message stringlengths 2 59.7k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 37 108k | cluster float64 20 20 | __index_level_0__ int64 74 217k |
|---|---|---|---|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
Amr doesn't like Maths as he finds it really boring, so he usually sleeps in Maths lectures. But one day the teacher suspected that Amr is sleeping and asked him a question to make sure he wasn't.
First he gave Amr two positive integers n and k. Then he asked Amr, how many integer numbers x > 0 exist such that:
* Decimal representation of x (without leading zeroes) consists of exactly n digits;
* There exists some integer y > 0 such that:
* <image>;
* decimal representation of y is a suffix of decimal representation of x.
As the answer to this question may be pretty huge the teacher asked Amr to output only its remainder modulo a number m.
Can you help Amr escape this embarrassing situation?
Input
Input consists of three integers n, k, m (1 ≤ n ≤ 1000, 1 ≤ k ≤ 100, 1 ≤ m ≤ 109).
Output
Print the required number modulo m.
Examples
Input
1 2 1000
Output
4
Input
2 2 1000
Output
45
Input
5 3 1103
Output
590
Note
A suffix of a string S is a non-empty string that can be obtained by removing some number (possibly, zero) of first characters from S. | instruction | 0 | 98,240 | 20 | 196,480 |
Tags: dp, implementation
Correct Solution:
```
n,k,m=map(int,input().split())
d,r,p,P=0,0,1%k,(10**(n-1))*9
F=[0]*k
F[0]=1
while d<n:
d+=1
P//=10
E=[0]*k
if P==0:P=1
i=1
# print("E=",E)
# print("F=",F)
while i<10:
j=(-i*p)%k
f=0
while f<k:
E[f]+=F[j]
f+=1
j+=1
if j==k:j=0
i+=1
r+=E[0]*P
p=p*10%k
E[0]=0
i=1
while i<k:
F[i]=(F[i]+E[i])%m
i+=1
# print(E,P)
F[0]=1
#print("r=",r)
print(r%m)
#i=10**n
#j=10**(n-1)
#r=0
#F=[0]*k
#while j<i:
# x=str(j)
# l=len(x)
# a=l
# while a:
# a-=1
# s=int(x[a:l])
# if s>0 and s%k==0:
# r+=1
# break
# j+=1
#print()
#print(r)
"""
3 6 9
13 16 19 12 15 18
23 26 29 21 24 27
33 36 39 30
43 46 49 42 45 48
53 56 59 51 54 57
63 66 69 60
73 76 79 72 75 78
83 86 89 81 84 87
93 96 99 90
"""
``` | output | 1 | 98,240 | 20 | 196,481 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Amr doesn't like Maths as he finds it really boring, so he usually sleeps in Maths lectures. But one day the teacher suspected that Amr is sleeping and asked him a question to make sure he wasn't.
First he gave Amr two positive integers n and k. Then he asked Amr, how many integer numbers x > 0 exist such that:
* Decimal representation of x (without leading zeroes) consists of exactly n digits;
* There exists some integer y > 0 such that:
* <image>;
* decimal representation of y is a suffix of decimal representation of x.
As the answer to this question may be pretty huge the teacher asked Amr to output only its remainder modulo a number m.
Can you help Amr escape this embarrassing situation?
Input
Input consists of three integers n, k, m (1 ≤ n ≤ 1000, 1 ≤ k ≤ 100, 1 ≤ m ≤ 109).
Output
Print the required number modulo m.
Examples
Input
1 2 1000
Output
4
Input
2 2 1000
Output
45
Input
5 3 1103
Output
590
Note
A suffix of a string S is a non-empty string that can be obtained by removing some number (possibly, zero) of first characters from S.
Submitted Solution:
```
s = input().split()
n,k,m = int(s[0]),int(s[1]),int(s[2])
b = [0 for x in range(n+1)]
ans,p = 0,0
s = 0
for i in range(1,n+1):
b[i] = ((10**i-1)//k - s)%m
s += b[i]
for i in range(1,n+1):
if i == n:
ans += b[i]%m
break
ans += b[i]* 9*10**(n-i)%m
print(ans%m)
``` | instruction | 0 | 98,241 | 20 | 196,482 |
No | output | 1 | 98,241 | 20 | 196,483 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Amr doesn't like Maths as he finds it really boring, so he usually sleeps in Maths lectures. But one day the teacher suspected that Amr is sleeping and asked him a question to make sure he wasn't.
First he gave Amr two positive integers n and k. Then he asked Amr, how many integer numbers x > 0 exist such that:
* Decimal representation of x (without leading zeroes) consists of exactly n digits;
* There exists some integer y > 0 such that:
* <image>;
* decimal representation of y is a suffix of decimal representation of x.
As the answer to this question may be pretty huge the teacher asked Amr to output only its remainder modulo a number m.
Can you help Amr escape this embarrassing situation?
Input
Input consists of three integers n, k, m (1 ≤ n ≤ 1000, 1 ≤ k ≤ 100, 1 ≤ m ≤ 109).
Output
Print the required number modulo m.
Examples
Input
1 2 1000
Output
4
Input
2 2 1000
Output
45
Input
5 3 1103
Output
590
Note
A suffix of a string S is a non-empty string that can be obtained by removing some number (possibly, zero) of first characters from S.
Submitted Solution:
```
n,k,m=map(int,input().split())
d,r,p,P=0,0,1%k,(10**(n-1))*9
F=[0]*k
F[0]=1
while d<n:
d+=1
P//=10
E=[0]*k
if P==0:P=1
i=1
# print("E=",E)
# print("F=",F)
while i<10:
j=(-i*p)%k
f=0
while f<k:
E[f]+=F[j]
f+=1
j+=1
if j==k:j=0
i+=1
r+=E[0]*P
p=p*10%k
E[0]=0
i=1
while i<k:
F[i]=(F[i]+E[i])%m
i+=1
# print(E,P)
F=E
F[0]=1
#print("r=",r)
print(r%m)
#i=10**n
#j=10**(n-1)
#r=0
#F=[0]*k
#while j<i:
# x=str(j)
# l=len(x)
# a=l
# while a:
# a-=1
# s=int(x[a:l])
# if s>0 and s%k==0:
# r+=1
# break
# j+=1
#print()
#print(r)
"""
3 6 9
13 16 19 12 15 18
23 26 29 21 24 27
33 36 39 30
43 46 49 42 45 48
53 56 59 51 54 57
63 66 69 60
73 76 79 72 75 78
83 86 89 81 84 87
93 96 99 90
"""
``` | instruction | 0 | 98,242 | 20 | 196,484 |
No | output | 1 | 98,242 | 20 | 196,485 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Amr doesn't like Maths as he finds it really boring, so he usually sleeps in Maths lectures. But one day the teacher suspected that Amr is sleeping and asked him a question to make sure he wasn't.
First he gave Amr two positive integers n and k. Then he asked Amr, how many integer numbers x > 0 exist such that:
* Decimal representation of x (without leading zeroes) consists of exactly n digits;
* There exists some integer y > 0 such that:
* <image>;
* decimal representation of y is a suffix of decimal representation of x.
As the answer to this question may be pretty huge the teacher asked Amr to output only its remainder modulo a number m.
Can you help Amr escape this embarrassing situation?
Input
Input consists of three integers n, k, m (1 ≤ n ≤ 1000, 1 ≤ k ≤ 100, 1 ≤ m ≤ 109).
Output
Print the required number modulo m.
Examples
Input
1 2 1000
Output
4
Input
2 2 1000
Output
45
Input
5 3 1103
Output
590
Note
A suffix of a string S is a non-empty string that can be obtained by removing some number (possibly, zero) of first characters from S.
