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 |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After learning about polynomial hashing, Heidi decided to learn about shift-xor hashing. In particular, she came across this interesting problem.
Given a bitstring y ∈ \{0,1\}^n find out the number of different k (0 ≤ k < n) such that there exists x ∈ \{0,1\}^n for which y = x ⊕ \mbox{shift}^k(x).
In the above, ⊕ is the xor operation and \mbox{shift}^k is the operation of shifting a bitstring cyclically to the right k times. For example, 001 ⊕ 111 = 110 and \mbox{shift}^3(00010010111000) = 00000010010111.
Input
The first line contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5), the length of the bitstring y.
The second line contains the bitstring y.
Output
Output a single integer: the number of suitable values of k.
Example
Input
4
1010
Output
3
Note
In the first example:
* 1100⊕ \mbox{shift}^1(1100) = 1010
* 1000⊕ \mbox{shift}^2(1000) = 1010
* 0110⊕ \mbox{shift}^3(0110) = 1010
There is no x such that x ⊕ x = 1010, hence the answer is 3.
Submitted Solution:
```
n=int(input())
y=input()
if y.count('1')==0:
print(n)
elif y.count('1')%2==1:
print(0)
else :
x1='01'*(n)
x2='10'*(n)
if y==x1[:n] or y==x2[:n]:
print(n-1)
else :
print(n//2)
``` | instruction | 0 | 71,733 | 20 | 143,466 |
No | output | 1 | 71,733 | 20 | 143,467 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After learning about polynomial hashing, Heidi decided to learn about shift-xor hashing. In particular, she came across this interesting problem.
Given a bitstring y ∈ \{0,1\}^n find out the number of different k (0 ≤ k < n) such that there exists x ∈ \{0,1\}^n for which y = x ⊕ \mbox{shift}^k(x).
In the above, ⊕ is the xor operation and \mbox{shift}^k is the operation of shifting a bitstring cyclically to the right k times. For example, 001 ⊕ 111 = 110 and \mbox{shift}^3(00010010111000) = 00000010010111.
Input
The first line contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5), the length of the bitstring y.
The second line contains the bitstring y.
Output
Output a single integer: the number of suitable values of k.
Example
Input
4
1010
Output
3
Note
In the first example:
* 1100⊕ \mbox{shift}^1(1100) = 1010
* 1000⊕ \mbox{shift}^2(1000) = 1010
* 0110⊕ \mbox{shift}^3(0110) = 1010
There is no x such that x ⊕ x = 1010, hence the answer is 3.
Submitted Solution:
```
n = int(input())
s = input()
cnt_1 = s.count('1')
res = n
if n == 1 and cnt_1 == 1:
res -= 1
elif cnt_1%2 == 0:
res -= 1
cnt_11 = s.count('11')
if s[0] == '1' and s[n-1] == '1':
cnt_11 += 1
if n%2 == 0 and cnt_11 > 0:
res -= 1
print(res)
``` | instruction | 0 | 71,734 | 20 | 143,468 |
No | output | 1 | 71,734 | 20 | 143,469 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After learning about polynomial hashing, Heidi decided to learn about shift-xor hashing. In particular, she came across this interesting problem.
Given a bitstring y ∈ \{0,1\}^n find out the number of different k (0 ≤ k < n) such that there exists x ∈ \{0,1\}^n for which y = x ⊕ \mbox{shift}^k(x).
In the above, ⊕ is the xor operation and \mbox{shift}^k is the operation of shifting a bitstring cyclically to the right k times. For example, 001 ⊕ 111 = 110 and \mbox{shift}^3(00010010111000) = 00000010010111.
Input
The first line contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5), the length of the bitstring y.
The second line contains the bitstring y.
Output
Output a single integer: the number of suitable values of k.
Example
Input
4
1010
Output
3
Note
In the first example:
* 1100⊕ \mbox{shift}^1(1100) = 1010
* 1000⊕ \mbox{shift}^2(1000) = 1010
* 0110⊕ \mbox{shift}^3(0110) = 1010
There is no x such that x ⊕ x = 1010, hence the answer is 3.
