack has 9 pens and 3 notebooks. He has more than enough pens but only the minimum needed number of notebooks.
In the third example, there are 8 participants but only 5 pens. Since the Cossack does not have enough pens, the answer is "No".
Submitted Solution:
```
q,w,e = input().split()
q = int(q)
w = int(w)
e = int(e)
def check(a,s,d):
if a/s >= 1 :
if a/d >= 1 :
print("yes")
else:
print("no")
else:
print("no")
check(q,w,e)
```
No
| 106,203 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vus the [Cossack](https://en.wikipedia.org/wiki/Cossacks) holds a programming competition, in which n people participate. He decided to award them all with pens and notebooks. It is known that Vus has exactly m pens and k notebooks.
Determine whether the Cossack can reward all participants, giving each of them at least one pen and at least one notebook.
Input
The first line contains three integers n, m, and k (1 ≤ n, m, k ≤ 100) — the number of participants, the number of pens, and the number of notebooks respectively.
Output
Print "Yes" if it possible to reward all the participants. Otherwise, print "No".
You can print each letter in any case (upper or lower).
Examples
Input
5 8 6
Output
Yes
Input
3 9 3
Output
Yes
Input
8 5 20
Output
No
Note
In the first example, there are 5 participants. The Cossack has 8 pens and 6 notebooks. Therefore, he has enough pens and notebooks.
In the second example, there are 3 participants. The Cossack has 9 pens and 3 notebooks. He has more than enough pens but only the minimum needed number of notebooks.
In the third example, there are 8 participants but only 5 pens. Since the Cossack does not have enough pens, the answer is "No".
Submitted Solution:
```
j=input().split()
n,m,k=j[0],j[1],j[2]
if n<=m or n<=k:
print("Yes")
else:
print("No")
```
No
| 106,204 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Tags: constructive algorithms, greedy, math
Correct Solution:
```
n=int(input())
if n%2:
print("YES")
ls=[0]*2*n
c=1
i=-1
while c<=2*n:
i=i+1
ls[i]=c
i=(i+n)%(2*n)
ls[i]=c+1
c=c+2
print(*ls)
else:
print("NO")
```
| 106,205 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Tags: constructive algorithms, greedy, math
Correct Solution:
```
def almost_equal(n):
if n%2==0:
return None
else:
r = [1]
r2 = [2]
m = 1
while m<n:
m += 2
r += [2*m,2*m -3]
r2 += [2*m-1,2*m-2]
return r+r2
n = int(input().strip())
r = almost_equal(n)
if r:
print("YES")
print(' '.join([str(x) for x in r]))
else:
print("NO")
```
| 106,206 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Tags: constructive algorithms, greedy, math
Correct Solution:
```
n = int(input())
a = [0] * (2*n)
curr = 1
for i in range(n):
if i%2 == 0:
a[i] = curr
curr += 1
a[i+n] = curr
curr += 1
else:
a[i+n] = curr
curr += 1
a[i] = curr
curr += 1
arr = a + a[:n-1]
s = set()
window = sum(a[:n])
s.add(window)
for i in range(n, 3*n-1):
window += arr[i]
window -= arr[i-n]
s.add(window)
if len(s) > 2:
print("NO")
else:
print("YES")
print(*a)
```
| 106,207 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Tags: constructive algorithms, greedy, math
Correct Solution:
```
n = int(input())
n2 = 2 * n
if n == 1:
print('YES\n1 2')
else:
a = [None] * n2
now = n2
flag = True
for i in range(n):
if flag:
a[i] = now
a[n + i] = now - 1
else:
a[i] = now - 1
a[n + i] = now
flag = 1 - flag
now -= 2
min_ans = sum(a[:n])
max_ans = min_ans
now = min_ans
for i in range(n2):
now -= a[i]
now += a[(n + i) % n2]
min_ans = min(min_ans, now)
max_ans = max(max_ans, now)
if max_ans - min_ans > 1:
print('NO')
else:
print('YES')
print(' '.join(list(map(str, a))))
```
| 106,208 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Tags: constructive algorithms, greedy, math
Correct Solution:
```
n=int(input())
if(n%2!=0):
a=[0]*(2*n+1)
for i in range(1,n+1):
if(i%2==1):
a[i]=2*i
a[n+i]=2*i-1
else:
a[i]=2*i-1
a[n+i]=2*i
print("YES")
for i in range(1,2*n+1):
print(a[i],end=' ')
else:
print("NO")
```
| 106,209 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Tags: constructive algorithms, greedy, math
Correct Solution:
```
n = int(input())
a = [1]
b = []
counter = 2
for i in range(2, 2*n + 1):
if counter < 2:
a.append(i)
else:
b.append(i)
counter = (counter + 1) % 4
c = a + b
sums = []
sum = 0
for i in range(n):
sum += c[i]
sums.append(sum)
for i in range(len(c) - n):
sum = sum - c[i] + c[i + n]
sums.append(sum)
sum = sum - c[len(c) - n] + c[0]
sums.append(sum)
answer = True
comp = sorted(sums)[-1]
for i in sums:
if(abs(i - comp) > 1):
answer = False
#print(sums)
if(answer):
print('YES')
print(*a, *b)
else: print('NO')
```
| 106,210 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Tags: constructive algorithms, greedy, math
Correct Solution:
```
def divisors(M):
d=[]
i=1
while M>=i**2:
if M%i==0:
d.append(i)
if i**2!=M:
d.append(M//i)
i=i+1
return d
def popcount(x):
x = x - ((x >> 1) & 0x55555555)
x = (x & 0x33333333) + ((x >> 2) & 0x33333333)
x = (x + (x >> 4)) & 0x0f0f0f0f
x = x + (x >> 8)
x = x + (x >> 16)
return x & 0x0000007f
def eratosthenes(n):
res=[0 for i in range(n+1)]
prime=set([])
for i in range(2,n+1):
if not res[i]:
prime.add(i)
for j in range(1,n//i+1):
res[i*j]=1
return prime
def factorization(n):
res=[]
for p in prime:
if n%p==0:
while n%p==0:
n//=p
res.append(p)
if n!=1:
res.append(n)
return res
def euler_phi(n):
res = n
for x in range(2,n+1):
if x ** 2 > n:
break
if n%x==0:
res = res//x * (x-1)
while n%x==0:
n //= x
if n!=1:
res = res//n * (n-1)
return res
def ind(b,n):
res=0
while n%b==0:
res+=1
n//=b
return res
def isPrimeMR(n):
d = n - 1
d = d // (d & -d)
L = [2, 3, 5, 7, 11, 13, 17]
for a in L:
t = d
y = pow(a, t, n)
if y == 1: continue
while y != n - 1:
y = (y * y) % n
if y == 1 or t == n - 1: return 0
t <<= 1
return 1
def findFactorRho(n):
from math import gcd
m = 1 << n.bit_length() // 8
for c in range(1, 99):
f = lambda x: (x * x + c) % n
y, r, q, g = 2, 1, 1, 1
while g == 1:
x = y
for i in range(r):
y = f(y)
k = 0
while k < r and g == 1:
ys = y
for i in range(min(m, r - k)):
y = f(y)
q = q * abs(x - y) % n
g = gcd(q, n)
k += m
r <<= 1
if g == n:
g = 1
while g == 1:
ys = f(ys)
g = gcd(abs(x - ys), n)
if g < n:
if isPrimeMR(g): return g
elif isPrimeMR(n // g): return n // g
return findFactorRho(g)
def primeFactor(n):
i = 2
ret = {}
rhoFlg = 0
while i*i <= n:
k = 0
while n % i == 0:
n //= i
k += 1
if k: ret[i] = k
i += 1 + i % 2
if i == 101 and n >= 2 ** 20:
while n > 1:
if isPrimeMR(n):
ret[n], n = 1, 1
else:
rhoFlg = 1
j = findFactorRho(n)
k = 0
while n % j == 0:
n //= j
k += 1
ret[j] = k
if n > 1: ret[n] = 1
if rhoFlg: ret = {x: ret[x] for x in sorted(ret)}
return ret
def divisors(n):
res = [1]
prime = primeFactor(n)
for p in prime:
newres = []
for d in res:
for j in range(prime[p]+1):
newres.append(d*p**j)
res = newres
res.sort()
return res
def xorfactorial(num):
if num==0:
return 0
elif num==1:
return 1
elif num==2:
return 3
elif num==3:
return 0
else:
x=baseorder(num)
return (2**x)*((num-2**x+1)%2)+function(num-2**x)
def xorconv(n,X,Y):
if n==0:
res=[(X[0]*Y[0])%mod]
return res
x=[X[i]+X[i+2**(n-1)] for i in range(2**(n-1))]
y=[Y[i]+Y[i+2**(n-1)] for i in range(2**(n-1))]
z=[X[i]-X[i+2**(n-1)] for i in range(2**(n-1))]
w=[Y[i]-Y[i+2**(n-1)] for i in range(2**(n-1))]
res1=xorconv(n-1,x,y)
res2=xorconv(n-1,z,w)
former=[(res1[i]+res2[i])*inv for i in range(2**(n-1))]
latter=[(res1[i]-res2[i])*inv for i in range(2**(n-1))]
former=list(map(lambda x:x%mod,former))
latter=list(map(lambda x:x%mod,latter))
return former+latter
def merge_sort(A,B):
pos_A,pos_B = 0,0
n,m = len(A),len(B)
res = []
while pos_A < n and pos_B < m:
a,b = A[pos_A],B[pos_B]
if a < b:
res.append(a)
pos_A += 1
else:
res.append(b)
pos_B += 1
res += A[pos_A:]
res += B[pos_B:]
return res
class UnionFindVerSize():
def __init__(self, N):
self._parent = [n for n in range(0, N)]
self._size = [1] * N
self.group = N
def find_root(self, x):
if self._parent[x] == x: return x
self._parent[x] = self.find_root(self._parent[x])
stack = [x]
while self._parent[stack[-1]]!=stack[-1]:
stack.append(self._parent[stack[-1]])
for v in stack:
self._parent[v] = stack[-1]
return self._parent[x]
def unite(self, x, y):
gx = self.find_root(x)
gy = self.find_root(y)
if gx == gy: return
self.group -= 1
if self._size[gx] < self._size[gy]:
self._parent[gx] = gy
self._size[gy] += self._size[gx]
else:
self._parent[gy] = gx
self._size[gx] += self._size[gy]
def get_size(self, x):
return self._size[self.find_root(x)]
def is_same_group(self, x, y):
return self.find_root(x) == self.find_root(y)
class WeightedUnionFind():
def __init__(self,N):
self.parent = [i for i in range(N)]
self.size = [1 for i in range(N)]
self.val = [0 for i in range(N)]
self.flag = True
self.edge = [[] for i in range(N)]
def dfs(self,v,pv):
stack = [(v,pv)]
new_parent = self.parent[pv]
while stack:
v,pv = stack.pop()
self.parent[v] = new_parent
for nv,w in self.edge[v]:
if nv!=pv:
self.val[nv] = self.val[v] + w
stack.append((nv,v))
def unite(self,x,y,w):
if not self.flag:
return
if self.parent[x]==self.parent[y]:
self.flag = (self.val[x] - self.val[y] == w)
return
if self.size[self.parent[x]]>self.size[self.parent[y]]:
self.edge[x].append((y,-w))
self.edge[y].append((x,w))
self.size[x] += self.size[y]
self.val[y] = self.val[x] - w
self.dfs(y,x)
else:
self.edge[x].append((y,-w))
self.edge[y].append((x,w))
self.size[y] += self.size[x]
self.val[x] = self.val[y] + w
self.dfs(x,y)
class Dijkstra():
class Edge():
def __init__(self, _to, _cost):
self.to = _to
self.cost = _cost
def __init__(self, V):
self.G = [[] for i in range(V)]
self._E = 0
self._V = V
@property
def E(self):
return self._E
@property
def V(self):
return self._V
def add_edge(self, _from, _to, _cost):
self.G[_from].append(self.Edge(_to, _cost))
self._E += 1
def shortest_path(self, s):
import heapq
que = []
d = [10**15] * self.V
d[s] = 0
heapq.heappush(que, (0, s))
while len(que) != 0:
cost, v = heapq.heappop(que)
if d[v] < cost: continue
for i in range(len(self.G[v])):
e = self.G[v][i]
if d[e.to] > d[v] + e.cost:
d[e.to] = d[v] + e.cost
heapq.heappush(que, (d[e.to], e.to))
return d
#Z[i]:length of the longest list starting from S[i] which is also a prefix of S
#O(|S|)
def Z_algorithm(s):
N = len(s)
Z_alg = [0]*N
Z_alg[0] = N
i = 1
j = 0
while i < N:
while i+j < N and s[j] == s[i+j]:
j += 1
Z_alg[i] = j
if j == 0:
i += 1
continue
k = 1
while i+k < N and k + Z_alg[k]<j:
Z_alg[i+k] = Z_alg[k]
k += 1
i += k
j -= k
return Z_alg
class BIT():
def __init__(self,n,mod=0):
self.BIT = [0]*(n+1)
self.num = n
self.mod = mod
def query(self,idx):
res_sum = 0
mod = self.mod
while idx > 0:
res_sum += self.BIT[idx]
if mod:
res_sum %= mod
idx -= idx&(-idx)
return res_sum
#Ai += x O(logN)
def update(self,idx,x):
mod = self.mod
while idx <= self.num:
self.BIT[idx] += x
if mod:
self.BIT[idx] %= mod
idx += idx&(-idx)
return
class dancinglink():
def __init__(self,n,debug=False):
self.n = n
self.debug = debug
self._left = [i-1 for i in range(n)]
self._right = [i+1 for i in range(n)]
self.exist = [True for i in range(n)]
def pop(self,k):
if self.debug:
assert self.exist[k]
L = self._left[k]
R = self._right[k]
if L!=-1:
if R!=self.n:
self._right[L],self._left[R] = R,L
else:
self._right[L] = self.n
elif R!=self.n:
self._left[R] = -1
self.exist[k] = False
def left(self,idx,k=1):
if self.debug:
assert self.exist[idx]
res = idx
while k:
res = self._left[res]
if res==-1:
break
k -= 1
return res
def right(self,idx,k=1):
if self.debug:
assert self.exist[idx]
res = idx
while k:
res = self._right[res]
if res==self.n:
break
k -= 1
return res
class SparseTable():
def __init__(self,A,merge_func,ide_ele):
N=len(A)
n=N.bit_length()
self.table=[[ide_ele for i in range(n)] for i in range(N)]
self.merge_func=merge_func
for i in range(N):
self.table[i][0]=A[i]
for j in range(1,n):
for i in range(0,N-2**j+1):
f=self.table[i][j-1]
s=self.table[i+2**(j-1)][j-1]
self.table[i][j]=self.merge_func(f,s)
def query(self,s,t):
b=t-s+1
m=b.bit_length()-1
return self.merge_func(self.table[s][m],self.table[t-2**m+1][m])
class BinaryTrie:
class node:
def __init__(self,val):
self.left = None
self.right = None
self.max = val
def __init__(self):
self.root = self.node(-10**15)
def append(self,key,val):
pos = self.root
for i in range(29,-1,-1):
pos.max = max(pos.max,val)
if key>>i & 1:
if pos.right is None:
pos.right = self.node(val)
pos = pos.right
else:
pos = pos.right
else:
if pos.left is None:
pos.left = self.node(val)
pos = pos.left
else:
pos = pos.left
pos.max = max(pos.max,val)
def search(self,M,xor):
res = -10**15
pos = self.root
for i in range(29,-1,-1):
if pos is None:
break
if M>>i & 1:
if xor>>i & 1:
if pos.right:
res = max(res,pos.right.max)
pos = pos.left
else:
if pos.left:
res = max(res,pos.left.max)
pos = pos.right
else:
if xor>>i & 1:
pos = pos.right
else:
pos = pos.left
if pos:
res = max(res,pos.max)
return res
def solveequation(edge,ans,n,m):
#edge=[[to,dire,id]...]
x=[0]*m
used=[False]*n
for v in range(n):
if used[v]:
continue
y = dfs(v)
if y!=0:
return False
return x
def dfs(v):
used[v]=True
r=ans[v]
for to,dire,id in edge[v]:
if used[to]:
continue
y=dfs(to)
if dire==-1:
x[id]=y
else:
x[id]=-y
r+=y
return r
class SegmentTree:
def __init__(self, init_val, segfunc, ide_ele):
n = len(init_val)
self.segfunc = segfunc
self.ide_ele = ide_ele
self.num = 1 << (n - 1).bit_length()
self.tree = [ide_ele] * 2 * self.num
self.size = n
for i in range(n):
self.tree[self.num + i] = init_val[i]
for i in range(self.num - 1, 0, -1):
self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])
def update(self, k, x):
k += self.num
self.tree[k] = x
while k > 1:
self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
k >>= 1
def query(self, l, r):
if r==self.size:
r = self.num
res = self.ide_ele
l += self.num
r += self.num
while l < r:
if l & 1:
res = self.segfunc(res, self.tree[l])
l += 1
if r & 1:
res = self.segfunc(res, self.tree[r - 1])
l >>= 1
r >>= 1
return res
def bisect_l(self,l,r,x):
l += self.num
r += self.num
Lmin = -1
Rmin = -1
while l<r:
if l & 1:
if self.tree[l] <= x and Lmin==-1:
Lmin = l
l += 1
if r & 1:
if self.tree[r-1] <=x:
Rmin = r-1
l >>= 1
r >>= 1
if Lmin != -1:
pos = Lmin
while pos<self.num:
if self.tree[2 * pos] <=x:
pos = 2 * pos
else:
pos = 2 * pos +1
return pos-self.num
elif Rmin != -1:
pos = Rmin
while pos<self.num:
if self.tree[2 * pos] <=x:
pos = 2 * pos
else:
pos = 2 * pos +1
return pos-self.num
else:
return -1
import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import gcd,log
input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())
n = int(input())
if n%2==0:
print("NO")
else:
print("YES")
ans = [0 for i in range(2*n)]
for i in range(n):
if i%2==0:
ans[i] = 2*i + 1
ans[i+n] = 2*i + 2
else:
ans[i] = 2*i + 2
ans[i+n] = 2*i + 1
print(*ans)
```
| 106,211 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Tags: constructive algorithms, greedy, math
Correct Solution:
```
import sys
readline = sys.stdin.readline
N = int(readline())
if N & 1:
print('YES')
Ans = list(range(1, 1+2*N, 2)) + list(range(2, 1+2*N, 2))
for i in range(0, N, 2):
Ans[i], Ans[i+N] = Ans[i+N], Ans[i]
print(*Ans)
else:
print('NO')
```
| 106,212 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Submitted Solution:
```
def solve():
arange=int(input())
if(arange%2==0):
print("NO")
return
diapasone=list(range(1,(arange*2)+1))
answer=[]
i=0
j=len(diapasone)-1
while(len(answer)<len(diapasone)):
temp_i=i
temp_j=j
counter=arange
while(counter>0):
answer.append(diapasone[temp_i])
counter-=1
if(counter>0):
answer.append(diapasone[temp_j])
counter-=1
temp_i+=2
temp_j-=2
i+=1
j-=1
answer_final=''
for i in answer:
answer_final+=str(i)
answer_final+=' '
print("YES")
print(answer_final[:-1])
solve()
```
Yes
| 106,213 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Submitted Solution:
```
n = int(input())
if n % 2 == 0: print("NO")
elif n == 1:
print("YES")
print("1 2")
else:
print("YES")
circleTop = []
circleBottom = []
for x in range(n):
if x % 2 == 0:
circleTop.append(x*2+1)
circleBottom.append(x*2+2)
else:
circleTop.append(x*2+2)
circleBottom.append(x*2+1)
# works
print(" ".join(map(str, circleTop+circleBottom)))
```
Yes
| 106,214 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Submitted Solution:
```
def find(n):
ans=[0]*(2*n)
if n%2==0:
return []
temp=0
for i in range(1,n+1):
left=2*i-1
right=2*i
if temp%2==0:
ans[i-1]=left
ans[i+n-1]=right
else:
ans[i-1]=right
ans[i+n-1]=left
temp+=1
return ans
n=int(input())
ans=find(n)
if ans==[]:
print("NO")
else:
print("YES")
print(*ans)
```
Yes
| 106,215 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Submitted Solution:
```
size1=int(input())
ar1=[]
ar2=[]
count=1
if size1%2==0:
print('NO')
else:
for i in range((size1)):
if i%2==0:
ar1.append(count)
count+=1
ar2.append(count)
count+=1
else:
ar2.append(count)
count += 1
ar1.append(count)
count+=1
print('YES')
ar1=ar1+ar2
for i in ar1:
print(i, end=" ")
print()
```
Yes
| 106,216 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Submitted Solution:
```
n = int(input())
if n&1 == 0:
print("NO")
else:
j = [1]
for y in range(n+1,2*n):
j.append(y)
for y in range(2,n+1):
j.append(y)
j.append(2*n)
print("YES")
print(*j)
```
No
| 106,217 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Submitted Solution:
```
n=int(input())
if(n%2==1):
print("YES")
else:
print("NO")
```
No
| 106,218 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Submitted Solution:
```
n = int(input())
c = 2*n
res = list(range(1,c+1))
res2=[]
print(res)
for i in range(1,int(len(res)/2)):
b = res[i]
res[i] = res[i+2]
res[i+2] = b
print(res)
for i in range(0,len(res)-2):
d = res[i]+res[i+1]+res[i+2]
res2.append(d)
for i in range(0,2):
d = res[i-2]+res[i-1]+res[i]
res2.append(d)
for i in range(0,len(res2)//n,2):
e = res2[i] -res2[i+1]
if e == -1 or e == 1:
f = 'True'
else:
print('NO')
quit()
print('YES')
print(res)
```
No
| 106,219 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.
For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.
<image>
Input
The first and the only line contain one integer n (1 ≤ n ≤ 10^5).