Submitted Solution:
```
n,k,m=map(int,input().split())
d,r,p,P=0,0,1%k,(10**(n-1))*9
F=[0]*k
F[0]=1
while d<n:
d+=1
P//=10
E=[0]*k
if P==0:P=1
i=1
while i<10:
j=0
while j<k:
E[j]+=F[(j-i*p)%k]
j+=1
i+=1
r+=E[0]*P
p=p*10%k
E[0]=0
F=E
F[0]=1
print(r%m)
``` | instruction | 0 | 98,243 | 20 | 196,486 |
No | output | 1 | 98,243 | 20 | 196,487 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Something happened in Uzhlyandia again... There are riots on the streets... Famous Uzhlyandian superheroes Shean the Sheep and Stas the Giraffe were called in order to save the situation. Upon the arriving, they found that citizens are worried about maximum values of the Main Uzhlyandian Function f, which is defined as follows:
<image>
In the above formula, 1 ≤ l < r ≤ n must hold, where n is the size of the Main Uzhlyandian Array a, and |x| means absolute value of x. But the heroes skipped their math lessons in school, so they asked you for help. Help them calculate the maximum value of f among all possible values of l and r for the given array a.
Input
The first line contains single integer n (2 ≤ n ≤ 105) — the size of the array a.
The second line contains n integers a1, a2, ..., an (-109 ≤ ai ≤ 109) — the array elements.
Output
Print the only integer — the maximum value of f.
Examples
Input
5
1 4 2 3 1
Output
3
Input
4
1 5 4 7
Output
6
Note
In the first sample case, the optimal value of f is reached on intervals [1, 2] and [2, 5].
In the second case maximal value of f is reachable only on the whole array. | instruction | 0 | 98,314 | 20 | 196,628 |
Tags: dp, two pointers
Correct Solution:
```
def main():
n = int(input())
a = list(map(int, input().split()))
b = []
for i in range(len(a) - 1):
b.append(abs(a[i] - a[i + 1]))
max_odd = b[0]
max_even = 0
all_values = [max_odd, max_even]
for bi in b[1:]:
new_odd = max(max_even + bi, bi)
new_even = max(max_odd - bi, 0)
max_odd = new_odd
max_even = new_even
all_values += [max_odd, max_even]
print(max(all_values))
if __name__ == '__main__':
# import sys
# sys.stdin = open("C.txt")
main()
``` | output | 1 | 98,314 | 20 | 196,629 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Something happened in Uzhlyandia again... There are riots on the streets... Famous Uzhlyandian superheroes Shean the Sheep and Stas the Giraffe were called in order to save the situation. Upon the arriving, they found that citizens are worried about maximum values of the Main Uzhlyandian Function f, which is defined as follows:
<image>
In the above formula, 1 ≤ l < r ≤ n must hold, where n is the size of the Main Uzhlyandian Array a, and |x| means absolute value of x. But the heroes skipped their math lessons in school, so they asked you for help. Help them calculate the maximum value of f among all possible values of l and r for the given array a.
Input
The first line contains single integer n (2 ≤ n ≤ 105) — the size of the array a.
The second line contains n integers a1, a2, ..., an (-109 ≤ ai ≤ 109) — the array elements.
Output
Print the only integer — the maximum value of f.
Examples
Input
5
1 4 2 3 1
Output
3
Input
4
1 5 4 7
Output
6
Note
In the first sample case, the optimal value of f is reached on intervals [1, 2] and [2, 5].
In the second case maximal value of f is reachable only on the whole array. | instruction | 0 | 98,315 | 20 | 196,630 |
Tags: dp, two pointers
Correct Solution:
```
import math
from collections import defaultdict as dd
def main():
n = int(input())
A = list(map(int, input().split()))
# print(A)
B = []
for i in range(1, len(A)):
B.append(abs(A[i]-A[i-1]))
# print(B)
Dp = dd(int)
Dm = dd(int)
Dp[0]=0
MAX = 0
for i in range(n-1):
Dm[i] = Dp[i-1] + B[i]
Dp[i] = max(Dm[i-1] - B[i], 0)
MAX = max(Dm[i], Dp[i], MAX)
print(MAX)
if __name__ == "__main__":
main()
``` | output | 1 | 98,315 | 20 | 196,631 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an integer n (n ≥ 0) represented with k digits in base (radix) b. So,
$$$n = a_1 ⋅ b^{k-1} + a_2 ⋅ b^{k-2} + … a_{k-1} ⋅ b + a_k.$$$
For example, if b=17, k=3 and a=[11, 15, 7] then n=11⋅17^2+15⋅17+7=3179+255+7=3441.
Determine whether n is even or odd.
Input
The first line contains two integers b and k (2≤ b≤ 100, 1≤ k≤ 10^5) — the base of the number and the number of digits.
The second line contains k integers a_1, a_2, …, a_k (0≤ a_i < b) — the digits of n.
The representation of n contains no unnecessary leading zero. That is, a_1 can be equal to 0 only if k = 1.
Output
Print "even" if n is even, otherwise print "odd".
You can print each letter in any case (upper or lower).
Examples
Input
13 3
3 2 7
Output
even
Input
10 9
1 2 3 4 5 6 7 8 9
Output
odd
Input
99 5
32 92 85 74 4
Output
odd
Input
2 2
1 0
Output
even
Note
In the first example, n = 3 ⋅ 13^2 + 2 ⋅ 13 + 7 = 540, which is even.
In the second example, n = 123456789 is odd.
In the third example, n = 32 ⋅ 99^4 + 92 ⋅ 99^3 + 85 ⋅ 99^2 + 74 ⋅ 99 + 4 = 3164015155 is odd.
In the fourth example n = 2. | instruction | 0 | 98,641 | 20 | 197,282 |
Tags: math
Correct Solution:
```
import sys
input=sys.stdin.buffer.readline
from math import*
n,k=map(int,input().split())
arr=list(map(int,input().split()))
odd=0
for i in range(k-1):
if arr[i]%2==1:
odd+=1
even=k-odd-1
#print(even,odd)
if n%2==0:
if arr[-1]%2==0:
print("even")
else:
print("odd")
else:
if odd%2==0:
if arr[-1]%2==0:
print("even")
else:
print("odd")
else:
if arr[-1]%2==0:
print("odd")
else:
print("even")
``` | output | 1 | 98,641 | 20 | 197,283 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an integer n (n ≥ 0) represented with k digits in base (radix) b. So,
$$$n = a_1 ⋅ b^{k-1} + a_2 ⋅ b^{k-2} + … a_{k-1} ⋅ b + a_k.$$$
For example, if b=17, k=3 and a=[11, 15, 7] then n=11⋅17^2+15⋅17+7=3179+255+7=3441.
Determine whether n is even or odd.
Input
The first line contains two integers b and k (2≤ b≤ 100, 1≤ k≤ 10^5) — the base of the number and the number of digits.
The second line contains k integers a_1, a_2, …, a_k (0≤ a_i < b) — the digits of n.
The representation of n contains no unnecessary leading zero. That is, a_1 can be equal to 0 only if k = 1.
Output
Print "even" if n is even, otherwise print "odd".
You can print each letter in any case (upper or lower).
Examples
Input
13 3
3 2 7
Output
even
Input
10 9
1 2 3 4 5 6 7 8 9
Output
odd
Input
99 5
32 92 85 74 4
Output
odd
Input
2 2
1 0
Output
even
Note
In the first example, n = 3 ⋅ 13^2 + 2 ⋅ 13 + 7 = 540, which is even.
In the second example, n = 123456789 is odd.
In the third example, n = 32 ⋅ 99^4 + 92 ⋅ 99^3 + 85 ⋅ 99^2 + 74 ⋅ 99 + 4 = 3164015155 is odd.
In the fourth example n = 2. | instruction | 0 | 98,642 | 20 | 197,284 |
Tags: math
Correct Solution:
```
b, k = map(int, input().split())
a = list(map(int, input().split()))
if b % 2 == 0:
if a[k-1] % 2 == 0:
ans = 'even'
else:
ans = 'odd'
else:
sum = 0
for i in range(k):
sum += a[i]
if sum % 2 == 0:
ans = 'even'
else:
ans = 'odd'
print(ans)
``` | output | 1 | 98,642 | 20 | 197,285 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an integer n (n ≥ 0) represented with k digits in base (radix) b. So,
$$$n = a_1 ⋅ b^{k-1} + a_2 ⋅ b^{k-2} + … a_{k-1} ⋅ b + a_k.$$$
For example, if b=17, k=3 and a=[11, 15, 7] then n=11⋅17^2+15⋅17+7=3179+255+7=3441.