Submitted Solution:
```
import sys
# from collections import deque
input=sys.stdin.readline
# import time
n=int(input())
s=input()
one=0
zero=0
for i in range(n):
if(s[i]=="1"):
one+=1
else:
zero+=1
if(one%2!=0):
print(0)
else:
if(zero%2!=0):
ans=(one//2)+((zero//2)+1)
print(ans)
else:
ans=(one//2)+(zero)
print(ans)
``` | instruction | 0 | 71,735 | 20 | 143,470 |
No | output | 1 | 71,735 | 20 | 143,471 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
After learning about polynomial hashing, Heidi decided to learn about shift-xor hashing. In particular, she came across this interesting problem.
Given a bitstring y ∈ \{0,1\}^n find out the number of different k (0 ≤ k < n) such that there exists x ∈ \{0,1\}^n for which y = x ⊕ \mbox{shift}^k(x).
In the above, ⊕ is the xor operation and \mbox{shift}^k is the operation of shifting a bitstring cyclically to the right k times. For example, 001 ⊕ 111 = 110 and \mbox{shift}^3(00010010111000) = 00000010010111.
Input
The first line contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5), the length of the bitstring y.
The second line contains the bitstring y.
Output
Output a single integer: the number of suitable values of k.
Example
Input
4
1010
Output
3
Note
In the first example:
* 1100⊕ \mbox{shift}^1(1100) = 1010
* 1000⊕ \mbox{shift}^2(1000) = 1010
* 0110⊕ \mbox{shift}^3(0110) = 1010
There is no x such that x ⊕ x = 1010, hence the answer is 3.
Submitted Solution:
```
import sys
# from collections import deque
input=sys.stdin.readline
# import time
n=int(input())
s=input()
one=0
zero=0
for i in range(n):
if(s[i]=="1"):
one+=1
else:
zero+=1
ans=(one//2)+zero
print(ans)
``` | instruction | 0 | 71,736 | 20 | 143,472 |
No | output | 1 | 71,736 | 20 | 143,473 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A little girl loves problems on bitwise operations very much. Here's one of them.
You are given two integers l and r. Let's consider the values of <image> for all pairs of integers a and b (l ≤ a ≤ b ≤ r). Your task is to find the maximum value among all considered ones.
Expression <image> means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as "^", in Pascal — as "xor".
Input
The single line contains space-separated integers l and r (1 ≤ l ≤ r ≤ 1018).
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
In a single line print a single integer — the maximum value of <image> for all pairs of integers a, b (l ≤ a ≤ b ≤ r).
Examples
Input
1 2
Output
3
Input
8 16
Output
31
Input
1 1
Output
0 | instruction | 0 | 71,957 | 20 | 143,914 |
Tags: bitmasks, dp, greedy, implementation, math
Correct Solution:
```
#Problem A - Little Girl and Maximum XOR
numeros = [int(i) for i in input().split(' ')]
# numeros = [797162752288318119, 908416915938410706]
l = bin(numeros[0])
r = bin(numeros[1])
p = -1
# for i,j in range (len(l),len(r)):
if (len(r) == len(l)):
for i in range (len(l)):
if (l[i] != r[i]):
p = i
break
if(numeros[0] != numeros[1]):
# saida = 2**(len(r) - 2) - 1
saida = 2**(len(r) - p) - 1
print(saida)
else:
print(0)
else:
if(numeros[0] != numeros[1]):
saida = 2**(len(r) - 2) - 1
# saida = 2**(len(r) - p)
print(saida)
else:
print(0)
# print(bin(numeros[0]))
# print(r)
# print(p)
``` | output | 1 | 71,957 | 20 | 143,915 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains a single integer a (0 ≤ a ≤ 35).
Output
Output a single integer.