Output
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
Examples
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
Note
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
Submitted Solution:
```
n = int(input());
if n % 2 == 0:
print("NO");
else:
ans = [];
for i in range(2*n):
ans.append(0);
current = 1;
for i in range(n):
ans[i] = current if i % 2 == 0 else current+1;
ans[n+i] = current+1 if i % 2 == 0 else current;
current += 2;
print("YES");
print(ans);
```
No
| 106,220 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Tags: games
Correct Solution:
```
import sys
input = sys.stdin.readline
t = int(input())
for _ in range(t):
a,b = map(int,input().split())
s = input()
n = len(s)
ls = []
if s[0] == ".":
cnt = 1
else:
cnt = 0
for i in range(1,n+1):
if i < n and s[i] == ".":
cnt += 1
else:
if cnt >= b:
ls.append(cnt)
cnt = 0
if not ls:
print("NO")
continue
ls.sort()
if a >= 2*b:
if len(ls) >= 2 or ls[0] > a+(b-1)*2 or ls[0] < a:
print("NO")
else:
print("YES")
else:
if ls[0] < a:# or ls[-1] > a+(2*b-1)*2:
print("NO")
elif len(ls) >= 2 and ls[-2] >= 2*b:
print("NO")
else:
l = len(ls)-1
t = ls[-1]
for i in range(t):
if i+a <= t:
p,q = i,t-(i+a)
if not (b<=p<a or b<=q<a or p>=2*b or q>=2*b):
x = l+(a<=p<2*b)+(a<=q<2*b)
if x%2 == 0:
print("YES")
break
else:
print("NO")
```
| 106,221 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Tags: games
Correct Solution:
```
import sys
from itertools import groupby
readline = sys.stdin.readline
t = int(input())
for _ in range(t):
a, b = map(int, readline().split())
dots = [len(list(v))
for k, v in groupby(readline().rstrip()) if k == '.']
lose = 0
med = 0
long = 0
longest = 0
for x in dots:
if x < b:
continue
if b <= x < a:
lose = 1
elif 2*b <= x:
long += 1
if longest < x:
longest = x
elif a <= x < 2*b:
med += 1
if lose or long > 1:
print("NO")
continue
if long:
for left, right in zip(range(longest), range(longest-a, -1, -1)):
if (left < b or a <= left < 2*b) and (right < b or a <= right < 2*b):
if (((med + (1 if a <= left else 0) + (1 if a <= right else 0)) & 1) == 0):
print("YES")
break
else:
print("NO")
else:
print("YES" if med & 1 else "NO")
```
| 106,222 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Tags: games
Correct Solution:
```
# import sys
# input = sys.stdin.readline
Q = int(input())
for _ in range(Q):
a, b = map(int, input().split())
S = input() + "X"
s = 0
x = x1 = x2 = x3 = xx = 0
for i in range(len(S)):
if S[i] == "X":
if s < b:
pass
elif a <= s < 2*b:
x += 1
elif a < 2*b and (3*a <= s < a+3*b-1 or 2*a <= s < a+2*b-1):
xx += 1
elif a < 2*b and 3*a <= s < a+4*b-1:
x3 += 1
elif a < 2*b and 2*a <= s < a+3*b-1:
x2 += 1
elif a <= s < a+2*b-1:
x1 += 1
else:
# print("a, b, s =", a, b, s)
print("NO")
break
s = 0
else:
s += 1
else:
# print("x, x1, x2, x3 =", x, x1, x2, x3)
if xx+x1+x2+x3 >= 2:
print("NO")
elif xx:
print("YES")
elif (x + x1 + x2*2 + x3*3) % 2 == 0:
print("NO")
else:
print("YES")
```
| 106,223 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Tags: games
Correct Solution:
```
import os, sys
# zeilen = [l.strip() for l in sys.stdin.readlines()]
q = int(sys.stdin.readline().strip())
for _ in range(q):
a, b = map(int, sys.stdin.readline().strip().split())
word = sys.stdin.readline().strip()
gaps = sorted([len(gap) for gap in word.split('X') if len(gap)>= b])
if len(gaps) == 0:
print('NO')
elif gaps[0] < a:
print('NO')
elif len(gaps) > 1 and gaps[-2] >= 2*b:
print('NO')
elif gaps[-1] < 2*b: # no problematic, need only count
print('YES' if (len(gaps) % 2) else 'NO')
else: # exactly one problematic gap
p = gaps[-1]
if (len(gaps) % 2): # A tries to make this gap into zero or two
if p <= (a + 2*b - 2): # short enough for 0
print('YES')
elif p < 3*a: # we have to try two
print('NO') # not long enough
elif p > (a + 4*b - 2): # too long
print('NO')
else:
print('YES')
else: # A tries to make this gap into one
if p < 2*a: # too short
print('NO')
elif p > (a + 3*b - 2):# too long
print('NO')
else:
print('YES')
```
| 106,224 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Tags: games
Correct Solution:
```
import sys
input = sys.stdin.readline
q=int(input())
for testcases in range(q):
a,b=map(int,input().split())
S=input().strip()
S+="X"
T=[]
NOW=0
for s in S:
if s==".":
NOW+=1
else:
if NOW!=0:
T.append(NOW)
NOW=0
count=0
noflag=0
other=[]
for t in T:
if b<=t<a:
noflag=1
break
if a<=t<2*b:
count+=1
elif t>=2*b:
other.append(t)
if len(other)>=2:
noflag=1
if noflag==1:
print("NO")
continue
if len(other)==0:
if count%2==1:
print("YES")
else:
print("NO")
continue
OTHER=other[0]
for left in range(OTHER-a+1):
right=OTHER-a-left
if left>=2*b or right>=2*b or b<=left<a or b<=right<a:
continue
count2=count
if left>=a:
count2+=1
if right>=a:
count2+=1
if count2%2==0:
print("YES")
break
else:
print("NO")
```
| 106,225 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Tags: games
Correct Solution:
```
def sol():
a, b = map(int, input().split())
s = input().replace("X", " ")
small_segs = 0
critical_region = -1
for p in map(len, s.split()):
if p < b:
continue
if p < a and p >= b:
return False
if ((p - a) % 2 == 0 and (p >= a + 4 * b)) or ((p - a) % 2 == 1 and p >= a + 4 * b - 1):
return False
if p >= 2*b:
if critical_region != -1:
return False
critical_region = p
elif p >= a:
small_segs += 1
if critical_region == -1:
return small_segs % 2 == 1
can = [0] * 3
for l in range(critical_region+1-a):
r = critical_region - l - a
if (l >= b and l < a) or l >= 2 * b:
continue
if (r >= b and r < a) or r >= 2 * b:
continue
canl = int(l >= a)
canr = int(r >= a)
can[canl + canr] = 1
for choice, val in enumerate(can):
if val and (small_segs + choice) % 2 == 0:
return True
return False
n = int(input())
for _ in range(n):
print("YES" if sol() else "NO")
```
| 106,226 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Tags: games
Correct Solution:
```
q = int(input())
for rwer in range(q):
a, b = map(int,input().split())
s = input()
tab = []
count = 0
for i in range(len(s)):
if s[i] == '.':
count += 1
if s[i] == 'X':
if count > 0:
tab.append(count)
count = 0
if count > 0:
tab.append(count)
#print(tab)
bat = [j for j in tab if j >= b]
tab = bat.copy()
if len(tab) == 0:
print("no")
else:
roomb = 0
for i in tab:
if i >= 2*b:
roomb += 1
if roomb > 1:
print("no")
else:
alice = 1
for i in tab:
if i < a:
alice = 0
break
if alice == 0:
print("no")
else:
if roomb == 0:
if len(tab) % 2 == 1:
print("yes")
else:
print("no")
if roomb == 1:
jednostrzaly = len(tab) - 1
duzy = max(tab)
#alice gra w duzym i co ona tam moze zrobic?
if duzy >= (a + 4*b - 1):
print("no")
else:
if jednostrzaly % 2 == 0:
#jesli alice da rade zostawic 0 albo 2 sloty to wygrala
if duzy <= a + 2 * b - 2: ########poprawka z -1
print("yes")
elif duzy >= 3 * a:
print("yes")
else:
print("no")
if jednostrzaly % 2 == 1:
#alice musi zostawic 1 slota
if duzy >= 2*a and duzy <= (a + 3*b-2):
print("yes")
else:
print("no")
```
| 106,227 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Tags: games
Correct Solution:
```
def removeX(s,p):
if (p==len(s)):
return s
while s[p]!='X':
p+=1
if (p==len(s)):
return s
j=0
while s[p+j]=='X':
j+=1
if (p+j==len(s)):
break
return removeX(s[0:p+1]+s[p+j:],p+1)
def doable(lenght,a,b,parity):
for x in range((lenght-a)//2+1):
y=lenght-a-x
#print(x,y)
if ((not((x>=b) & (x<a)))&(not(x>=2*b))&(not((y>=b) & (y<a)))&(not(y>=2*b))):
e=0
#print('oui')
if((x>=a)&(x<2*b)):
e+=1
if((y>=a)&(y<2*b)):
e+=1
if((parity+e)%2==0):
return 1
return 0
for i in range(int(input())):
a,b=[int(x) for x in input().split()]
v=[0,0,0]
s=removeX(input(),0)
for y in s.split('X'):
k=len(y)
if ((k>=b) & (k<a)):
v[0]+=1
elif ((k>=a) & (k<2*b)):
v[1]+=1
elif (k>=2*b):
v[2]+=1
lenght=k
#print(v)
if ((v[0]>0) | (v[2]>1)):
print('NO')
elif (v[2]==1):
if (lenght-a>=4*b):
print('NO')
else:
if (doable(lenght,a,b,v[1]%2)==1):
print('YES')
else:
print('NO')
else:
if (v[1]%2==0):
print('NO')
else:
print('YES')
```
| 106,228 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Submitted Solution:
```
import sys
input = lambda: sys.stdin.readline().rstrip()
Q = int(input())
for _ in range(Q):
a, b = map(int, input().split())
S = input() + "X"
s = 0
x = x1 = x2 = x3 = xx = 0
for i in range(len(S)):
if S[i] == "X":
if s < b:
pass
elif a <= s < 2*b:
x += 1
elif a < 2*b and (3*a <= s < a+3*b-1 or 2*a <= s < a+2*b-1):
xx += 1
elif a < 2*b and 3*a <= s < a+4*b-1:
x3 += 1
elif a < 2*b and 2*a <= s < a+3*b-1:
x2 += 1
elif a <= s < a+2*b-1:
x1 += 1
else:
# print("a, b, s =", a, b, s)
print("NO")
break
s = 0
else:
s += 1
else:
# print("x, x1, x2, x3 =", x, x1, x2, x3)
if xx+x1+x2+x3 >= 2:
print("NO")
elif xx:
print("YES")
elif (x + x1 + x2*2 + x3*3) % 2 == 0:
print("NO")
else:
print("YES")
```
Yes
| 106,229 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Submitted Solution:
```
def solve(a, b, s):
l = map(lambda x: len(x), s.split('X'))
tot = 0
mx = 0
for j in l:
if j < b:
continue
if j < a:
return 'NO'
if j >= 2 * b:
if mx > 0:
return 'NO'
mx = j
tot += 1
if mx > 0:
if a < 2 * b:
one = mx >= a and mx <= a + 2 * b - 2
two = mx >= 2 * a and mx <= a + 3 * b - 2
three = mx >= 3 * a and mx <= a + 4 * b - 2
if not (one or two or three):
return 'NO'
if (one and two) or (two and three):
return 'YES'
if two:
tot += 1
if a >= 2 * b:
if not (mx >= a and mx <= a + 2 * b - 2):
return 'NO'
if tot % 2 == 1:
return 'YES'
else:
return 'NO'
q = int(input())
for i in range(q):
a, b = map(int, input().split())
s = input()
print(solve(a, b, s))
```
Yes
| 106,230 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Submitted Solution:
```
def main():
import sys
input = sys.stdin.readline
q = int(input())
for _ in range(q):
a, b = map(int, input().split())
S = input().rstrip('\n')
S += '!'