Determine whether n is even or odd.
Input
The first line contains two integers b and k (2≤ b≤ 100, 1≤ k≤ 10^5) — the base of the number and the number of digits.
The second line contains k integers a_1, a_2, …, a_k (0≤ a_i < b) — the digits of n.
The representation of n contains no unnecessary leading zero. That is, a_1 can be equal to 0 only if k = 1.
Output
Print "even" if n is even, otherwise print "odd".
You can print each letter in any case (upper or lower).
Examples
Input
13 3
3 2 7
Output
even
Input
10 9
1 2 3 4 5 6 7 8 9
Output
odd
Input
99 5
32 92 85 74 4
Output
odd
Input
2 2
1 0
Output
even
Note
In the first example, n = 3 ⋅ 13^2 + 2 ⋅ 13 + 7 = 540, which is even.
In the second example, n = 123456789 is odd.
In the third example, n = 32 ⋅ 99^4 + 92 ⋅ 99^3 + 85 ⋅ 99^2 + 74 ⋅ 99 + 4 = 3164015155 is odd.
In the fourth example n = 2. | instruction | 0 | 98,643 | 20 | 197,286 |
Tags: math
Correct Solution:
```
f=lambda:map(int,input().split())
b,k=f()
b=b%10
l=list(f())
l1=[]
if b%2==0:
print('even' if l[-1]%2==0 else 'odd')
else:
for i in l:
if i%2!=0:
l1.append(1)
print('even' if sum(l1) % 2 == 0 else 'odd')
``` | output | 1 | 98,643 | 20 | 197,287 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an integer n (n ≥ 0) represented with k digits in base (radix) b. So,
$$$n = a_1 ⋅ b^{k-1} + a_2 ⋅ b^{k-2} + … a_{k-1} ⋅ b + a_k.$$$
For example, if b=17, k=3 and a=[11, 15, 7] then n=11⋅17^2+15⋅17+7=3179+255+7=3441.
Determine whether n is even or odd.
Input
The first line contains two integers b and k (2≤ b≤ 100, 1≤ k≤ 10^5) — the base of the number and the number of digits.
The second line contains k integers a_1, a_2, …, a_k (0≤ a_i < b) — the digits of n.
The representation of n contains no unnecessary leading zero. That is, a_1 can be equal to 0 only if k = 1.
Output
Print "even" if n is even, otherwise print "odd".
You can print each letter in any case (upper or lower).
Examples
Input
13 3
3 2 7
Output
even
Input
10 9
1 2 3 4 5 6 7 8 9
Output
odd
Input
99 5
32 92 85 74 4
Output
odd
Input
2 2
1 0
Output
even
Note
In the first example, n = 3 ⋅ 13^2 + 2 ⋅ 13 + 7 = 540, which is even.
In the second example, n = 123456789 is odd.
In the third example, n = 32 ⋅ 99^4 + 92 ⋅ 99^3 + 85 ⋅ 99^2 + 74 ⋅ 99 + 4 = 3164015155 is odd.
In the fourth example n = 2. | instruction | 0 | 98,644 | 20 | 197,288 |
Tags: math
Correct Solution:
```
b,k=map(int,input().split())
a=list(map(int,input().split()))
if(b%2==0):
if(a[k-1]%2==0):print('even')
else:print('odd')
else:
cnt=0
for i in range(k):
if(a[i]%2==1):cnt+=1
if(cnt%2==0):print('even')
else:print('odd')
``` | output | 1 | 98,644 | 20 | 197,289 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an integer n (n ≥ 0) represented with k digits in base (radix) b. So,
$$$n = a_1 ⋅ b^{k-1} + a_2 ⋅ b^{k-2} + … a_{k-1} ⋅ b + a_k.$$$
For example, if b=17, k=3 and a=[11, 15, 7] then n=11⋅17^2+15⋅17+7=3179+255+7=3441.
Determine whether n is even or odd.
Input
The first line contains two integers b and k (2≤ b≤ 100, 1≤ k≤ 10^5) — the base of the number and the number of digits.
The second line contains k integers a_1, a_2, …, a_k (0≤ a_i < b) — the digits of n.
The representation of n contains no unnecessary leading zero. That is, a_1 can be equal to 0 only if k = 1.
Output
Print "even" if n is even, otherwise print "odd".
You can print each letter in any case (upper or lower).
Examples
Input
13 3
3 2 7
Output
even
Input
10 9
1 2 3 4 5 6 7 8 9
Output
odd
Input
99 5
32 92 85 74 4
Output
odd
Input
2 2
1 0
Output
even
Note
In the first example, n = 3 ⋅ 13^2 + 2 ⋅ 13 + 7 = 540, which is even.
In the second example, n = 123456789 is odd.
In the third example, n = 32 ⋅ 99^4 + 92 ⋅ 99^3 + 85 ⋅ 99^2 + 74 ⋅ 99 + 4 = 3164015155 is odd.
In the fourth example n = 2. | instruction | 0 | 98,645 | 20 | 197,290 |
Tags: math
Correct Solution:
```
#!/usr/bin/python3
b, k = map(int, input().split())
a = list(map(int, input().split()))
cur = 0
for c in a:
cur = (cur * b + c) % 2
if cur == 0:
print("even")
else:
print("odd")
``` | output | 1 | 98,645 | 20 | 197,291 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an integer n (n ≥ 0) represented with k digits in base (radix) b. So,
$$$n = a_1 ⋅ b^{k-1} + a_2 ⋅ b^{k-2} + … a_{k-1} ⋅ b + a_k.$$$
For example, if b=17, k=3 and a=[11, 15, 7] then n=11⋅17^2+15⋅17+7=3179+255+7=3441.
Determine whether n is even or odd.
Input
The first line contains two integers b and k (2≤ b≤ 100, 1≤ k≤ 10^5) — the base of the number and the number of digits.
The second line contains k integers a_1, a_2, …, a_k (0≤ a_i < b) — the digits of n.
The representation of n contains no unnecessary leading zero. That is, a_1 can be equal to 0 only if k = 1.
Output
Print "even" if n is even, otherwise print "odd".
You can print each letter in any case (upper or lower).
Examples
Input
13 3
3 2 7
Output
even
Input
10 9
1 2 3 4 5 6 7 8 9
Output
odd
Input
99 5
32 92 85 74 4
Output
odd
Input
2 2
1 0
Output
even
Note
In the first example, n = 3 ⋅ 13^2 + 2 ⋅ 13 + 7 = 540, which is even.
In the second example, n = 123456789 is odd.
In the third example, n = 32 ⋅ 99^4 + 92 ⋅ 99^3 + 85 ⋅ 99^2 + 74 ⋅ 99 + 4 = 3164015155 is odd.
In the fourth example n = 2. | instruction | 0 | 98,646 | 20 | 197,292 |
Tags: math
Correct Solution:
```
b,k=map(int,input().split())
a=list(map(int,input().split()))
l=a[-1]
if(b%2==0):
if(l%2==0):
print("even")
else:
print("odd")
else:
for i in range(k-1):
l+=a[i]%2
if(l%2==0):
print("even")
else:
print("odd")
``` | output | 1 | 98,646 | 20 | 197,293 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an integer n (n ≥ 0) represented with k digits in base (radix) b. So,
$$$n = a_1 ⋅ b^{k-1} + a_2 ⋅ b^{k-2} + … a_{k-1} ⋅ b + a_k.$$$
For example, if b=17, k=3 and a=[11, 15, 7] then n=11⋅17^2+15⋅17+7=3179+255+7=3441.
Determine whether n is even or odd.
Input
The first line contains two integers b and k (2≤ b≤ 100, 1≤ k≤ 10^5) — the base of the number and the number of digits.
The second line contains k integers a_1, a_2, …, a_k (0≤ a_i < b) — the digits of n.
The representation of n contains no unnecessary leading zero. That is, a_1 can be equal to 0 only if k = 1.
Output
Print "even" if n is even, otherwise print "odd".
You can print each letter in any case (upper or lower).