Examples
Input
3
Output
8
Input
10
Output
1024 | instruction | 0 | 72,105 | 20 | 144,210 |
Tags: *special
Correct Solution:
```
n = int(input())
print(int(n%2==1))
``` | output | 1 | 72,105 | 20 | 144,211 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains a single integer a (0 ≤ a ≤ 35).
Output
Output a single integer.
Examples
Input
3
Output
8
Input
10
Output
1024 | instruction | 0 | 72,106 | 20 | 144,212 |
Tags: *special
Correct Solution:
```
a = int(input())
if a%2 == 0:
print(0)
else: print(1)
``` | output | 1 | 72,106 | 20 | 144,213 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains a single integer a (0 ≤ a ≤ 35).
Output
Output a single integer.
Examples
Input
3
Output
8
Input
10
Output
1024 | instruction | 0 | 72,107 | 20 | 144,214 |
Tags: *special
Correct Solution:
```
li=[1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8092, 16184, 32368, 64736, 129472, 258944, 517888, 1035776, 2071552, 4143104, 8286208, 16572416, 33144832, 66289664, 132579328, 265158656, 530317312, 1060634624, 2121269248, 4242538496, 8485076992, 16970153984, 33940307968]
x=int(input())
print(li[x])
``` | output | 1 | 72,107 | 20 | 144,215 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains a single integer a (0 ≤ a ≤ 35).
Output
Output a single integer.
Examples
Input
3
Output
8
Input
10
Output
1024 | instruction | 0 | 72,109 | 20 | 144,218 |
Tags: *special
Correct Solution:
```
# -*- coding: utf - 8 -*-
"""""""""""""""""""""""""""""""""""""""""""""
| author: mr.math - Hakimov Rahimjon |
| e-mail: mr.math0777@gmail.com |
| created: 01.04.2018 16:00 |
"""""""""""""""""""""""""""""""""""""""""""""
# inp = open("input.txt", "r"); input = inp.readline; out = open("output.txt", "w"); print = out.write
TN = 1
# ===========================================
def solution():
a = int(input())
print(a%2)
# ===========================================
while TN != 0:
solution()
TN -= 1
# ===========================================
# inp.close()
# out.close()
``` | output | 1 | 72,109 | 20 | 144,219 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains a single integer a (0 ≤ a ≤ 35).
Output
Output a single integer.
Examples
Input
3
Output
8
Input
10
Output
1024 | instruction | 0 | 72,110 | 20 | 144,220 |
Tags: *special
Correct Solution:
```
n = int(input())
print (n%2)
#asdfasdfasdfasdfasdfadsfasdfadsfasdfa
``` | output | 1 | 72,110 | 20 | 144,221 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains a single integer a (0 ≤ a ≤ 35).
Output
Output a single integer.
Examples
Input
3
Output
8
Input
10
Output
1024 | instruction | 0 | 72,111 | 20 | 144,222 |
Tags: *special
Correct Solution:
```
powers = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8092, 16184, 32368, 64736, 129472, 258944, 517888, 1035776, 2071552, 4143104, 8286208, 16572416, 33144832, 66289664, 132579328, 265158656, 530317312, 1060634624, 2121269248, 4242538496, 8485076992, 16970153984, 33940307968]
print(powers[int(input())])
``` | output | 1 | 72,111 | 20 | 144,223 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Input
The input contains a single integer a (0 ≤ a ≤ 35).
Output
Output a single integer.
Examples
Input
3
Output
8
Input
10
Output
1024 | instruction | 0 | 72,112 | 20 | 144,224 |
Tags: *special
Correct Solution:
```
a = int(input())
if a%2 == 1:
print(1)
else:
print(0)
``` | output | 1 | 72,112 | 20 | 144,225 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Cengiz recently learned Fibonacci numbers and now he is studying different algorithms to find them. After getting bored of reading them, he came with his own new type of numbers that he named XORinacci numbers. He defined them as follows:
* f(0) = a;
* f(1) = b;
* f(n) = f(n-1) ⊕ f(n-2) when n > 1, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
You are given three integers a, b, and n, calculate f(n).