win = 1
cnt = 0
flg = 0
num = 0
for s in S:
if s == '.':
cnt += 1
else:
if cnt:
if b <= cnt < a:
win = 0
break
elif cnt < b:
pass
elif cnt < 2*b:
num += 1
else:
num += 1
if flg:
flg = 2
win = 0
break
else:
flg = 1
tmp = cnt
cnt = 0
if flg == 1:
if num % 2 == 0:
if a >= 2*b:
win = 0
else:
if not 2*a <= tmp <= a+3*b-2:
win = 0
else:
if tmp <= a+2*b-2:
pass
elif 3*a <= tmp <= a+4*b-2:
pass
else:
win = 0
elif flg == 0:
if num % 2 == 0:
win = 0
if win:
print('Yes')
else:
print('No')
if __name__ == '__main__':
main()
```
Yes
| 106,231 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Submitted Solution:
```
q = int(input())
for i in range(q):
a, b = [int(item) for item in input().split()]
s = input().rstrip() + "#"
cnt = 0
bob_world = 0
alice_world = 0
length = 0
bob_winning = False
for ch in s:
if ch == ".":
cnt += 1
else:
if cnt < b:
pass
elif b <= cnt < a:
bob_winning = True
break
elif a <= cnt < b * 2:
alice_world += 1
elif cnt >= b * 2:
length = cnt
bob_world += 1
if bob_world >= 2:
bob_winning = True
break
cnt = 0
if bob_winning:
print("No")
else:
if length == 0:
if alice_world % 2 == 1:
print("Yes")
else:
print("No")
continue
possibility = set()
for i in range(length - a + 1):
l = i; r = length - a - i
if b <= l < a or b <= r < a:
continue
if l >= b * 2 or r >= b * 2:
continue
val = 0
if a <= l < b * 2:
val += 1
if a <= r < b * 2:
val += 1
possibility.add(val + 1)
alice_win = False
for item in possibility:
if (alice_world + item) % 2 == 1:
alice_win = True
if alice_win:
print("Yes")
else:
print("No")
```
Yes
| 106,232 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Submitted Solution:
```
import sys
input = sys.stdin.readline
q=int(input())
for testcases in range(q):
a,b=map(int,input().split())
S=input().strip()
T=[]
NOW=0
for s in S:
if s==".":
NOW+=1
else:
if NOW!=0:
T.append(NOW)
NOW=0
T.sort()
LA=[]
LB=[]
flag=0
SP=0
for t in T:
LA.append(t//a)
LB.append(t//b)
SP+=t//b-t//a
if sum(LA)%2==1 and SP<=1:
print("YES")
else:
print("NO")
```
No
| 106,233 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Submitted Solution:
```
T = int(input())
for i in range(T):
[a, b] = [int(i) for i in input().split()]
game = input()
length = 0
spaces = []
aspace = 0
bspace = 0
for g in game:
if(g=='.'):length+=1
else:
if(length>=b): spaces.append(length)
length = 0
for s in spaces:
if(s >= a):
aspace+=s//a
bspace+=int((s%a+1)//2 >= b)
elif(s >= b): bspace+=1
if(bspace>1 or aspace%3==2): print("NO")
else: print("YES")
```
No
| 106,234 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Submitted Solution:
```
def main():
import sys
input = sys.stdin.readline
q = int(input())
for _ in range(q):
a, b = map(int, input().split())
S = input().rstrip('\n')
S += '!'
win = 1
cnt = 0
flg = 0
num = 0
for s in S:
if s == '.':
cnt += 1
else:
if cnt:
if b <= cnt < a:
win = 0
break
elif cnt < b:
pass
elif cnt < 2*b:
num += 1
else:
num += 1
if flg:
flg = 2
win = 0
break
else:
flg = 1
tmp = cnt
cnt = 0
if flg == 1:
if num % 2 == 0:
if a >= 2*b:
win = 0
else:
if not 2*a <= tmp <= a+3*b-2:
win = 0
else:
if tmp > a+2*b-2:
win = 0
elif flg == 0:
if num % 2 == 0:
win = 0
if win:
print('Yes')
else:
print('No')
if __name__ == '__main__':
main()
```
No
| 106,235 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Alice and Bob play a game. Initially they have a string s_1, s_2, ..., s_n, consisting of only characters . and X. They take alternating turns, and Alice is moving first. During each turn, the player has to select a contiguous substring consisting only of characters . and replaces each of them with X. Alice must select a substing of length a, and Bob must select a substring of length b. It is guaranteed that a > b.
For example, if s = ...X.. and a = 3, b = 2, then after Alice's move string can turn only into XXXX... And if it's Bob's turn and the string s = ...X.., then after Bob's move the string can turn into XX.X.., .XXX.. or ...XXX.
Whoever is unable to make a move, loses. You have to determine who wins if they both play optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.
The first line of each query contains two integers a and b (1 ≤ b < a ≤ 3 ⋅ 10^5).
The second line of each query contains the string s (1 ≤ |s| ≤ 3 ⋅ 10^5), consisting of only characters . and X.
It is guaranteed that sum of all |s| over all queries not exceed 3 ⋅ 10^5.
Output
For each test case print YES if Alice can win and NO otherwise.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES will all be recognized as positive answer).
Example
Input
3
3 2
XX......XX...X
4 2
X...X.X..X
5 3
.......X..X
Output
YES
NO
YES
Note
In the first query Alice can select substring s_3 ... s_5. After that s turns into XXXXX...XX...X. After that, no matter what move Bob makes, Alice can make the move (this will be her second move), but Bob can't make his second move.
In the second query Alice can not win because she cannot even make one move.
In the third query Alice can choose substring s_2 ... s_6. After that s turns into .XXXXX.X..X, and Bob can't make a move after that.
Submitted Solution:
```
Q = int(input())
for q in range(Q):
a, b = tuple(map(int, input().split()))
s = input()
ones = []
count = 0
flag = False
for i in s:
if i == "X":
if a > count >= b:
print('NO')
flag = True
break
elif count >= b:
ones.append(count)
count = 0
else:
count += 1
if count != 0:
ones.append(count)
if a > count >= b:
print('NO')
continue
if flag:
continue
if len(ones) == 0:
print('NO')
continue
count_more2b = 0
more2b = 0
for one in ones:
if one >= 2 * b:
count_more2b += 1
more2b = one
if count_more2b >= 2:
print('NO')
flag = True
break
if flag:
continue
if count_more2b == 0:
if len(ones) % 2 == 0:
print('NO')
else:
print('YES')
continue
elif more2b - a >= 2 * b:
print('NO')
continue
else:
if a > more2b - a >= b:
print('NO')
continue
if more2b - a < b:
ones.pop()
if len(ones) % 2 == 0:
print('YES')
else:
print('NO')
```
No
| 106,236 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Tags: greedy, math, sortings
Correct Solution:
```
x = int(input())
y = list(map(int, input().split()))
a = int(x/2)
b = 0
c = 0
y.sort()
for i in range(a, x):
b+=y[i]
for i in range(a):
c+=y[i]
print(b**2+c**2)
```
| 106,237 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Tags: greedy, math, sortings
Correct Solution:
```
def ii(): return int(input())
def si(): return input()
def mi(): return map(int,input().split())
def li(): return list(mi())
n=ii()
a=li()
a.sort()
x=y=0
for i in range(n//2):
x+=a[i]
y+=a[n-i-1]
if n%2:
y+=a[n//2]
print(x*x+y*y)
```
| 106,238 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Tags: greedy, math, sortings
Correct Solution:
```
n = int(input())
a = list(map(int, input().split()))
a.sort()
mp = n // 2
sl = sum(a[:mp])
sm = sum(a[mp:])
smd = sl**2 + sm**2
print(smd)
```
| 106,239 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Tags: greedy, math, sortings
Correct Solution:
```
n = int(input())
ar = list(map(int, input().split()))
ar.sort()
x, y = 0, 0
for i in range((n + 1) // 2):
if i * 2 == n - 1:
y += ar[i]
else:
x += ar[i]
y += ar[n - i - 1]
print(x * x + y * y)
```
| 106,240 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Tags: greedy, math, sortings
Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
a.sort()
if n%2==0:
d=(n//2)
else:
d=((n//2)+1)-1
b=sum(a[0:d])
c=sum(a[d:n])
print((b*b)+(c*c))
```
| 106,241 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Tags: greedy, math, sortings
Correct Solution:
```
from collections import deque
n = int(input())
a = deque(sorted(map(int, input().split())))
up = 0
right = 0
for i in range(n):
if i % 2:
up += a.popleft()
else:
right += a.pop()
print(up * up + right * right)
```
| 106,242 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Tags: greedy, math, sortings
Correct Solution:
```
n=int(input())
a=list(map(int,input().split(" ")))
a.sort()
sum1=0
sum2=0
for i in range (n):
if(i<int(n/2)):
sum1+=a[i]
else:
sum2+=a[i]
print(sum1*sum1+sum2*sum2)
```
| 106,243 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Tags: greedy, math, sortings
Correct Solution:
```
n = int(input())
u = list(map(int, input().split()))
u.sort()
a = sum(u[:n // 2])
b = sum(u) - a
print(a * a + b * b)
```
| 106,244 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Submitted Solution:
```
n=int(input())
l=list(map(int,input().split()))
l.sort()
v=n//2
s1=sum(l[:v])
s=sum(l)
s2=s-s1
print(pow(s2,2)+pow(s1,2))
```
Yes
| 106,245 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Submitted Solution:
```
a = int(input())
b = list(map(int, input().split()))
X = 0
Y = 0
b.sort()
for i in range(0,len(b)):
if (i < len(b) // 2):
Y += b[i];
else:
X += b[i];
print(Y**2 + X**2)
```
Yes
| 106,246 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Submitted Solution:
```
# Aaditya Upadhyay
# ..............
# ╭━┳━╭━╭━╮╮
# ┃┈┈┈┣▅╋▅┫┃
# ┃┈┃┈╰━╰━━━━━━╮
# ╰┳╯┈┈┈┈┈┈┈┈┈◢▉◣
# ╲┃┈┈┈┈┈┈┈┈┈┈▉▉▉
# ╲┃┈┈┈┈┈┈┈┈┈┈◥▉◤
# ╲┃┈┈┈┈╭━┳━━━━╯
# ╲┣━━━━━━┫
# ……….
# .……. /´¯/)………….(\¯`\
# …………/….//……….. …\….\
# ………/….//……………....\….\
# …./´¯/…./´¯\……/¯ `\…..\¯`\
# ././…/…/…./|_…|.\….\….\…\.\
# (.(….(….(…./.)..)...(.\.).).)
# .\…………….\/../…....\….\/…………/
# ..\…………….. /……...\………………../
# …..\…………… (………....)……………./
from sys import stdin,stdout
from collections import *
from math import gcd,floor,ceil
st=lambda:list(stdin.readline().strip())
li=lambda:list(map(int,stdin.readline().split()))
mp=lambda:map(int,stdin.readline().split())
inp=lambda:int(stdin.readline())
pr=lambda n: stdout.write(str(n)+"\n")
mod=1000000007
INF=float('inf')
def solve():
n=inp()
l=li()
l.sort()
i,j=0,n-1
x,y =0,0
c=1
while i<=j:
if c:
x+=l[j]
c=0
j-=1
else:
y+=l[i]
c=1
i+=1
pr(x*x + y*y)
for _ in range(1):
solve()
```
Yes
| 106,247 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Submitted Solution:
```
#設定
import sys
input = sys.stdin.buffer.readline
#ライブラリインポート
from collections import defaultdict
INF = float("inf")
def getlist():
return list(map(int, input().split()))
#処理内容
def main():
n = int(input())
a = getlist()
a = sorted(a)
x = 0
y = 0
for i in range(int(n // 2)):
x += a[i]
y = sum(a) - x
ans = (x ** 2) + (y ** 2)
print(ans)
if __name__ == '__main__':
main()
```
Yes
| 106,248 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Submitted Solution:
```
n = int(input(''))
a = list(map(int,input('').split(' ')))
a.sort()
r = n//2
t = sum(a)
s = 0
for i in range(n//2):
s = s + a[i]**2
t = t-s
print(t**2 + s**2)
```
No
| 106,249 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Submitted Solution:
```
import math
n = int(input())
ar = list(sorted(list(map(int, input().split(' ')))))
x = n//2
a, b = (0, 0)
for idx, num in enumerate(ar):
if idx < x:
a += num
else:
b += num
print(int(math.pow(a, 2) + math.pow(b, 2)))
```
No
| 106,250 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Submitted Solution:
```
# cf 1248 B 900
import math
n = int(input())
A = [*map(int, input().split())]
A.sort(reverse=True)
w, h = 0, 0
i, j = 0, len(A) - 1
while i < j:
w += A[i]
i += 1
h += A[j]
j -= 1
if i == j:
w += A[i]
print(w, h)
print(w*w + h*h)
```
No
| 106,251 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.