Examples
Input
13 3
3 2 7
Output
even
Input
10 9
1 2 3 4 5 6 7 8 9
Output
odd
Input
99 5
32 92 85 74 4
Output
odd
Input
2 2
1 0
Output
even
Note
In the first example, n = 3 ⋅ 13^2 + 2 ⋅ 13 + 7 = 540, which is even.
In the second example, n = 123456789 is odd.
In the third example, n = 32 ⋅ 99^4 + 92 ⋅ 99^3 + 85 ⋅ 99^2 + 74 ⋅ 99 + 4 = 3164015155 is odd.
In the fourth example n = 2. | instruction | 0 | 98,647 | 20 | 197,294 |
Tags: math
Correct Solution:
```
b,k=map(int,input().split())
l=list(map(int,input().split()))
if b%2==0:
if l[-1]%2==0:
print('even')
else:
print('odd')
else:
c=0
for i in l:
if i%2!=0:
c+=1
if c%2!=0:
print('odd')
else:
print('even')
``` | output | 1 | 98,647 | 20 | 197,295 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given an integer n (n ≥ 0) represented with k digits in base (radix) b. So,
$$$n = a_1 ⋅ b^{k-1} + a_2 ⋅ b^{k-2} + … a_{k-1} ⋅ b + a_k.$$$
For example, if b=17, k=3 and a=[11, 15, 7] then n=11⋅17^2+15⋅17+7=3179+255+7=3441.
Determine whether n is even or odd.
Input
The first line contains two integers b and k (2≤ b≤ 100, 1≤ k≤ 10^5) — the base of the number and the number of digits.
The second line contains k integers a_1, a_2, …, a_k (0≤ a_i < b) — the digits of n.
The representation of n contains no unnecessary leading zero. That is, a_1 can be equal to 0 only if k = 1.
Output
Print "even" if n is even, otherwise print "odd".
You can print each letter in any case (upper or lower).
Examples
Input
13 3
3 2 7
Output
even
Input
10 9
1 2 3 4 5 6 7 8 9
Output
odd
Input
99 5
32 92 85 74 4
Output
odd
Input
2 2
1 0
Output
even
Note
In the first example, n = 3 ⋅ 13^2 + 2 ⋅ 13 + 7 = 540, which is even.
In the second example, n = 123456789 is odd.
In the third example, n = 32 ⋅ 99^4 + 92 ⋅ 99^3 + 85 ⋅ 99^2 + 74 ⋅ 99 + 4 = 3164015155 is odd.
In the fourth example n = 2. | instruction | 0 | 98,648 | 20 | 197,296 |
Tags: math
Correct Solution:
```
def main():
b,k = map(int,input().split())
a = list(map(int,input().split()))
even = 0
odd = 0
for i in a:
if i%2 == 0:
even += 1
else:
odd += 1
if b%2 == 0:
if a[-1]%2 == 0:
print ('even')
else:
print ('odd')
else:
if odd%2 == 0:
print ('even')
else:
print ('odd')
main()
``` | output | 1 | 98,648 | 20 | 197,297 |
Provide tags and a correct Python 3 solution for this coding contest problem.
At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.
Fortunately, Picks remembers something about his set S:
* its elements were distinct integers from 1 to limit;
* the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation).
Can you help Picks and find any set S, that satisfies all the above conditions?
Input
The first line contains two integers: sum, limit (1 ≤ sum, limit ≤ 105).
Output
In the first line print an integer n (1 ≤ n ≤ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.
If it's impossible to find a suitable set, print -1.
Examples
Input
5 5
Output
2
4 5
Input
4 3
Output
3
2 3 1
Input
5 1
Output
-1
Note
In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.
In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4. | instruction | 0 | 99,006 | 20 | 198,012 |
Tags: bitmasks, greedy, implementation, sortings
Correct Solution:
```
while True:
try:
def solution(s, l ):
ans = list()
i = l
idn= t = 1
while i >= 1:
tr = i & t
if tr > 0 and t <= s:
s -= t
ans.append(i)
t, i= 1, i-1
elif tr > 0 and t > s:
i -= 1
t = 1
else:
t *= 2
if s == 0:
break
if s==0:
print(len(ans))
print(*ans)
else:print(-1)
def read():
sum, limit = map(int, input().split())
solution(sum, limit)
if __name__ == "__main__":
read()
except EOFError:
break
``` | output | 1 | 99,006 | 20 | 198,013 |
Provide tags and a correct Python 3 solution for this coding contest problem.
At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.
Fortunately, Picks remembers something about his set S:
* its elements were distinct integers from 1 to limit;
* the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation).
Can you help Picks and find any set S, that satisfies all the above conditions?
Input
The first line contains two integers: sum, limit (1 ≤ sum, limit ≤ 105).
Output
In the first line print an integer n (1 ≤ n ≤ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.
If it's impossible to find a suitable set, print -1.
Examples
Input
5 5
Output
2
4 5
Input
4 3
Output
3
2 3 1
Input
5 1
Output
-1
Note
In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.
In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4. | instruction | 0 | 99,008 | 20 | 198,016 |
Tags: bitmasks, greedy, implementation, sortings
Correct Solution:
```
import math
def lowerbit(x):
val = bin(x)[::-1]
a,b = val.split("1",1)
a +="1"
return int(a[::-1],2)
s,limit = map(int,input().split())
org = s
ans = 0
ones = math.ceil(limit/2)
if s<= ones:
print(s)
for i in range(1,limit+1,2):
if s == 0:
exit(0)
else:
s-=1
print(i,end=" ")
exit(0)
if limit%2==1:
high = limit-1
else:
high = limit
red = []
for i in range(high,0,-2):
if s <= ones or s==0:
break
elif s- lowerbit(i) >= 0:
red.append(i)
#print("red ",red)
s-=lowerbit(i)
#print(" s ",s)
ans += lowerbit(i)
#print(" ans ",ans)
if org == ans:
print(len(red))
for i in red:
print(i,end=" ")
elif ans+ones>=org:
for i in range(1,limit+1,2):
ans+=1
red.append(i)
if ans == org:
print(len(red))
for j in red:
print(j,end=" ")
exit(0)
else:
print(-1)
``` | output | 1 | 99,008 | 20 | 198,017 |
Provide tags and a correct Python 3 solution for this coding contest problem.
At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.
Fortunately, Picks remembers something about his set S:
* its elements were distinct integers from 1 to limit;
* the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation).
Can you help Picks and find any set S, that satisfies all the above conditions?
Input
The first line contains two integers: sum, limit (1 ≤ sum, limit ≤ 105).
Output
In the first line print an integer n (1 ≤ n ≤ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.
If it's impossible to find a suitable set, print -1.
Examples
Input
5 5
Output
2
4 5
Input
4 3
Output
3
2 3 1
Input
5 1
Output
-1
Note
In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.
In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4. | instruction | 0 | 99,009 | 20 | 198,018 |
Tags: bitmasks, greedy, implementation, sortings
Correct Solution:
```
s,l=map(int,input().split())
odd=l%2+l//2
even=l//2
limit=l
from math import log2,ceil,floor
allf=0
def less(i):#smallest power of 2 less than i
a=2**floor(log2(i))
return a
def rt(n):
for i in range(30):
if n&(1<<i):
return (1<<i)
for i in range(1,l+1):
allf+=(rt(i))
if s>allf:
print(-1)
exit()
else:
res=[rt(i) for i in range(1,limit+1)]
r=0
ans=[]
for i in range(limit,0,-1):
c=rt(i)
if r+c<=s:
r+=c
ans.append(i)
print(len(ans))
print(*ans)
``` | output | 1 | 99,009 | 20 | 198,019 |
Provide tags and a correct Python 3 solution for this coding contest problem.
At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.
Fortunately, Picks remembers something about his set S:
* its elements were distinct integers from 1 to limit;
* the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation).
Can you help Picks and find any set S, that satisfies all the above conditions?
Input
The first line contains two integers: sum, limit (1 ≤ sum, limit ≤ 105).
Output
In the first line print an integer n (1 ≤ n ≤ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.
If it's impossible to find a suitable set, print -1.
Examples
Input
5 5
Output
2
4 5
Input
4 3
Output
3
2 3 1
Input
5 1
Output
-1
Note
In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.