You have to answer for T independent test cases.
Input
The input contains one or more independent test cases.
The first line of input contains a single integer T (1 ≤ T ≤ 10^3), the number of test cases.
Each of the T following lines contains three space-separated integers a, b, and n (0 ≤ a, b, n ≤ 10^9) respectively.
Output
For each test case, output f(n).
Example
Input
3
3 4 2
4 5 0
325 265 1231232
Output
7
4
76
Note
In the first example, f(2) = f(0) ⊕ f(1) = 3 ⊕ 4 = 7. | instruction | 0 | 72,571 | 20 | 145,142 |
Tags: math
Correct Solution:
```
t = int(input())
for i in range(t):
a, b, n = map(int, input().split())
c = a ^ b
if n == 0:
print(a)
elif n == 1:
print(b)
else:
if n % 3 == 0:
print(a)
elif n % 3 == 1:
print(b)
elif n % 3 == 2:
print(c)
``` | output | 1 | 72,571 | 20 | 145,143 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Cengiz recently learned Fibonacci numbers and now he is studying different algorithms to find them. After getting bored of reading them, he came with his own new type of numbers that he named XORinacci numbers. He defined them as follows:
* f(0) = a;
* f(1) = b;
* f(n) = f(n-1) ⊕ f(n-2) when n > 1, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
You are given three integers a, b, and n, calculate f(n).
You have to answer for T independent test cases.
Input
The input contains one or more independent test cases.
The first line of input contains a single integer T (1 ≤ T ≤ 10^3), the number of test cases.
Each of the T following lines contains three space-separated integers a, b, and n (0 ≤ a, b, n ≤ 10^9) respectively.
Output
For each test case, output f(n).
Example
Input
3
3 4 2
4 5 0
325 265 1231232
Output
7
4
76
Note
In the first example, f(2) = f(0) ⊕ f(1) = 3 ⊕ 4 = 7. | instruction | 0 | 72,572 | 20 | 145,144 |
Tags: math
Correct Solution:
```
tc = int(input())
for i in range(tc):
a,b,n = map(int,input().split())
arr=[]
arr.append(a)
arr.append(b)
arr.append(a^b)
if (n==0 or n%3==0):
print(arr[0])
elif(n==1 or n%3==1):
print(arr[1])
else:
print(arr[2])
``` | output | 1 | 72,572 | 20 | 145,145 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Cengiz recently learned Fibonacci numbers and now he is studying different algorithms to find them. After getting bored of reading them, he came with his own new type of numbers that he named XORinacci numbers. He defined them as follows:
* f(0) = a;
* f(1) = b;
* f(n) = f(n-1) ⊕ f(n-2) when n > 1, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
You are given three integers a, b, and n, calculate f(n).
You have to answer for T independent test cases.
Input
The input contains one or more independent test cases.
The first line of input contains a single integer T (1 ≤ T ≤ 10^3), the number of test cases.
Each of the T following lines contains three space-separated integers a, b, and n (0 ≤ a, b, n ≤ 10^9) respectively.
Output
For each test case, output f(n).
Example
Input
3
3 4 2
4 5 0
325 265 1231232
Output
7
4
76
Note
In the first example, f(2) = f(0) ⊕ f(1) = 3 ⊕ 4 = 7. | instruction | 0 | 72,573 | 20 | 145,146 |
Tags: math
Correct Solution:
```
def findXORInAcci(a, b, n):
n = n % 3
if n == 0:
return a
elif n == 1:
return b
return a ^ b
T = int(input())
for _ in range(T):
ABN = input().split(" ")
a = int(ABN[0])
b = int(ABN[1])
n = int(ABN[2])
print(findXORInAcci(a, b, n))
``` | output | 1 | 72,573 | 20 | 145,147 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Cengiz recently learned Fibonacci numbers and now he is studying different algorithms to find them. After getting bored of reading them, he came with his own new type of numbers that he named XORinacci numbers. He defined them as follows:
* f(0) = a;
* f(1) = b;
* f(n) = f(n-1) ⊕ f(n-2) when n > 1, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
You are given three integers a, b, and n, calculate f(n).