The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point (0, 0). While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to OX or OY axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.
Alexey wants to make a polyline in such a way that its end is as far as possible from (0, 0). Please help him to grow the tree this way.
Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.
Input
The first line contains an integer n (1 ≤ n ≤ 100 000) — the number of sticks Alexey got as a present.
The second line contains n integers a_1, …, a_n (1 ≤ a_i ≤ 10 000) — the lengths of the sticks.
Output
Print one integer — the square of the largest possible distance from (0, 0) to the tree end.
Examples
Input
3
1 2 3
Output
26
Input
4
1 1 2 2
Output
20
Note
The following pictures show optimal trees for example tests. The squared distance in the first example equals 5 ⋅ 5 + 1 ⋅ 1 = 26, and in the second example 4 ⋅ 4 + 2 ⋅ 2 = 20.
<image> <image>
Submitted Solution:
```
# B. Выращивание дерева
a = int(input())
b = input().split()
X = 0
Y = 0
b.sort()
for i in range(0,len(b)):
if (i < a / 2):
Y += int(b[i]);
else:
X += int(b[i]);
print(Y**2 + X**2)
```
No
| 106,252 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let G be a simple graph. Let W be a non-empty subset of vertices. Then W is almost-k-uniform if for each pair of distinct vertices u,v ∈ W the distance between u and v is either k or k+1.
You are given a tree on n vertices. For each i between 1 and n, find the maximum size of an almost-i-uniform set.
Input
The first line contains a single integer n (2 ≤ n ≤ 5 ⋅ 10^5) – the number of vertices of the tree.
Then n-1 lines follows, the i-th of which consisting of two space separated integers u_i, v_i (1 ≤ u_i, v_i ≤ n) meaning that there is an edge between vertices u_i and v_i.
It is guaranteed that the given graph is tree.
Output
Output a single line containing n space separated integers a_i, where a_i is the maximum size of an almost-i-uniform set.
Examples
Input
5
1 2
1 3
1 4
4 5
Output
4 3 2 1 1
Input
6
1 2
1 3
1 4
4 5
4 6
Output
4 4 2 1 1 1
Note
Consider the first example.
* The only maximum almost-1-uniform set is \{1, 2, 3, 4\}.
* One of the maximum almost-2-uniform sets is or \{2, 3, 5\}, another one is \{2, 3, 4\}.
* A maximum almost-3-uniform set is any pair of vertices on distance 3.
* Any single vertex is an almost-k-uniform set for k ≥ 1.
In the second sample there is an almost-2-uniform set of size 4, and that is \{2, 3, 5, 6\}.
Submitted Solution:
```
def almost_same_distance(n,adj,edges):
max_deg =max_degree(adj)
result = [max_deg+1]
for k in range(2,n+1):
max = find_almost_k_uniform(n,k,adj,edges)
result.append(max)
return result
def find_almost_k_uniform(n,k,adj,edges):
max_len = 0
if k % 2 == 1:
max_len = find_k_odd(n,k,adj,edges)
else:
max_len = find_k_even(n,k,adj,edges)
return max_len
def find_k_odd(n,k,adj,edges):
d_s = {}
max_len = 0
for v in range(1,n+1):
d_s[v] = bfs(n,v,adj)
l = k//2
for v in range(1,n+1):
r = {i:-1 for i in range(1,n+1)}
#buscar un vertice de longitud l o l+1 por subarbol
depth,subtree = d_s[v]
for w in range(1,n+1):
if depth[w] == l+1:
r[subtree[w]] = l+1
if depth[w] == l and r[subtree[w]] == -1:
r[subtree[w]] = l
len_r = 0
found_l = False
for t in r.values():
if t != -1:
if t == l and not found_l:
len_r += 1
found_l =True
elif t== l+1:
len_r += 1
if len_r > max_len:
max_len = len_r
return max_len
def find_k_even(n,k,adj,edges):
d_s = {}
for v in range(1,n+1):
d_s[v] = bfs(n,v,adj)
max_len = 0
l = k/2
for v in range(1,n+1):
depth,subtree = d_s[v]
r = {}
for w in range(1,n+1):
if depth[w] == l:
r[subtree[w]] = w
if len(r) > max_len:
max_len = len(r)
#print("max_lena vert--", max_len)
for e in edges:#O(n-1)
u = e[0]
v = e[1]
r_u = {}
r_v = {}
depth_u,subtree_u = bfs(n,u,adj,v)#O(n-1)
depth_v,subtree_v = bfs(n,v,adj,u)
#print(e)
#print("u--",depth_u,"--",subtree_u)
#print("v--",depth_v,"--",subtree_v)
for w in range(1,n+1):#O(n-1)
if depth_u[w] == l:
r_u[subtree_u[w]] = w
for w in range(1,n+1):#O(n-1)
if depth_v[w] == l:
r_v[subtree_v[w]] = w
t = len(r_u) + len(r_v)
if t > max_len:
max_len = t
#print("edge",e,"---",max_len)
#print("max_lena vert--", max_len)
return max_len
def bfs(n,x,adj,y=-1):
#depth[x]: longitud camino entre el vertice inicial y x
visited = [False for i in range(n+1)]
visited [x] = True
depth = [-1 for _ in range(n+1)]
subtree = [-1 for _ in range(n+1)]
if y!=-1:
visited[y] =True
q = [x]
depth[x] = 0
for w in adj[x]:
subtree[w] = w
while len(q) > 0:
v = q[0]
q.remove(v)
for w in adj[v]:
if not visited[w]:
q.append(w)
depth[w] = depth[v] + 1
if v!= x:
subtree[w] = subtree[v]
visited[w] = True
return depth,subtree
def max_degree(adj):
m_d = 0
for x in adj:
x_degree = len(x)
if m_d < x_degree:
m_d = x_degree
return m_d
def main():
n= int(input())
adj = [[]for i in range(n+1)]
edges = []
for _ in range(n-1):
x,y = [ int(i) for i in input().split()]
edges.append((x,y))
adj[x].append(y)
adj[y].append(x)
max_len = almost_same_distance(n,adj,edges)
print(' '.join(str(i) for i in max_len))
main()
```
No
| 106,253 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let G be a simple graph. Let W be a non-empty subset of vertices. Then W is almost-k-uniform if for each pair of distinct vertices u,v ∈ W the distance between u and v is either k or k+1.
You are given a tree on n vertices. For each i between 1 and n, find the maximum size of an almost-i-uniform set.
Input
The first line contains a single integer n (2 ≤ n ≤ 5 ⋅ 10^5) – the number of vertices of the tree.
Then n-1 lines follows, the i-th of which consisting of two space separated integers u_i, v_i (1 ≤ u_i, v_i ≤ n) meaning that there is an edge between vertices u_i and v_i.
It is guaranteed that the given graph is tree.
Output
Output a single line containing n space separated integers a_i, where a_i is the maximum size of an almost-i-uniform set.
Examples
Input
5
1 2
1 3
1 4
4 5
Output
4 3 2 1 1
Input
6
1 2
1 3
1 4
4 5
4 6
Output
4 4 2 1 1 1
Note
Consider the first example.
* The only maximum almost-1-uniform set is \{1, 2, 3, 4\}.
* One of the maximum almost-2-uniform sets is or \{2, 3, 5\}, another one is \{2, 3, 4\}.
* A maximum almost-3-uniform set is any pair of vertices on distance 3.
* Any single vertex is an almost-k-uniform set for k ≥ 1.
In the second sample there is an almost-2-uniform set of size 4, and that is \{2, 3, 5, 6\}.
Submitted Solution:
```
v = int(input())
graph = dict.fromkeys(range(1, v+1))
for _ in range(v-1):
key, value = map(int, input().split())
try:
graph[key].append(value)
except AttributeError:
graph[key] = [value]
try:
graph[value].append(key)
except AttributeError:
graph[value] = [key]
def dfs(graph, key, search_level):
stack = [(key, 0)]
vertex_set = set()
vertex_set.add(key)
visited = set()
visited.add(key)
while len(stack) > 0:
current, level = stack.pop()
if level == search_level or level == search_level+1:
vertex_set.add(current)
for i in graph[current]:
if i not in visited:
stack.append((i, level+1))
visited.add(i)
return vertex_set
n = 1
from functools import reduce
from itertools import combinations
redu = reduce
comb = combinations
for i in range(v):
current_result = {}
max_set_len = 0
for j in graph.keys():
current_result[j] = dfs(graph, j, n)
for key in graph.keys():
sizes = len(current_result[key])+1
for size in range(2, sizes):
for c in comb(current_result[key], size):
length = len(redu(set.intersection, [current_result[j] for j in c]))
if length > max_set_len and length == len(c):
max_set_len = length
n += 1
print(max_set_len if max_set_len > 0 else 1, end=' ')
```
No
| 106,254 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let G be a simple graph. Let W be a non-empty subset of vertices. Then W is almost-k-uniform if for each pair of distinct vertices u,v ∈ W the distance between u and v is either k or k+1.
You are given a tree on n vertices. For each i between 1 and n, find the maximum size of an almost-i-uniform set.
Input
The first line contains a single integer n (2 ≤ n ≤ 5 ⋅ 10^5) – the number of vertices of the tree.
Then n-1 lines follows, the i-th of which consisting of two space separated integers u_i, v_i (1 ≤ u_i, v_i ≤ n) meaning that there is an edge between vertices u_i and v_i.
It is guaranteed that the given graph is tree.
Output
Output a single line containing n space separated integers a_i, where a_i is the maximum size of an almost-i-uniform set.
Examples
Input
5
1 2
1 3
1 4
4 5
Output
4 3 2 1 1
Input
6
1 2
1 3
1 4
4 5
4 6
Output
4 4 2 1 1 1
Note
Consider the first example.
* The only maximum almost-1-uniform set is \{1, 2, 3, 4\}.
* One of the maximum almost-2-uniform sets is or \{2, 3, 5\}, another one is \{2, 3, 4\}.
* A maximum almost-3-uniform set is any pair of vertices on distance 3.
* Any single vertex is an almost-k-uniform set for k ≥ 1.
In the second sample there is an almost-2-uniform set of size 4, and that is \{2, 3, 5, 6\}.