In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4. | instruction | 0 | 99,010 | 20 | 198,020 |
Tags: bitmasks, greedy, implementation, sortings
Correct Solution:
```
s,limit = map(int,input().split())
ans = []
for i in range(limit,0,-1):
if s-(i&-i) >=0:ans.append(i);s-=(i&-i)
if s == 0:
print(len(ans))
print(" ".join(map(str, ans)))
else:
print(-1)
``` | output | 1 | 99,010 | 20 | 198,021 |
Provide tags and a correct Python 3 solution for this coding contest problem.
At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.
Fortunately, Picks remembers something about his set S:
* its elements were distinct integers from 1 to limit;
* the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation).
Can you help Picks and find any set S, that satisfies all the above conditions?
Input
The first line contains two integers: sum, limit (1 ≤ sum, limit ≤ 105).
Output
In the first line print an integer n (1 ≤ n ≤ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.
If it's impossible to find a suitable set, print -1.
Examples
Input
5 5
Output
2
4 5
Input
4 3
Output
3
2 3 1
Input
5 1
Output
-1
Note
In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.
In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4. | instruction | 0 | 99,011 | 20 | 198,022 |
Tags: bitmasks, greedy, implementation, sortings
Correct Solution:
```
s,n=list(map(int,input().split()))
y=[]
y1=[]
sum1=0
for i in range(1,n+1):
power=0
de=i
while(i%2==0):
power+=1
i=i//2
if sum1+2**power<=s:
sum1+=2**power
y.append(de)
sum2=0
for i in range(n,0,-1):
power=0
de=i
while(i%2==0):
power+=1
i=i//2
if sum2+2**power<=s:
sum2+=2**power
y1.append(de)
if sum1==s:
print(len(y))
print(*y)
elif sum2==s:
print(len(y1))
print(*y1)
else:
print(-1)
``` | output | 1 | 99,011 | 20 | 198,023 |
Provide tags and a correct Python 3 solution for this coding contest problem.
At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.
Fortunately, Picks remembers something about his set S:
* its elements were distinct integers from 1 to limit;
* the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation).
Can you help Picks and find any set S, that satisfies all the above conditions?
Input
The first line contains two integers: sum, limit (1 ≤ sum, limit ≤ 105).
Output
In the first line print an integer n (1 ≤ n ≤ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.
If it's impossible to find a suitable set, print -1.
Examples
Input
5 5
Output
2
4 5
Input
4 3
Output
3
2 3 1
Input
5 1
Output
-1
Note
In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.
In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4. | instruction | 0 | 99,013 | 20 | 198,026 |
Tags: bitmasks, greedy, implementation, sortings
Correct Solution:
```
"""
Template written to be used by Python Programmers.
Use at your own risk!!!!
Owned by enraged(rating - 5 star at CodeChef and Specialist at Codeforces).
"""
import sys
import bisect
import heapq
from math import *
from collections import defaultdict as dd # defaultdict(<datatype>) Free of KeyError.
from collections import deque # deque(list) append(), appendleft(), pop(), popleft() - O(1)
from collections import Counter as c # Counter(list) return a dict with {key: count}
from itertools import combinations as comb
from bisect import bisect_left as bl, bisect_right as br, bisect
# sys.setrecursionlimit(2*pow(10, 6))
# sys.stdin = open("input.txt", "r")
# sys.stdout = open("output.txt", "w")
mod = pow(10, 9) + 7
mod2 = 998244353
def data(): return sys.stdin.readline().strip()
def out(var): sys.stdout.write(var)
def l(): return list(map(int, data().split()))
def sl(): return list(map(str, data().split()))
def sp(): return map(int, data().split())
def ssp(): return map(str, data().split())
def l1d(n, val=0): return [val for i in range(n)]
def l2d(n, m, val=0): return [[val for i in range(n)] for j in range(m)]
def lower_two(n):
i = 17
answer = 1
while i >= 0:
answer = max(answer, gcd(int(pow(2, i)), n))
i -= 1
return answer
s, limit = sp()
dp = dict()
for i in range(1, limit+1):
dp[i] = lower_two(i)
prefix = sum(dp.values())
dp = sorted(dp.items(), key=lambda x: x[1])
if s > prefix:
out("-1")
exit(0)
answer = []
for i in range(len(dp)-1, -1, -1):
if dp[i][1] <= s:
answer.append(dp[i][0])
s -= dp[i][1]
if s == 0:
break
out(str(len(answer))+"\n")
for i in answer:
out(str(i)+" ")
exit()
``` | output | 1 | 99,013 | 20 | 198,027 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer. | instruction | 0 | 99,087 | 20 | 198,174 |
Tags: math
Correct Solution:
```
a,b,c = map(int, input().split())
if a>b and c>0:
print('NO')
elif b>a and c<0:
print('NO')
elif a!=b and c==0:
print('NO')
elif a==b:
print('YES')
elif (b-a)==c or (b-a)%c==0:
print('YES')
else:
print('NO')
``` | output | 1 | 99,087 | 20 | 198,175 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer. | instruction | 0 | 99,088 | 20 | 198,176 |
Tags: math
Correct Solution:
```
def fx(a,b,c):
if (c==0 and a!=b) or (c>0 and a>b) or (c<0 and a<b):
return print("NO")
if (c==0 and a==b) or ((b-a)%c==0):
return print("Yes")
return print("NO")
a,b,c=input().split()
fx(int(a),int(b),int(c))
``` | output | 1 | 99,088 | 20 | 198,177 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer. | instruction | 0 | 99,089 | 20 | 198,178 |
Tags: math
Correct Solution:
```
inp = input('')
def returnstatus(inp):
firstelement, favnumber, diff = [int(i) for i in inp.split(' ')]
if diff == 0:
return 'YES' if firstelement == favnumber else 'NO'
return 'YES' if ((favnumber - firstelement)%diff == 0 and (favnumber - firstelement)/diff >=0) else 'NO'
print(returnstatus(inp))
``` | output | 1 | 99,089 | 20 | 198,179 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer. | instruction | 0 | 99,090 | 20 | 198,180 |
Tags: math
Correct Solution:
```
a, b, c = map(int, input().split(' '))
if ((a != b and c == 0) or (b > a and c < 0)):
print("NO")
elif ((a == b) or (b > a and c > 0 and ((b - a) % c == 0)) or (a > b and c < 0 and ((a - b) % c == 0))):
print("YES")
else:
print("NO")
``` | output | 1 | 99,090 | 20 | 198,181 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer. | instruction | 0 | 99,091 | 20 | 198,182 |
Tags: math
Correct Solution:
```
a,b,c=map(int,input().split())
if(b<a) and (c>0):
print("NO")
elif(b>a) and (c<0):
print("NO")
elif(c==0):
if (a==b):
print("YES")
else:
print("NO")
else:
b=b-a
if(b%c==0):
print("YES")
else:
print("NO")
``` | output | 1 | 99,091 | 20 | 198,183 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer. | instruction | 0 | 99,092 | 20 | 198,184 |
Tags: math
Correct Solution:
```
a, b, c = list(map(int, input().split()))
if c == 0:
print("YES" if a == b else "NO")
else:
print("YES" if (((b - a) % c == 0) and (((b - a) // c) >= 0)) else "NO")
``` | output | 1 | 99,092 | 20 | 198,185 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer. | instruction | 0 | 99,093 | 20 | 198,186 |
Tags: math
Correct Solution:
```
import math
inp = input()
a = int(inp.split()[0])
b = int(inp.split()[1])
c = int(inp.split()[2])
if c == 0:
if a == b:
print('YES')
else:
print('NO')
else:
flag = (b + c - a) / c
if flag > 0 and flag - math.floor(flag) == 0.0:
print('YES')
else:
print('NO')
``` | output | 1 | 99,093 | 20 | 198,187 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer. | instruction | 0 | 99,094 | 20 | 198,188 |
Tags: math
Correct Solution:
```
a,b,c = map(int,input().split())
if a == b:
print("YES")
elif a > b and c < 0 and (a-b)%c == 0:
print("YES")
elif a < b and c >0 and (b-a)%c == 0:
print("YES")
else:
print("NO")
``` | output | 1 | 99,094 | 20 | 198,189 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer.