You have to answer for T independent test cases.
Input
The input contains one or more independent test cases.
The first line of input contains a single integer T (1 ≤ T ≤ 10^3), the number of test cases.
Each of the T following lines contains three space-separated integers a, b, and n (0 ≤ a, b, n ≤ 10^9) respectively.
Output
For each test case, output f(n).
Example
Input
3
3 4 2
4 5 0
325 265 1231232
Output
7
4
76
Note
In the first example, f(2) = f(0) ⊕ f(1) = 3 ⊕ 4 = 7. | instruction | 0 | 72,574 | 20 | 145,148 |
Tags: math
Correct Solution:
```
def xor(a, b):
ans = ''
ma = a if len(a) > len(b) else b
mi = a if len(a) < len(b) else b
for d in range(1, len(mi)-1):
ans = '1'+ans if a[-d] != b[-d] else '0'+ans
ans = ma[2:2+len(ma)-len(mi)]+ans
return '0b'+ans
def f(a, b, n):
if n == 0:
return a
if n == 1:
return b
return xor(f(a, b, n-1), f(a, b, n-2))
arr = []
for i in range(int(input())):
p = input().split()
x, y = bin(int(p[0])), bin(int(p[1]))
z = int(p[2]) % 3
arr.append(int(f(x, y, z), 2))
print(*arr, sep='\n')
``` | output | 1 | 72,574 | 20 | 145,149 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Cengiz recently learned Fibonacci numbers and now he is studying different algorithms to find them. After getting bored of reading them, he came with his own new type of numbers that he named XORinacci numbers. He defined them as follows:
* f(0) = a;
* f(1) = b;
* f(n) = f(n-1) ⊕ f(n-2) when n > 1, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
You are given three integers a, b, and n, calculate f(n).
You have to answer for T independent test cases.
Input
The input contains one or more independent test cases.
The first line of input contains a single integer T (1 ≤ T ≤ 10^3), the number of test cases.
Each of the T following lines contains three space-separated integers a, b, and n (0 ≤ a, b, n ≤ 10^9) respectively.
Output
For each test case, output f(n).
Example
Input
3
3 4 2
4 5 0
325 265 1231232
Output
7
4
76
Note
In the first example, f(2) = f(0) ⊕ f(1) = 3 ⊕ 4 = 7. | instruction | 0 | 72,575 | 20 | 145,150 |
Tags: math
Correct Solution:
```
t = int(input())
for i in range(t):
a, b, n = map(int, input().split())
c = a ^ b
if n % 3 == 0:
print(a)
elif n % 3 == 1:
print(b)
else:
print(c)
``` | output | 1 | 72,575 | 20 | 145,151 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Cengiz recently learned Fibonacci numbers and now he is studying different algorithms to find them. After getting bored of reading them, he came with his own new type of numbers that he named XORinacci numbers. He defined them as follows:
* f(0) = a;
* f(1) = b;
* f(n) = f(n-1) ⊕ f(n-2) when n > 1, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
You are given three integers a, b, and n, calculate f(n).
You have to answer for T independent test cases.
Input
The input contains one or more independent test cases.
The first line of input contains a single integer T (1 ≤ T ≤ 10^3), the number of test cases.
Each of the T following lines contains three space-separated integers a, b, and n (0 ≤ a, b, n ≤ 10^9) respectively.
Output
For each test case, output f(n).