Submitted Solution:
```
def almost_same_distance(n,adj,edges):
max_deg =max_degree(adj)
result = [max_deg+1]
#max = find_almost_k_uniform(n,3,adj,edges)
#print(4,"--->",max)
for k in range(2,n+1):
max = find_almost_k_uniform(n,k,adj,edges)
result.append(max)
return result
def find_almost_k_uniform(n,k,adj,edges):
max_len = 0
if k % 2 == 1:
max_len = find_k_odd(n,k,adj,edges)
else:
max_len = find_k_even(n,k,adj,edges)
return max_len
def find_k_odd(n,k,adj,edges):
d_s = {}
max_len = 0
for v in range(1,n+1):
d_s[v] = bfs(n,v,adj)
l = k//2
for v in range(1,n+1):
r = {i:-1 for i in range(1,n+1)}
#buscar un vertice de longitud l o l+1 por subarbol
depth,subtree = d_s[v]
for w in range(1,n+1):
if depth[w] == l+1:
r[subtree[w]] = l+1
if depth[w] == l and r[subtree[w]] == -1:
r[subtree[w]] = l
len_r = 0
found_l = False
for t in r.values():
if t != -1:
if t == l and not found_l:
len_r += 1
found_l =True
elif t== l+1:
len_r += 1
if len_r > max_len:
max_len = len_r
return max_len
def find_k_even(n,k,adj,edges):
d_s = {}
for v in range(1,n+1):
d_s[v] = bfs(n,v,adj)
max_len = 0
l = k/2
for v in range(1,n+1):
depth,subtree = d_s[v]
r = {}
for w in range(1,n+1):
if depth[w] == l:
r[subtree[w]] = w
if len(r) > max_len:
max_len = len(r)
#print("max_lena vert--", max_len)
for e in edges:#O(n-1)
u = e[0]
v = e[1]
r_u = {}
r_v = {}
depth_u,subtree_u = bfs(n,u,adj,v)#O(n-1)
depth_v,subtree_v = bfs(n,v,adj,u)
#print(e)
#print("u--",depth_u,"--",subtree_u)
#print("v--",depth_v,"--",subtree_v)
for w in range(1,n+1):#O(n-1)
if depth_u[w] == l:
r_u[subtree_u[w]] = w
for w in range(1,n+1):#O(n-1)
if depth_v[w] == l:
r_v[subtree_v[w]] = w
t = len(r_u) + len(r_v)
if t > max_len:
max_len = t
#print("edge",e,"---",max_len)
#print("max_lena vert--", max_len)
return max_len
def bfs(n,x,adj,y=-1):
#depth[x]: longitud camino entre el vertice inicial y x
visited = [False for i in range(n+1)]
visited [x] = True
depth = [-1 for _ in range(n+1)]
subtree = [-1 for _ in range(n+1)]
if y!=-1:
visited[y] =True
q = [x]
depth[x] = 0
for w in adj[x]:
subtree[w] = w
while len(q) > 0:
v = q[0]
q.remove(v)
for w in adj[v]:
if not visited[w]:
q.append(w)
depth[w] = depth[v] + 1
if v!= x:
subtree[w] = subtree[v]
visited[w] = True
return depth,subtree
def max_degree(adj):
m_d = 0
for x in adj:
x_degree = len(x)
if m_d < x_degree:
m_d = x_degree
return m_d
def main():
n= int(input())
adj = [[]for i in range(n+1)]
edges = []
for _ in range(n-1):
x,y = [ int(i) for i in input().split()]
edges.append((x,y))
adj[x].append(y)
adj[y].append(x)
max_len = almost_same_distance(n,adj,edges)
print(' '.join(str(i) for i in max_len))
main()
```
No
| 106,255 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Let G be a simple graph. Let W be a non-empty subset of vertices. Then W is almost-k-uniform if for each pair of distinct vertices u,v ∈ W the distance between u and v is either k or k+1.
You are given a tree on n vertices. For each i between 1 and n, find the maximum size of an almost-i-uniform set.
Input
The first line contains a single integer n (2 ≤ n ≤ 5 ⋅ 10^5) – the number of vertices of the tree.
Then n-1 lines follows, the i-th of which consisting of two space separated integers u_i, v_i (1 ≤ u_i, v_i ≤ n) meaning that there is an edge between vertices u_i and v_i.
It is guaranteed that the given graph is tree.
Output
Output a single line containing n space separated integers a_i, where a_i is the maximum size of an almost-i-uniform set.
Examples
Input
5
1 2
1 3
1 4
4 5
Output
4 3 2 1 1
Input
6
1 2
1 3
1 4
4 5
4 6
Output
4 4 2 1 1 1
Note
Consider the first example.
* The only maximum almost-1-uniform set is \{1, 2, 3, 4\}.
* One of the maximum almost-2-uniform sets is or \{2, 3, 5\}, another one is \{2, 3, 4\}.
* A maximum almost-3-uniform set is any pair of vertices on distance 3.
* Any single vertex is an almost-k-uniform set for k ≥ 1.
In the second sample there is an almost-2-uniform set of size 4, and that is \{2, 3, 5, 6\}.
Submitted Solution:
```
def almost_same_distance(n,adj,edges):
max_deg =max_degree(adj)
result = [max_deg+1]
for k in range(2,n+1):
max = find_almost_k_uniform(n,k,adj,edges)
result.append(max)
return result
def find_almost_k_uniform(n,k,adj,edges):
max_len = 0
if k % 2 == 1:
max_len = find_k_odd(n,k,adj,edges)
else:
max_len = find_k_even(n,k,adj,edges)
return max_len
def find_k_odd(n,k,adj,edges):
d_s = {}
max_len = 0
for v in range(1,n+1):
d_s[v] = bfs(n,v,adj)
l = k//2
for v in range(1,n+1):
r = {i:-1 for i in range(1,n+1)}
#buscar un vertice de longitud l o l+1 por subarbol
depth,subtree = d_s[v]
for w in range(1,n+1):
if depth[w] == l+1:
r[subtree[w]] = l+1
if depth[w] == l and r[subtree[w]] == -1:
r[subtree[w]] = l
len_r = 0
found_l = False
for t in r.values():
if t != -1:
if t == l and not found_l:
len_r += 1
found_l =True
elif t== l+1:
len_r += 1
if len_r > max_len:
max_len = len_r
print(r)
return max_len
def find_k_even(n,k,adj,edges):
d_s = {}
for v in range(1,n+1):
d_s[v] = bfs(n,v,adj)
max_len = 0
l = k/2
for v in range(1,n+1):
depth,subtree = d_s[v]
r = {}
for w in range(1,n+1):
if depth[w] == l:
r[subtree[w]] = w
if len(r) > max_len:
max_len = len(r)
#print("max_lena vert--", max_len)
for e in edges:#O(n-1)
u = e[0]
v = e[1]
r_u = {}
r_v = {}
depth_u,subtree_u = bfs(n,u,adj,v)#O(n-1)
depth_v,subtree_v = bfs(n,v,adj,u)
#print(e)
#print("u--",depth_u,"--",subtree_u)
#print("v--",depth_v,"--",subtree_v)
for w in range(1,n+1):#O(n-1)
if depth_u[w] == l:
r_u[subtree_u[w]] = w
for w in range(1,n+1):#O(n-1)
if depth_v[w] == l:
r_v[subtree_v[w]] = w
t = len(r_u) + len(r_v)
if t > max_len:
max_len = t
#print("edge",e,"---",max_len)
#print("max_lena vert--", max_len)
return max_len
def bfs(n,x,adj,y=-1):
#depth[x]: longitud camino entre el vertice inicial y x
visited = [False for i in range(n+1)]
visited [x] = True
depth = [-1 for _ in range(n+1)]
subtree = [-1 for _ in range(n+1)]
if y!=-1:
visited[y] =True
q = [x]
depth[x] = 0
for w in adj[x]:
subtree[w] = w
while len(q) > 0:
v = q[0]
q.remove(v)
for w in adj[v]:
if not visited[w]:
q.append(w)
depth[w] = depth[v] + 1
if v!= x:
subtree[w] = subtree[v]
visited[w] = True
return depth,subtree
def max_degree(adj):
m_d = 0
for x in adj:
x_degree = len(x)
if m_d < x_degree:
m_d = x_degree
return m_d
def main():
n= int(input())
adj = [[]for i in range(n+1)]
edges = []
for _ in range(n-1):
x,y = [ int(i) for i in input().split()]
edges.append((x,y))
adj[x].append(y)
adj[y].append(x)
max_len = almost_same_distance(n,adj,edges)
print(' '.join(str(i) for i in max_len))
main()
```
No
| 106,256 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Tags: binary search, brute force, math, ternary search
Correct Solution:
```
from math import ceil
a = int(input())
for i in range(a):
# n - days before deadline, d - days for the program to work
n, d = map(int, input().split())
if d <= n:
print("YES")
else:
counter = 1
current_n_of_days = counter + (ceil(d / (counter + 1)))
previous_result = current_n_of_days + 1
while current_n_of_days <= previous_result:
if current_n_of_days <= n:
print("YES")
break
else:
counter += 1
previous_result = current_n_of_days
current_n_of_days = counter + (ceil(d / (counter + 1)))
else:
print("NO")
```
| 106,257 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Tags: binary search, brute force, math, ternary search
Correct Solution:
```
import os,sys
from io import BytesIO, IOBase
def ii(): return int(input())
def si(): return input()
def mi(): return map(int,input().split())
def li(): return list(mi())
import math
for i in range(ii()):
n,d=mi()
if d<=n:
print("YES")
else:
a=math.ceil(d/(n//2+1))
a+=n//2
if a<=n:
print("YES")
else:
print("NO")
```
| 106,258 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Tags: binary search, brute force, math, ternary search
Correct Solution:
```
def arr_inp():
return [int(x) for x in stdin.readline().split()]
from sys import stdin
from math import ceil
for i in range(int(input())):
n, d = arr_inp()
if n == d:
print('YES')
else:
a, b, c, mi = 0, d, 2, d
while (b >= a):
b, a = ceil(d / c), a + 1
mi = min(mi, a + b)
c += 1
print('YES' if n >= mi else 'NO')
```
| 106,259 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Tags: binary search, brute force, math, ternary search
Correct Solution:
```
import math
#print(math.ceil(4.0))
t = int(input())
for i in range(0, t):
n, d = map(int, input().split())
k = int(math.sqrt(d))
x = d
#print("k=",k)
if n <= k:
x = min(x, int(n + 1 + math.ceil(d / (n + 1))-1) )
# print("x=",x)
if k <= n:
x = min(x, k + 1 + math.ceil(d / (k + 1))- 1)
# print("x=", x)
if k <= n + 1:
x = min(x, k + math.ceil(d / k) -1)
# print("x=", x)
#print("n=",n)
if x <= n:
print("YES")
else:
print("NO")
```
| 106,260 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Tags: binary search, brute force, math, ternary search
Correct Solution:
```
import collections
import math
local = False
if local:
file = open("A.txt", "r")
def inp():
if local:
return file.readline().rstrip()
else:
return input().rstrip()
def ints():
return [int(_) for _ in inp().split()]
t = int(inp())
for _ in range(t):
n, d = ints()
if d<=n:
print("YES")
else:
found = False
for i in range(n):
if i+math.ceil(d/(i+1))<=n:
found=True
break
if found:
print("YES")
else:
print("NO")
```
| 106,261 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Tags: binary search, brute force, math, ternary search
Correct Solution:
```
import io
import os
from collections import Counter, defaultdict, deque
def solve(N, D):
x = int((D + 0.25) ** 0.5 - 0.5)
for i in range(max(0, x - 10), x + 10):
days = i + D // (i + 1)
if D % (i + 1) != 0:
days += 1
if days <= N:
return "YES"
return "NO"
if __name__ == "__main__":
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
T = int(input())
for t in range(T):
N, D = [int(x) for x in input().split()]
ans = solve(N, D)
print(ans)
```
| 106,262 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Tags: binary search, brute force, math, ternary search
Correct Solution:
```
import math
T=int(input())
for iT in range(T):
n,d=[int(i) for i in input().split()]
x=int(math.sqrt(d))-1
temp=x+math.ceil(d/(x+1))
print("YES" if (temp<=n or d==1 )else "NO")
```
| 106,263 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Tags: binary search, brute force, math, ternary search
Correct Solution:
```
'''input
3
1 1
4 5
5 11
'''
# A coding delight
from sys import stdin, stdout
import gc
gc.disable()
input = stdin.readline
import math
def check(num):
return num + math.ceil(d/(num + 1)) <= n
# main starts
t = int(input().strip())
for _ in range(t):
n, d = list(map(int, input().split()))
x = math.ceil(math.sqrt(d) - 1)
if x + math.ceil(d/(x + 1)) <= n:
print("YES")
elif x - 1 >= 1 and x - 1 + math.ceil(d/x) <= n:
print("YES")
elif x + 1 + math.ceil(d/(x + 2)) <= n:
print("YES")
else:
print("NO")
```
| 106,264 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Submitted Solution:
```
import sys
from math import ceil
tests = int(input())
for _ in range(tests):
n, d = list(map(int, sys.stdin.readline().split()))
ok = False
for i in range(n, -1 ,-1):
result = i + ceil(d/(i + 1))
if result <= n:
print("YES")
ok = True
break
if not ok:
print("NO")
```
Yes
| 106,265 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Submitted Solution:
```
def func(x, d):
#d_div_x = d // (x + 1) if d % (x + 1) == 0 else d // (x + 1) + 1
return x + d / (x + 1)
# 14
def ternary_search_min(l, r, d):
while r - l >= 3:
m1 = int(r - 2 * (r - l) / 3)
m2 = int(r - (r - l) / 3)
if func(m1, d) <= func(m2, d):
r = m2
else:
l = m1
remain_args = [i for i in range(l, r + 1)]
func_values = list(map(lambda x: func(x, d), remain_args))
return min(func_values)
test_size = int(input())
for i in range(test_size):
n, d = map(int, input().split())
min_days = ternary_search_min(0, n, d)
if min_days <= n or d <= n:
print("YES")
else:
print("NO")
```
Yes
| 106,266 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Submitted Solution:
```
from math import sqrt
for w in range(int(input())):
n,d = map(int,input().split())
print('yes') if 2*sqrt(d) <= n+1 else print('no')
```
Yes
| 106,267 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Submitted Solution:
```
import math
t=int(input())
for _ in range(t):
n,d=map(int,input().split())
x=n//2
y=math.ceil(d/(x+1))
if(x+y<=n):
print('YES')
else:
print('NO')
```
Yes
| 106,268 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Submitted Solution:
```
for t in range(int(input())):
n, d = [int(i) for i in input().split()]
if d <= n:
print("YES")
elif (n-1)**2 + 4*(n-d) > 0:
print("YES")
else:
print("NO")
```
No
| 106,269 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Submitted Solution:
```
import math
t=int(input())
for i in range(t):
n,d=map(int,input().split())
if d<=n:
print("YES")
else:
m=int(pow(d,0.5))
z=m+math.ceil(d/(m+1))
#print(m)
if z<=n:
print("YES")
else:
print("NO")
```
No
| 106,270 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Submitted Solution:
```
import math
for _ in range(int(input())):
n,d=map(int,input().split())
if n>=d:
print("YES")
else:
g=1
for i in range(1,n+1):
if math.ceil((d/(i+1)))+i<=n:
k=0
print("YES")
break
if g==1:
print("NO")
```
No
| 106,271 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Adilbek was assigned to a special project. For Adilbek it means that he has n days to run a special program and provide its results. But there is a problem: the program needs to run for d days to calculate the results.