Submitted Solution:
```
a, b, c = map(int, input().split(' '))
if b > a and c > 0:
if (b-a) % c == 0:
print("YES")
else:
print("NO")
elif b <= a and c < 0:
if (a-b) % -c == 0:
print("YES")
else:
print("NO")
elif b == a:
print("YES")
else:
print("NO")
``` | instruction | 0 | 99,095 | 20 | 198,190 |
Yes | output | 1 | 99,095 | 20 | 198,191 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer.
Submitted Solution:
```
from sys import stdin
input = stdin.readline
a, b, c = map(int, input().split())
print(["NO", "YES"][ c > 0 and b >= a and not (b - a)%c or c < 0 and a >= b and not (b - a)%c or c == 0 and a == b])
``` | instruction | 0 | 99,096 | 20 | 198,192 |
Yes | output | 1 | 99,096 | 20 | 198,193 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer.
Submitted Solution:
```
if __name__ == "__main__":
#n, m = list(map(int, input().split()))
a, b, c = map(int, input().split())
if c == 0:
if a == b:
print("YES")
else:
print("NO")
elif (b - a) // c >= 0 and (b - a) % c == 0:
print("YES")
else:
print("NO")
``` | instruction | 0 | 99,097 | 20 | 198,194 |
Yes | output | 1 | 99,097 | 20 | 198,195 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer.
Submitted Solution:
```
a,b,c=map(int,input().split())
a
flag=0
if (b==a):
print ("YES")
elif(b<a)and (c>0):
print ("NO")
elif (b>a) and (c<0):
print ("NO")
elif (c==0):
print ("NO")
elif (c!=0) and (a%c==0) and (b%c==0):
print ("YES")
else:
if (c>0):
while (a<=b) and (flag==0):
if (a==b):
print ("YES")
flag=1
break
else:
a+=c
flag=0
if (flag==0):
print ("NO")
else:
while (a>=b) and (flag==0):
if (a==b):
print ("YES")
flag=1
break
else:
a+=c
flag=0
if (flag==0):
print ("NO")
``` | instruction | 0 | 99,098 | 20 | 198,196 |
Yes | output | 1 | 99,098 | 20 | 198,197 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer.
Submitted Solution:
```
a,b,c = map(int,input().split())
if c!=0:
if b>a and (b-a)%c == 0:
print('YES')
else:
print('NO')
else:
if b==a:
print('YES')
else :
print('NO')
``` | instruction | 0 | 99,099 | 20 | 198,198 |
No | output | 1 | 99,099 | 20 | 198,199 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer.
Submitted Solution:
```
a,b,c=map(int,input().split())
if c==0 and a==b:exit(print("YES"))
elif c==0 and a!=b:exit(print("NO"))
l,r=0,10**9
while l<=r:
mid=(l+r)//2
s=a+mid*c
if s==b:exit(print("YES"))
elif s>b:r=mid-1
else:l=mid+1
print("NO")
``` | instruction | 0 | 99,100 | 20 | 198,200 |
No | output | 1 | 99,100 | 20 | 198,201 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer.
Submitted Solution:
```
a, b, c = (int(s) for s in input().strip().split())
if a==b: print('YES')
elif c==0: print('NO')
if a > b:
c = -c
a, b = b, a
if c > 0 and (b-a)%c == 0: print('YES')
else: print('NO')
``` | instruction | 0 | 99,101 | 20 | 198,202 |
No | output | 1 | 99,101 | 20 | 198,203 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.
Input
The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.
Output
If b appears in the sequence s print "YES" (without quotes), otherwise print "NO" (without quotes).
Examples
Input
1 7 3
Output
YES
Input
10 10 0
Output
YES
Input
1 -4 5
Output
NO
Input
0 60 50
Output
NO
Note
In the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.
In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.
In the third sample all elements of the sequence are greater than Vasya's favorite integer.
In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer.
Submitted Solution:
```
a,b,c = list(map(int,input().rstrip().split()))
if c==0:
if a==b:
print("YES")
else:
print("NO")
else:
if (b-a)%c==0 and b-a>0:
print("YES")
else:
print("NO")
``` | instruction | 0 | 99,102 | 20 | 198,204 |
No | output | 1 | 99,102 | 20 | 198,205 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.
In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.
Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.
Input
The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.
Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.
Output
Output an integer k (0 ≤ k ≤ 5) — the length of your program.
Next k lines must contain commands in the same format as in the input.
Examples
Input
3
| 3
^ 2
| 1
Output
2
| 3
^ 2
Input
3
& 1
& 3
& 5
Output
1
& 1
Input
3
^ 1
^ 2
^ 3
Output
0
Note
You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.
Second sample:
Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs. | instruction | 0 | 99,176 | 20 | 198,352 |
Tags: bitmasks, constructive algorithms
Correct Solution:
```
n=int(input())
bits0=[0]*10
bits1=[1]*10
b0=0
b1=1023
fname=['&','|','^']
f=[[[0,0],[0,1]],[[0,1],[1,1]],[[0,1],[1,0]]]
for i in range(n):
s=input()
e=str(bin(int(s[2:])))
d=int(s[2:])
if s[0]=='^':
b0=b0^d
b1 = b1 ^ d
elif s[0]=='|':
b0=b0|d
b1 = b1 | d
elif s[0]=='&':
b0=b0&d
b1 = b1 & d
for j in range(10):
bits0[9-j]=b0%2
b0=b0//2
bits1[9 - j] = b1 % 2
b1 = b1 // 2
c=[[0]*10,[0]*10,[1]*10]
for j in range(10):
if bits0[j]==bits1[j]:
if bits0[j]==0:
c[2][j]=0
else:
c[1][j]=1
else:
if bits0[j]==1:
c[0][j]=1
print(3)
c0,c1,c2=[0,0,0]
for i in range(10):
c0+=c[0][i]*(2**(9-i))
c1 += c[1][i] * (2 ** (9 - i))
c2 += c[2][i] * (2 ** (9 - i))
print("^ "+str(c0))
print("| "+str(c1))
print("& "+str(c2))
``` | output | 1 | 99,176 | 20 | 198,353 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.
In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.
Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.
Input
The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.
Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.
Output
Output an integer k (0 ≤ k ≤ 5) — the length of your program.
Next k lines must contain commands in the same format as in the input.
Examples
Input
3
| 3
^ 2
| 1
Output
2
| 3
^ 2
Input
3
& 1
& 3
& 5
Output
1
& 1
Input
3
^ 1
^ 2
^ 3
Output
0
Note
You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.
Second sample:
Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs. | instruction | 0 | 99,177 | 20 | 198,354 |
Tags: bitmasks, constructive algorithms
Correct Solution:
```
n = int(input())
a, b = 1023, 0
for _ in range(n):
c, d = input().split()
d = int(d)
if c == '|':
a, b = a | d, b | d
elif c == '&':
a, b = a & d, b & d
elif c == '^':
a, b = a ^ d, b ^ d
print('2\n| {}\n^ {}'.format(a ^ b ^ 1023, a ^ 1023))
# Made By Mostafa_Khaled
``` | output | 1 | 99,177 | 20 | 198,355 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.
In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.
Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.
Input
The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.
Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.
Output
Output an integer k (0 ≤ k ≤ 5) — the length of your program.
Next k lines must contain commands in the same format as in the input.
Examples
Input
3
| 3
^ 2
| 1
Output
2
| 3
^ 2
Input
3
& 1
& 3
& 5
Output
1
& 1
Input
3
^ 1
^ 2
^ 3
Output
0
Note
You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.