Example
Input
3
3 4 2
4 5 0
325 265 1231232
Output
7
4
76
Note
In the first example, f(2) = f(0) ⊕ f(1) = 3 ⊕ 4 = 7. | instruction | 0 | 72,576 | 20 | 145,152 |
Tags: math
Correct Solution:
```
def printXOR(a,b,n):
n= n - 1
x = 0
while(n):
x = a ^ b
a = b
b = x
n-=1
print(x)
x = int(input())
for _ in range(x):
a,b,n = map(int,input().split(" "))
n = n%3
if(n == 0):
print(a)
elif(n == 1):
print(b)
else:
printXOR(a,b,n)
``` | output | 1 | 72,576 | 20 | 145,153 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Cengiz recently learned Fibonacci numbers and now he is studying different algorithms to find them. After getting bored of reading them, he came with his own new type of numbers that he named XORinacci numbers. He defined them as follows:
* f(0) = a;
* f(1) = b;
* f(n) = f(n-1) ⊕ f(n-2) when n > 1, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
You are given three integers a, b, and n, calculate f(n).
You have to answer for T independent test cases.
Input
The input contains one or more independent test cases.
The first line of input contains a single integer T (1 ≤ T ≤ 10^3), the number of test cases.
Each of the T following lines contains three space-separated integers a, b, and n (0 ≤ a, b, n ≤ 10^9) respectively.
Output
For each test case, output f(n).
Example
Input
3
3 4 2
4 5 0
325 265 1231232
Output
7
4
76
Note
In the first example, f(2) = f(0) ⊕ f(1) = 3 ⊕ 4 = 7. | instruction | 0 | 72,577 | 20 | 145,154 |
Tags: math
Correct Solution:
```
t=int(input())
ass=[]
bs=[]
ns=[]
for i in range(t):
a, b, n = map(int,input().split(' '))
ass.append(a)
bs.append(b)
ns.append(n)
for i in range(t):
if ns[i] % 3 == 0:
print(ass[i])
elif ns[i]%3 == 1:
print(bs[i])
else :
print(ass[i]^bs[i])
``` | output | 1 | 72,577 | 20 | 145,155 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Cengiz recently learned Fibonacci numbers and now he is studying different algorithms to find them. After getting bored of reading them, he came with his own new type of numbers that he named XORinacci numbers. He defined them as follows:
* f(0) = a;
* f(1) = b;
* f(n) = f(n-1) ⊕ f(n-2) when n > 1, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
You are given three integers a, b, and n, calculate f(n).
You have to answer for T independent test cases.
Input
The input contains one or more independent test cases.
The first line of input contains a single integer T (1 ≤ T ≤ 10^3), the number of test cases.
Each of the T following lines contains three space-separated integers a, b, and n (0 ≤ a, b, n ≤ 10^9) respectively.
Output
For each test case, output f(n).
Example
Input
3
3 4 2
4 5 0
325 265 1231232
Output
7
4
76
Note
In the first example, f(2) = f(0) ⊕ f(1) = 3 ⊕ 4 = 7. | instruction | 0 | 72,578 | 20 | 145,156 |
Tags: math
Correct Solution:
```
for _ in range(int(input())):
a,b,n = [*map(int,input().split(" "))]
n = n%3
fn = 0
if n ==0:
fn = a
elif(n==1):
fn = b
elif(n==2):
fn = a^b
print(fn)
``` | output | 1 | 72,578 | 20 | 145,157 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Jzzhu have n non-negative integers a1, a2, ..., an. We will call a sequence of indexes i1, i2, ..., ik (1 ≤ i1 < i2 < ... < ik ≤ n) a group of size k.
Jzzhu wonders, how many groups exists such that ai1 & ai2 & ... & aik = 0 (1 ≤ k ≤ n)? Help him and print this number modulo 1000000007 (109 + 7). Operation x & y denotes bitwise AND operation of two numbers.
Input
The first line contains a single integer n (1 ≤ n ≤ 106). The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 106).
Output
Output a single integer representing the number of required groups modulo 1000000007 (109 + 7).