Fortunately, Adilbek can optimize the program. If he spends x (x is a non-negative integer) days optimizing the program, he will make the program run in \left⌈ (d)/(x + 1) \right⌉ days (\left⌈ a \right⌉ is the ceiling function: \left⌈ 2.4 \right⌉ = 3, \left⌈ 2 \right⌉ = 2). The program cannot be run and optimized simultaneously, so the total number of days he will spend is equal to x + \left⌈ (d)/(x + 1) \right⌉.
Will Adilbek be able to provide the generated results in no more than n days?
Input
The first line contains a single integer T (1 ≤ T ≤ 50) — the number of test cases.
The next T lines contain test cases – one per line. Each line contains two integers n and d (1 ≤ n ≤ 10^9, 1 ≤ d ≤ 10^9) — the number of days before the deadline and the number of days the program runs.
Output
Print T answers — one per test case. For each test case print YES (case insensitive) if Adilbek can fit in n days or NO (case insensitive) otherwise.
Example
Input
3
1 1
4 5
5 11
Output
YES
YES
NO
Note
In the first test case, Adilbek decides not to optimize the program at all, since d ≤ n.
In the second test case, Adilbek can spend 1 day optimizing the program and it will run \left⌈ 5/2 \right⌉ = 3 days. In total, he will spend 4 days and will fit in the limit.
In the third test case, it's impossible to fit in the limit. For example, if Adilbek will optimize the program 2 days, it'll still work \left⌈ (11)/(2+1) \right⌉ = 4 days.
Submitted Solution:
```
import math
t = int(input())
while t:
t-=1
n,d = map(int,input().split())
if d<=n or 1+math.ceil(d/(2))<=n or 2+math.ceil(d/3)<=n:
print("YES")
else:
print("NO")
```
No
| 106,272 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Tags: *special, implementation
Correct Solution:
```
k=input().lower()
h=int(k,16)
print(h%2)
```
| 106,273 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Tags: *special, implementation
Correct Solution:
```
# d = {'0':0, '1': 1, '2':1, '3':2, '4':1,'5':2, '6':2,'7':3,'8':1,'9':2,'A':2}
s = input()
# count = 0
# for i in s:
# count+=d[i]
count = int(s[-1])
if(count%2==0):
print('0')
else:
print('1')
```
| 106,274 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Tags: *special, implementation
Correct Solution:
```
if int(input(),16)%2==0:
print(0)
else:
print(1)
```
| 106,275 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Tags: *special, implementation
Correct Solution:
```
n=input()
if(int(n[len(n)-1])%2==0):
print("0")
else:
print("1")
```
| 106,276 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Tags: *special, implementation
Correct Solution:
```
N = int(input()[-1])
print(N%2)
```
| 106,277 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Tags: *special, implementation
Correct Solution:
```
ans = int(input(), 16)
if ans%2 == 0:
print(0)
else:
print(1)
```
| 106,278 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Tags: *special, implementation
Correct Solution:
```
import math
# Initialising hex string
ini_string = input()
# Code to convert hex to binary
n = int(ini_string, 16)
bStr = ''
while n > 0:
bStr = str(n % 2) + bStr
n = n >> 1
res = bStr
# Print the resultant string
print(res[len(res) - 1])
```
| 106,279 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Tags: *special, implementation
Correct Solution:
```
str = input()
res = int(str, 16)
if res & 1 == 0:
print(0)
else:
print(1)
```
| 106,280 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Submitted Solution:
```
# your code goes here
a=input()
if int(a[6])%2==0:
print('0')
else:
print('1')
```
Yes
| 106,281 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Submitted Solution:
```
s=str(input())
t=0
if(int(s[len(s)-1])%2==0):
print(0)
else:
print(1)
```
Yes
| 106,282 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Submitted Solution:
```
s = str(input())
a = int(s[-1])
if a % 2 == 0:
print("0")
else:
print("1")
```
Yes
| 106,283 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Submitted Solution:
```
x = input()
x = int(x,16)
print(x % 2)
```
Yes
| 106,284 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Submitted Solution:
```
import random
a=input()
print(random.randrange(0,2,1))
```
No
| 106,285 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Submitted Solution:
```
print("1")
```
No
| 106,286 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Submitted Solution:
```
def ii():
return int(input())
def mi():
return map(int, input().split())
def li():
return list(mi())
s = input()
s = s[1:]
sum = 0
for x in s:
sum += int(x)
if sum % 10 == 8:
print(1)
else:
print(0)
```
No
| 106,287 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Input
The only line of the input contains a 7-digit hexadecimal number. The first "digit" of the number is letter A, the rest of the "digits" are decimal digits 0-9.
Output
Output a single integer.
Examples
Input
A278832
Output
0
Input
A089956
Output
0
Input
A089957
Output
1
Input
A144045
Output
1
Submitted Solution:
```
inp = input()
import random
random.seed(inp)
print(random.randint(0, 1))
```
No
| 106,288 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya claims that he had a paper square. He cut it into two rectangular parts using one vertical or horizontal cut. Then Vasya informed you the dimensions of these two rectangular parts. You need to check whether Vasya originally had a square. In other words, check if it is possible to make a square using two given rectangles.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines.
The first line contains two integers a_1 and b_1 (1 ≤ a_1, b_1 ≤ 100) — the dimensions of the first one obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
The second line contains two integers a_2 and b_2 (1 ≤ a_2, b_2 ≤ 100) — the dimensions of the second obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
Output
Print t answers, each of which is a string "YES" (in the case of a positive answer) or "NO" (in the case of a negative answer). The letters in words can be printed in any case (upper or lower).
Example
Input
3
2 3
3 1
3 2
1 3
3 3
1 3
Output
Yes
Yes
No
Tags: brute force, implementation, math
Correct Solution:
```
t = int(input())
for _ in range(t):
a1, b1 = map(int, input().split())
a2, b2 = map(int, input().split())
x1 = min(a1, b1) + min(a2, b2)
if max(a1, b1) == max(a2, b2):
if x1 == max(a1, b1):
print("YES")
else:
print("NO")
else:
print("NO")
```
| 106,289 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya claims that he had a paper square. He cut it into two rectangular parts using one vertical or horizontal cut. Then Vasya informed you the dimensions of these two rectangular parts. You need to check whether Vasya originally had a square. In other words, check if it is possible to make a square using two given rectangles.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines.
The first line contains two integers a_1 and b_1 (1 ≤ a_1, b_1 ≤ 100) — the dimensions of the first one obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
The second line contains two integers a_2 and b_2 (1 ≤ a_2, b_2 ≤ 100) — the dimensions of the second obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
Output
Print t answers, each of which is a string "YES" (in the case of a positive answer) or "NO" (in the case of a negative answer). The letters in words can be printed in any case (upper or lower).
Example
Input
3
2 3
3 1
3 2
1 3
3 3
1 3
Output
Yes
Yes
No
Tags: brute force, implementation, math
Correct Solution:
```
for _ in range(int(input())):
a = list(map(int,input().split()))
b = list(map(int,input().split()))
print('YES') if min(a)==(abs(b[1]-b[0])) and max(a)==max(b) else print('NO')
```
| 106,290 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya claims that he had a paper square. He cut it into two rectangular parts using one vertical or horizontal cut. Then Vasya informed you the dimensions of these two rectangular parts. You need to check whether Vasya originally had a square. In other words, check if it is possible to make a square using two given rectangles.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines.
The first line contains two integers a_1 and b_1 (1 ≤ a_1, b_1 ≤ 100) — the dimensions of the first one obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
The second line contains two integers a_2 and b_2 (1 ≤ a_2, b_2 ≤ 100) — the dimensions of the second obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
Output
Print t answers, each of which is a string "YES" (in the case of a positive answer) or "NO" (in the case of a negative answer). The letters in words can be printed in any case (upper or lower).
Example
Input
3
2 3
3 1
3 2
1 3
3 3
1 3
Output
Yes
Yes
No
Tags: brute force, implementation, math
Correct Solution:
```
import os
import sys
from io import BytesIO, IOBase
def main():
pass
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# endregion
if __name__ == "__main__":
main()
def test():
r1 = sorted(map(int, input().split()))
r2 = sorted(map(int, input().split()))
return ['No', 'Yes'][r1[0] + r2[0] == r1[1] == r2[1]]
t = int(input())
for _ in range(t):
print(test())
```
| 106,291 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya claims that he had a paper square. He cut it into two rectangular parts using one vertical or horizontal cut. Then Vasya informed you the dimensions of these two rectangular parts. You need to check whether Vasya originally had a square. In other words, check if it is possible to make a square using two given rectangles.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines.
The first line contains two integers a_1 and b_1 (1 ≤ a_1, b_1 ≤ 100) — the dimensions of the first one obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
The second line contains two integers a_2 and b_2 (1 ≤ a_2, b_2 ≤ 100) — the dimensions of the second obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
Output
Print t answers, each of which is a string "YES" (in the case of a positive answer) or "NO" (in the case of a negative answer). The letters in words can be printed in any case (upper or lower).