Second sample:
Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs. | instruction | 0 | 99,178 | 20 | 198,356 |
Tags: bitmasks, constructive algorithms
Correct Solution:
```
n = int(input())
A = 1023
B = 0
a = 1023
b = 0
print(4)
for i in range(n):
s = str(input())
if s[0] == '&':
a = a & int(s[2:])
b = b & int(s[2:])
elif s[0] == '|':
a = a | int(s[2:])
b = b | int(s[2:])
elif s[0] == '^':
a = a ^ int(s[2:])
b = b ^ int(s[2:])
Al = [1,1,1,1,1,1,1,1,1,1]
Bl = [0,0,0,0,0,0,0,0,0,0]
al = [0 for kk in range(10)]
bl = [0 for kk in range(10)]
#print(a,b)
for i in range(9,-1,-1):
if a >= 2 ** i:
al[i] = 1
a -= 2**i
for i in range(9,-1,-1):
if b >= 2 ** i:
bl[i] = 1
b -= 2**i
#print(al,bl)
And = []
Or = []
Xor = []
for i in range(10):
if al[i] == 0 and bl[i] == 0:
And.append(i)
if al[i] == 0 and bl[i] == 1:
Xor.append(i)
if al[i] == 1 and bl[i] == 1:
Or.append(i)
#print(And, Or, Xor)
###
r = 0
for i in range(10):
if i not in And:
r += 2**i
print("&", r)
###
r = 0
if Xor == []:
print("^ 0")
print("^ 0")
elif Xor == [0]:
print("^ 0")
print("& 1")
#elif len(Xor) == 1:
#r = 2**(max(Xor)+1) - 1
#print("^", r)
#print("| 1")
else:
r = 2**(max(Xor)+1) - 1
print("^", r)
r = 0
for i in range(max(Xor) + 1):
if i not in Xor:
r += 2**i
print("^", r)
###
r = 0
for i in range(10):
if i in Or:
r += 2**i
print("|", r)
#print((1023 | 999)^689)
#print((0 | 999)^689)
#print((300 | 999)^689)
#print((((300 & 350)^31)^15)|326)
``` | output | 1 | 99,178 | 20 | 198,357 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.
In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.
Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.
Input
The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.
Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.
Output
Output an integer k (0 ≤ k ≤ 5) — the length of your program.
Next k lines must contain commands in the same format as in the input.
Examples
Input
3
| 3
^ 2
| 1
Output
2
| 3
^ 2
Input
3
& 1
& 3
& 5
Output
1
& 1
Input
3
^ 1
^ 2
^ 3
Output
0
Note
You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.
Second sample:
Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs. | instruction | 0 | 99,179 | 20 | 198,358 |
Tags: bitmasks, constructive algorithms
Correct Solution:
```
import sys
input=sys.stdin.readline
n=int(input())
start1=0
start2=1023
for _ in range(n):
a,b=map(str,input().split())
b=int(b)
if a=='|':
start1=b|start1
start2=b|start2
elif a=='^':
start1=b^start1
start2=b^start2
else:
start1=b&start1
start2=b&start2
ans=[]
ands=1023
xors=0
ors=0
for i in range(10):
k=1<<i
if start1&k and start2&k:
ors+=k
elif start1&k and not start2&k:
xors+=k
elif (not start1&k) and (not start2&k):
ands-=k
print(3)
print('&',ands)
print('^',xors)
print('|',ors)
``` | output | 1 | 99,179 | 20 | 198,359 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.
In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.
Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.
Input
The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.
Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.
Output
Output an integer k (0 ≤ k ≤ 5) — the length of your program.
Next k lines must contain commands in the same format as in the input.
Examples
Input
3
| 3
^ 2
| 1
Output
2
| 3
^ 2
Input
3
& 1
& 3
& 5
Output
1
& 1
Input
3
^ 1
^ 2
^ 3
Output
0
Note
You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.
Second sample:
Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs. | instruction | 0 | 99,180 | 20 | 198,360 |
Tags: bitmasks, constructive algorithms
Correct Solution:
```
from math import*
n = int(input())
x = 0
y = 1023
for i in range(n):
gg = input().split()
if gg[0] == '&':
x &= int(gg[1])
y &= int(gg[1])
if gg[0] == '|':
x |= int(gg[1])
y |= int(gg[1])
if gg[0] == '^':
x ^= int(gg[1])
y ^= int(gg[1])
print(3)
print('|', x & y)
print('&', x | y)
print('^', x & (y ^ 1023))
``` | output | 1 | 99,180 | 20 | 198,361 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.
In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.
Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.
Input
The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.
Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.
Output
Output an integer k (0 ≤ k ≤ 5) — the length of your program.
Next k lines must contain commands in the same format as in the input.
Examples
Input
3
| 3
^ 2
| 1
Output
2
| 3
^ 2
Input
3
& 1
& 3
& 5
Output
1
& 1
Input
3
^ 1
^ 2
^ 3
Output
0
Note
You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.
Second sample:
Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs. | instruction | 0 | 99,181 | 20 | 198,362 |
Tags: bitmasks, constructive algorithms
Correct Solution:
```
import queue
def readTuple():
return input().split()
def readInts():
return tuple(map(int, readTuple()))
def to_int(x):
x=x[::-1]
res = 0
for i in x:
res <<= 1
res |= i
return res
def solve():
res = ['X']*10
n, = readInts()
a,b = 0, 1023
for _ in range(n):
char, num = readTuple()
num = int(num)
if char == '|':
a |= num
b |= num
if char == '&':
a &= num
b &= num
if char == '^':
a ^= num
b ^= num
XOR, OR = [],[]
for i in range(10):
b1 = a&(1<<i)
b2 = b&(1<<i)
if b1 and b2:
OR.append(1)
XOR.append(0)
if not b1 and not b2:
OR.append(1)
XOR.append(1)
if b1 and not b2:
OR.append(0)
XOR.append(1)
if not b1 and b2:
OR.append(0)
XOR.append(0)
print(2)
print(f"| {to_int(OR)}")
print(f"^ {to_int(XOR)}")
if __name__ == '__main__':
solve()
``` | output | 1 | 99,181 | 20 | 198,363 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.
In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.
Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.
Input
The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.
Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.
Output
Output an integer k (0 ≤ k ≤ 5) — the length of your program.
Next k lines must contain commands in the same format as in the input.
Examples
Input
3
| 3
^ 2
| 1
Output
2
| 3
^ 2
Input
3
& 1
& 3
& 5
Output
1
& 1
Input
3
^ 1
^ 2
^ 3
Output
0
Note
You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.
Second sample:
Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs. | instruction | 0 | 99,182 | 20 | 198,364 |
Tags: bitmasks, constructive algorithms
Correct Solution:
```
def fun (n1,o,n2):
if o=="|":
return n1|n2
elif o=="&":
return n1&n2
else:
return n1^n2
def fun2(n):
l=[0 for i in range(10)]
for i in range(9,-1,-1):
if 1<<i <=n:
l[i]=1
n-=1<<i
return l
n=int(input())
a=0
b=1023
for i in range(n):
o,n2=input().split()
n2=int(n2)
a=fun(a,o,n2)
b=fun(b,o,n2)
l1=fun2(a)
l2=fun2(b)
a=0
b=0
for i in range(10):
if l1[i]==1 and l2[i]==1:
a+=1<<i
elif l1[i]==0 and l2[i]==0:
a+=1<<i
b+=1<<i
elif l1[i]==1 and l2[i]==0:
b+=1<<i
print(2)
print("|",a)
print("^",b)
``` | output | 1 | 99,182 | 20 | 198,365 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.
In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.
Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.
Input
The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.
Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.
Output
Output an integer k (0 ≤ k ≤ 5) — the length of your program.
Next k lines must contain commands in the same format as in the input.
Examples
Input
3
| 3
^ 2
| 1
Output
2
| 3
^ 2
Input
3
& 1
& 3
& 5
Output
1
& 1
Input
3
^ 1
^ 2
^ 3
Output
0
Note
You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.
Second sample:
Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs. | instruction | 0 | 99,183 | 20 | 198,366 |
Tags: bitmasks, constructive algorithms
Correct Solution:
```
n = int(input())
mask_ans1 = 1023
mask_ans2 = 0
for i in range(n):
com, x = input().split()
x = int(x)
if com == '&':
mask_ans1 &= x
mask_ans2 &= x
elif com == '|':
mask_ans1 |= x
mask_ans2 |= x
elif com == '^':
mask_ans1 ^= x
mask_ans2 ^= x
ans11 = 1023 & ~mask_ans2
ans12 = mask_ans1
ans13 = 1023&(1023^mask_ans1)
ans1 = 1023^(1023 & ~mask_ans1) & ans11
ans2 = mask_ans2 & ans12
ans3 = 1023&(mask_ans2^0) & ans13
lst = []
cnt = 3
if ans1 == 1023:
cnt -= 1
if ans2 == 0:
cnt -= 1
if ans3 == 0:
cnt -= 1
print(cnt)
if ans1 != 1023:
print('&', ans1)
if ans2 != 0:
print('|', ans2)
if ans3 != 0:
print('^', ans3)
``` | output | 1 | 99,183 | 20 | 198,367 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.