Example
Input
3
2 3
3 1
3 2
1 3
3 3
1 3
Output
Yes
Yes
No
Tags: brute force, implementation, math
Correct Solution:
```
num = int(input())
results = []
for T in range(num):
x = [int(i) for i in input().split()]
y = [int(i) for i in input().split()]
"""
x[0] y[1]
|--- | --|
x[1] | | | y[0]
|___ | __|
x[0]
x[1] |--------|
|--------|
y[0] |________|
y[1]
x[0] y[0]
|--- | --|
x[1] | | | y[1]
|___ | __|
x[1] y[1]
|--- | --|
x[0] | | | y[0]
|___ | __|
x[1] y[0]
|--- | --|
x[0] | | | y[1]
|___ | __|
"""
result = \
((x[1] == y[0]) and (x[1] == x[0] + y[1])) or \
((x[1] == y[1]) and (x[1] == x[0] + y[0])) or \
((x[0] == y[0]) and (x[0] == x[1] + y[1])) or \
((x[0] == y[1]) and (x[0] == x[1] + y[0])) or \
((y[1] == x[0]) and (y[1] == y[0] + x[1])) or \
((y[1] == x[1]) and (y[1] == y[0] + x[0])) or \
((y[0] == x[0]) and (y[0] == y[1] + x[1])) or \
((y[0] == x[1]) and (y[0] == y[1] + x[0]))
results.append(result)
for result in results:
print("Yes" if result else "No")
```
| 106,292 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya claims that he had a paper square. He cut it into two rectangular parts using one vertical or horizontal cut. Then Vasya informed you the dimensions of these two rectangular parts. You need to check whether Vasya originally had a square. In other words, check if it is possible to make a square using two given rectangles.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines.
The first line contains two integers a_1 and b_1 (1 ≤ a_1, b_1 ≤ 100) — the dimensions of the first one obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
The second line contains two integers a_2 and b_2 (1 ≤ a_2, b_2 ≤ 100) — the dimensions of the second obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
Output
Print t answers, each of which is a string "YES" (in the case of a positive answer) or "NO" (in the case of a negative answer). The letters in words can be printed in any case (upper or lower).
Example
Input
3
2 3
3 1
3 2
1 3
3 3
1 3
Output
Yes
Yes
No
Tags: brute force, implementation, math
Correct Solution:
```
import math
n=int(input())
for i in range(n):
a=list(map(int,input().split()))
b=list(map(int,input().split()))
if(a[0]==b[0] and a[1]+b[1]==a[0]):
print("Yes")
elif(a[0]==b[1] and a[1]+b[0]==a[0]):
print("Yes")
elif(a[1]==b[0] and a[0]+b[1]==a[1]):
print("Yes")
elif(a[1]==b[1] and a[0]+b[0]==a[1]):
print("Yes")
else:
print("No")
```
| 106,293 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya claims that he had a paper square. He cut it into two rectangular parts using one vertical or horizontal cut. Then Vasya informed you the dimensions of these two rectangular parts. You need to check whether Vasya originally had a square. In other words, check if it is possible to make a square using two given rectangles.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines.
The first line contains two integers a_1 and b_1 (1 ≤ a_1, b_1 ≤ 100) — the dimensions of the first one obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
The second line contains two integers a_2 and b_2 (1 ≤ a_2, b_2 ≤ 100) — the dimensions of the second obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
Output
Print t answers, each of which is a string "YES" (in the case of a positive answer) or "NO" (in the case of a negative answer). The letters in words can be printed in any case (upper or lower).
Example
Input
3
2 3
3 1
3 2
1 3
3 3
1 3
Output
Yes
Yes
No
Tags: brute force, implementation, math
Correct Solution:
```
from itertools import combinations
t = int(input())
for i in range(t):
a1, b1 = input().split()
a2, b2 = input().split()
f = 0
if a1 == a2:
if int(a1) == int(b1) + int(b2):
print("YES")
f = 1
if a1 == b2:
if int(a1) == int(a2) + int(b1):
print("YES")
f = 1
if b1 == a2:
if int(b1) == int(a1) + int(b2):
print("YES")
f = 1
if b1 == b2:
if int(b1) == int(a2) + int(a1):
print("YES")
f = 1
if f == 0:
print("NO")
```
| 106,294 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya claims that he had a paper square. He cut it into two rectangular parts using one vertical or horizontal cut. Then Vasya informed you the dimensions of these two rectangular parts. You need to check whether Vasya originally had a square. In other words, check if it is possible to make a square using two given rectangles.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines.
The first line contains two integers a_1 and b_1 (1 ≤ a_1, b_1 ≤ 100) — the dimensions of the first one obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
The second line contains two integers a_2 and b_2 (1 ≤ a_2, b_2 ≤ 100) — the dimensions of the second obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
Output
Print t answers, each of which is a string "YES" (in the case of a positive answer) or "NO" (in the case of a negative answer). The letters in words can be printed in any case (upper or lower).
Example
Input
3
2 3
3 1
3 2
1 3
3 3
1 3
Output
Yes
Yes
No
Tags: brute force, implementation, math
Correct Solution:
```
t=int(input())
for _ in range(t):
arr1 = list(map(int, input().split()))
arr2 = list(map(int, input().split()))
arr3=[i for i in arr1 for j in arr2 if i==j]
c1=0
c2=0
if(len(arr3)==0):
print("No")
continue
#print(arr3)
arr3[0]=max(arr3)
for i in arr1:
if arr3[0]!=i:
c1=i
for i in arr2:
if arr3[0]!=i:
c2=i
#print(c1,c2)
if arr3[0]==c1+c2:
print("Yes")
else:
print("No")
```
| 106,295 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya claims that he had a paper square. He cut it into two rectangular parts using one vertical or horizontal cut. Then Vasya informed you the dimensions of these two rectangular parts. You need to check whether Vasya originally had a square. In other words, check if it is possible to make a square using two given rectangles.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines.
The first line contains two integers a_1 and b_1 (1 ≤ a_1, b_1 ≤ 100) — the dimensions of the first one obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
The second line contains two integers a_2 and b_2 (1 ≤ a_2, b_2 ≤ 100) — the dimensions of the second obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
Output
Print t answers, each of which is a string "YES" (in the case of a positive answer) or "NO" (in the case of a negative answer). The letters in words can be printed in any case (upper or lower).
Example
Input
3
2 3
3 1
3 2
1 3
3 3
1 3
Output
Yes
Yes
No
Tags: brute force, implementation, math
Correct Solution:
```
# Vasya claims that he had a paper square. He cut it into two rectangular parts using one vertical or horizontal cut. Then Vasya informed you the dimensions of these two rectangular parts. You need to check whether Vasya originally had a square. In other words, check if it is possible to make a square using two given rectangles.
# Input
# The first line contains an integer t
# (1≤t≤104) — the number of test cases in the input. Then t
# test cases follow.
# Each test case is given in two lines.
# The first line contains two integers a1
# and b1 (1≤a1,b1≤100
# ) — the dimensions of the first one obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
# The second line contains two integers a2
# and b2 (1≤a2,b2≤100
# ) — the dimensions of the second obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
# Output
# Print t
# answers, each of which is a string "YES" (in the case of a positive answer) or "NO" (in the case of a negative answer). The letters in words can be printed in any case (upper or lower).
def fun(a,b,c,d):
if a ==b or c==d:
return False
if max(a,b)==max(c,d) and min(a,b) + min(c,d) == max(a,b):
return True
return False
for _ in range(int(input())):
a,b = list(map(int,input().split()))
c,d = list(map(int,input().split()))
if fun(a,b,c,d):
print("Yes")
else:
print("No")
```
| 106,296 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya claims that he had a paper square. He cut it into two rectangular parts using one vertical or horizontal cut. Then Vasya informed you the dimensions of these two rectangular parts. You need to check whether Vasya originally had a square. In other words, check if it is possible to make a square using two given rectangles.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines.
The first line contains two integers a_1 and b_1 (1 ≤ a_1, b_1 ≤ 100) — the dimensions of the first one obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
The second line contains two integers a_2 and b_2 (1 ≤ a_2, b_2 ≤ 100) — the dimensions of the second obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
Output
Print t answers, each of which is a string "YES" (in the case of a positive answer) or "NO" (in the case of a negative answer). The letters in words can be printed in any case (upper or lower).
Example
Input
3
2 3
3 1
3 2
1 3
3 3
1 3
Output
Yes
Yes
No
Submitted Solution:
```
t = int(input())
for _ in range(t) :
n = [ int(i) for i in input().split() ]
m = [ int(i) for i in input().split() ]
ans = False
if ( n[0] == m[0] and n[1]+m[1] == n[0] ) :
ans = True
elif ( n[0] == m[1] and n[1]+m[0] == n[0] ) :
ans = True
elif ( n[1] == m[0] and n[0]+m[1] == n[1] ) :
ans = True
elif ( n[1] == m[1] and n[0]+m[0] == n[1] ) :
ans = True
if ( ans ) :
print("Yes")
else :
print("No")
```
Yes
| 106,297 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya claims that he had a paper square. He cut it into two rectangular parts using one vertical or horizontal cut. Then Vasya informed you the dimensions of these two rectangular parts. You need to check whether Vasya originally had a square. In other words, check if it is possible to make a square using two given rectangles.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines.
The first line contains two integers a_1 and b_1 (1 ≤ a_1, b_1 ≤ 100) — the dimensions of the first one obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
The second line contains two integers a_2 and b_2 (1 ≤ a_2, b_2 ≤ 100) — the dimensions of the second obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
Output
Print t answers, each of which is a string "YES" (in the case of a positive answer) or "NO" (in the case of a negative answer). The letters in words can be printed in any case (upper or lower).
Example
Input
3
2 3
3 1
3 2
1 3
3 3
1 3
Output
Yes
Yes
No
Submitted Solution:
```
def sqr(a,b):
if max(sq1)==max(sq2):
if min(sq1)+min(sq2)==max(sq1):
return 'YES'
return 'NO'
n=int(input())
ans=[]
for i in range(n):
sq1=list(map(int,input().split()))
sq2 = list(map(int, input().split()))
ans.append(sqr(sq1,sq2))
for i in ans:
print(i)
```
Yes
| 106,298 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya claims that he had a paper square. He cut it into two rectangular parts using one vertical or horizontal cut. Then Vasya informed you the dimensions of these two rectangular parts. You need to check whether Vasya originally had a square. In other words, check if it is possible to make a square using two given rectangles.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given in two lines.
The first line contains two integers a_1 and b_1 (1 ≤ a_1, b_1 ≤ 100) — the dimensions of the first one obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
The second line contains two integers a_2 and b_2 (1 ≤ a_2, b_2 ≤ 100) — the dimensions of the second obtained after cutting rectangle. The sizes are given in random order (that is, it is not known which of the numbers is the width, and which of the numbers is the length).
Output
Print t answers, each of which is a string "YES" (in the case of a positive answer) or "NO" (in the case of a negative answer). The letters in words can be printed in any case (upper or lower).
Example
Input
3
2 3
3 1
3 2
1 3
3 3
1 3
Output
Yes
Yes
No
Submitted Solution:
```
t=int(input())
for i in range(t):
a, b=map(int,input().split())
c, d=map(int,input().split())
if a==d and a == b+c:
print("YES")
elif a==c and a==b+d:
print("YES")
elif b==d and b==a+c:
print("YES")
elif b==c and b==a+d:
print("YES")
else:
print("NO")
```
Yes
| 106,299 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.