In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.
Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.
Input
The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.
Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.
Output
Output an integer k (0 ≤ k ≤ 5) — the length of your program.
Next k lines must contain commands in the same format as in the input.
Examples
Input
3
| 3
^ 2
| 1
Output
2
| 3
^ 2
Input
3
& 1
& 3
& 5
Output
1
& 1
Input
3
^ 1
^ 2
^ 3
Output
0
Note
You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.
Second sample:
Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs.
Submitted Solution:
```
import sys, math
def main():
ops = getops(sys.stdin)
n1 = 0
n2 = 1023
for op in ops:
n1 = calc(op, n1)
n2 = calc(op, n2)
if n2 == 1023 and n1 == 0:
print(0)
else:
and_ = 1023
or_ = 0
xor_ = 0
for i in range(10):
b1 = n1 % 2
b2 = n2 % 2
n1 = n1 // 2
n2 = n2 // 2
if b1 == 1 and b2 == 1:
or_ = or_ | 2**i
elif b1 == 1 and b2 == 0:
xor_ = xor_ | 2**i
elif b1 == 0 and b2 == 0:
and_ = and_ - 2**i
print(3)
print('&', and_)
print('|', or_)
print('^', xor_)
def getops(fh):
n = int(fh.readline())
ops = []
for i in range(n):
opi, numi = fh.readline().split()
numi = int(numi)
ops.append((opi, numi))
return ops
def calc(op, res):
opi, numi = op
if opi == '|':
res = res | numi
elif opi == '&':
res = res & numi
else:
res = res ^ numi
return res
if __name__ == "__main__":
main()
``` | instruction | 0 | 99,184 | 20 | 198,368 |
Yes | output | 1 | 99,184 | 20 | 198,369 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.
In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.
Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.
Input
The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.
Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.
Output
Output an integer k (0 ≤ k ≤ 5) — the length of your program.
Next k lines must contain commands in the same format as in the input.
Examples
Input
3
| 3
^ 2
| 1
Output
2
| 3
^ 2
Input
3
& 1
& 3
& 5
Output
1
& 1
Input
3
^ 1
^ 2
^ 3
Output
0
Note
You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.
Second sample:
Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs.
Submitted Solution:
```
n = int(input())
a, b = 1023, 0
for _ in range(n):
c, d = input().split()
d = int(d)
if c == '|':
a, b = a | d, b | d
elif c == '&':
a, b = a & d, b & d
elif c == '^':
a, b = a ^ d, b ^ d
print('2\n| {}\n^ {}'.format(a ^ b ^ 1023, a ^ 1023))
``` | instruction | 0 | 99,185 | 20 | 198,370 |
Yes | output | 1 | 99,185 | 20 | 198,371 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.
In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.
Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.
Input
The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.
Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.
Output
Output an integer k (0 ≤ k ≤ 5) — the length of your program.
Next k lines must contain commands in the same format as in the input.
Examples
Input
3
| 3
^ 2
| 1
Output
2
| 3
^ 2
Input
3
& 1
& 3
& 5
Output
1
& 1
Input
3
^ 1
^ 2
^ 3
Output
0
Note
You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.
Second sample:
Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs.
Submitted Solution:
```
import sys
import math
import collections
import heapq
n=int(input())
a,b=1023,0
for i in range(n):
x,y=(i for i in input().split())
y=int(y)
if(x=='&'):
a&=y
b&=y
elif(x=='|'):
a|=y
b|=y
else:
a^=y
b^=y
print(2)
print("|",a^b^1023)
print("^",a^1023)
``` | instruction | 0 | 99,186 | 20 | 198,372 |
Yes | output | 1 | 99,186 | 20 | 198,373 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.
In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.
Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.
Input
The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.
Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.
Output
Output an integer k (0 ≤ k ≤ 5) — the length of your program.
Next k lines must contain commands in the same format as in the input.
Examples
Input
3
| 3
^ 2
| 1
Output
2
| 3
^ 2
Input
3
& 1
& 3
& 5
Output
1
& 1
Input
3
^ 1
^ 2
^ 3
Output
0
Note
You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.
Second sample:
Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs.
Submitted Solution:
```
'''input
3
& 1
& 3
& 5
'''
'''
Author : dhanyaabhirami
Great things never come from comfort zones
'''
from collections import defaultdict as dd
from collections import Counter as ccd
from itertools import permutations as pp
from itertools import combinations as cc
from random import randint as rd
from bisect import bisect_left as bl
from bisect import bisect_right as br
import heapq as hq
import math
mod=pow(10,9) +7
def inp(flag=0):
if flag==0:
return list(map(int,input().strip().split(' ')))
else:
return int(input())
# Code credits
# assert(debug()==true)
# for _ in range(int(input())):
# n=inp(1)
n=int(input())
a=0
b=1023
for i in range(n):
c,k= input().strip().split(' ')
k=int(k)
if (c=='|'):
a|=k
b|=k
elif (c=='^'):
a^=k
b^=k
elif (c=='&'):
a&=k
b&=k
OR = 0
XOR = 0
for i in range(10):
x=1<<i
if a&x and b&x: # set 1
OR|=x
if a&x and ~b&x: # swap
XOR|=x
if ~a&x and ~b&x: # set 0
OR|=x
XOR|=x
print('2')
print('|',OR)
print('^',XOR)
``` | instruction | 0 | 99,187 | 20 | 198,374 |
Yes | output | 1 | 99,187 | 20 | 198,375 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.
In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.
Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.
Input
The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.
Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.
Output
Output an integer k (0 ≤ k ≤ 5) — the length of your program.
Next k lines must contain commands in the same format as in the input.
Examples
Input
3
| 3
^ 2
| 1
Output
2
| 3
^ 2
Input
3
& 1
& 3
& 5
Output
1
& 1
Input
3
^ 1
^ 2
^ 3
Output
0
Note
You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.
Second sample:
Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs.
Submitted Solution:
```
a, b = 0, 1023
n=int(input())
for i in range(n):
cmd = input()
c, x = cmd.split()
x = int(x)
if c == "|":
a, b = a | x, b | x
elif c == "&":
a, b = a & x, b & x
else:
a, b = a ^ x, b ^ x
x = 0
y = 1023
z = 0
for i in range(10):
a_i = (a << i) & 1
b_i = (b << i) & 1
if a_i and b_i:
x |= 1 << i
if (not a_i) and (not b_i):
y ^= 1 << i
if a_i and (not b_i):
z ^= 1 << i
print("3\n| {}\n& {}\n^ {}".format(x, y, z))
``` | instruction | 0 | 99,188 | 20 | 198,376 |
No | output | 1 | 99,188 | 20 | 198,377 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.
In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.
Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.
Input
The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.
Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.
Output
Output an integer k (0 ≤ k ≤ 5) — the length of your program.
Next k lines must contain commands in the same format as in the input.
Examples
Input
3
| 3
^ 2
| 1
Output
2
| 3
^ 2
Input
3
& 1
& 3
& 5
Output
1
& 1
Input
3
^ 1
^ 2
^ 3
Output
0
Note
You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.
Second sample:
Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs.
Submitted Solution:
```
n = int(input())
stack = []
p = 1023
d = {'&':1023, '|':0, '^':0}
for i in range(n):
com = list(map(str, input().split()))
c, x = com[0], int(com[1])
if c == '&':
for k in d.keys():
d[k] &= x
elif c == '|':
d[c] |= x
else:
d[c] ^= x
ans = []
ans.append(('&', d['&']))
ans.append(('|', d['|']))
ans.append(('^', d['^']))
print(len(ans))
for i in range(len(ans)):
print(*ans[i])
``` | instruction | 0 | 99,189 | 20 | 198,378 |
No | output | 1 | 99,189 | 20 | 198,379 |
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