Examples
Input
3
2 3 3
Output
0
Input
4
0 1 2 3
Output
10
Input
6
5 2 0 5 2 1
Output
53 | instruction | 0 | 72,870 | 20 | 145,740 |
Tags: bitmasks, combinatorics, dp
Correct Solution:
```
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(2*10**5+10)
write = lambda x: sys.stdout.write(x+"\n")
debug = lambda x: sys.stderr.write(x+"\n")
writef = lambda x: print("{:.12f}".format(x))
# zeta mebius
def zeta_super(val, n):
# len(val)==2^n
out = val[:]
for i in range(n):
for j in range(1<<n):
if not j>>i&1:
out[j] += out[j^(1<<i)]
return out
n = int(input())
a = list(map(int, input().split()))
m = max(a).bit_length()
M = 10**9+7
v = [0]*(1<<m)
for item in a:
v[item] += 1
v2 = [1]
for i in range(n+1):
v2.append(v2[-1]*2%M)
nv = zeta_super(v, m)
ans = 0
for b in range(1<<m):
ans += (v2[nv[b]]-1)*pow(-1, bin(b).count("1"))
ans %= M
print(ans%M)
``` | output | 1 | 72,870 | 20 | 145,741 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1. | instruction | 0 | 73,351 | 20 | 146,702 |
Tags: binary search, constructive algorithms, interactive
Correct Solution:
```
a=input()
while a!="end":
if a=="start":
for i in range(30):
print("?",2**i,2*2**i)
if input()=="x":
break
bot=2**i
top=min(2**(i+1),1000000000)
if bot==1:
print("?",2,1)
if input()=="x":
print("!",1)
else:
print("!",2)
else:
bot+=1
while top!=bot:
mid=(bot+top)//2
print("?",2*mid,mid)
if input()=="x":
top=mid
else:
bot=mid+1
print("!",top)
a=input()
``` | output | 1 | 73,351 | 20 | 146,703 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1. | instruction | 0 | 73,352 | 20 | 146,704 |
Tags: binary search, constructive algorithms, interactive
Correct Solution:
```
def get_range():
left = 0
right = 1
while True:
print('?', left, right)
in_value = input()
if in_value == 'x':
break
left = right
right *= 2
return left, right
def solve():
in_value = input()
while in_value == 'start':
left, right = get_range()
while left != right:
middle = (right + left) // 2
if left == middle:
break
print('?', left, middle)
in_value = input()
if in_value == 'y':
left = middle
if in_value == 'x':
right = middle
print('!', left + 1)
in_value = input()
solve()
``` | output | 1 | 73,352 | 20 | 146,705 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1. | instruction | 0 | 73,353 | 20 | 146,706 |
Tags: binary search, constructive algorithms, interactive
Correct Solution:
```
#!/usr/bin/env python
# coding: utf-8
# In[ ]:
# In[ ]:
# In[ ]:
# In[ ]:
while True:
if input()=='start':
print(*['?',0,1],flush=True)
result=input()
if result=='x':
print(*['!', 1],flush=True)
continue
i=0
while True:
print(*['?', 2**i, 2**(i+1)],flush=True)
result=input()
if result=='y':
i+=1
else:
break
j=i-1
result=2**i
while j>=0:
print(*['?', result, result+2**j],flush=True)
read=input()
if read=='y':
result=result+2**(j)
j=j-1
else:
j=j-1
print(*['!', result+1],flush=True)
else:
break
``` | output | 1 | 73,353 | 20 | 146,707 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1. | instruction | 0 | 73,354 | 20 | 146,708 |
Tags: binary search, constructive algorithms, interactive
Correct Solution:
```
#!/usr/bin/env python
def main():
s = input()
while s == 'start':
print('?', 0, 1)
v = input()
i = 0
while v != 'x':
print('?', 1 << i, 1 << (i + 1))
v = input()
i += 1
if i == 0:
print('!', 1)
else:
lo, hi = (1 << (i - 1)) + 1, (1 << i)
while lo < hi:
mi = (lo + hi) // 2
print('?', (1 << (i - 1)), mi)
if input() == 'x':
hi = mi
else:
lo = mi + 1
print('!', lo)
s = input()
return
if __name__ == '__main__':
main()
``` | output | 1 | 73,354 | 20 | 146,709 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1. | instruction | 0 | 73,355 | 20 | 146,710 |
Tags: binary search, constructive algorithms, interactive
Correct Solution:
```
from sys import stdout
def ask(x, y):
print('?', x, y)
stdout.flush()
x = input()
return x == 'x'
def show_res(res):
print('!', res)
stdout.flush()
def prepare_game():
gm = input()
if gm[0] != 's':
exit(0)
INF = int(1e9) + 1
def play():
L = 0
R = 1
while R < INF:
res = ask(L, R)
if (res):
break
else:
L = R
R *= 2
st = L
#print('L', L, 'R', R)
while R - L > 1:
m = (R + L) // 2
#print('L', L, 'R', R, 'm', m)
if ask(st, m):
R = m
else:
L = m
show_res(R)
while True:
prepare_game()
play()
``` | output | 1 | 73,355 | 20 | 146,711 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1. | instruction | 0 | 73,356 | 20 | 146,712 |
Tags: binary search, constructive algorithms, interactive
Correct Solution:
```
import sys
v = sys.stdin.readline().strip()
while v == "start":
print("? 0 2")
sys.stdout.flush()
ans = sys.stdin.readline().strip()
if ans == "x":
print("? 0 1")
sys.stdout.flush()
ans = sys.stdin.readline().strip()
if ans == "x":
print("! 1")
sys.stdout.flush()
else:
print("! 2")
sys.stdout.flush()
else:
i = 2
j = 4
while ans == "y":
print("? " + str(i) + " " + str(j))
sys.stdout.flush()
i = i * 2
j = j * 2
ans = sys.stdin.readline().strip()
i = i // 2
j = j // 2
while i != j and i + 1 != j:
print("? " + str(i) + " " + str((j + i) // 2))
sys.stdout.flush()
ans = sys.stdin.readline().strip()
if ans == "x":
j = (i + j) // 2
else:
i = (i + j) // 2
print("! " + str(i + 1))
sys.stdout.flush()
v = sys.stdin.readline().strip()
``` | output | 1 | 73,356 | 20 | 146,713 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1. | instruction | 0 | 73,357 | 20 | 146,714 |
Tags: binary search, constructive algorithms, interactive
Correct Solution:
```
import sys
while True:
S = input()
if S=='end':
sys.exit()
if S=='mistake':
sys.exit()
if S=='start':
while True:
i=0
print('?',0,1)
sys.stdout.flush()
T=input()
if T=='x':
print('!',1)
break
while i<32:
print('?',2**i,2**(i+1))
sys.stdout.flush()
T=input()
if T=='x':
b=2**i
break
i+=1
mi=2**i
ma=2**(i+1)
#print('?',0,mi)
#sys.stdout.flush()
#T=input()
#if T=='x':
#print('!',mi)
#break
while ma-mi>1:
mid=(ma+mi)//2
print('?',mi,mid)
sys.stdout.flush()
T = input()
if T=='x':
ma=mid
elif T=='y':
mi=mid
elif T=='e':
sys.exit()
print('!',ma)
break
``` | output | 1 | 73,357 | 20 | 146,715 |
Provide tags and a correct Python 3 solution for this coding contest problem.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1. | instruction | 0 | 73,358 | 20 | 146,716 |
Tags: binary search, constructive algorithms, interactive
Correct Solution:
```
#!/usr/bin/env python
"""
This file is part of https://github.com/cheran-senthil/PyRival
Copyright 2019 Cheran Senthilkumar <hello@cheran.io>
"""
import sys
input = lambda: sys.stdin.readline().rstrip('\r\n')
def main():
s = input()
while s == 'start':
print('?', 0, 1, flush=True)
v = input()
i = 0
while v != 'x':
print('?', 1 << i, 1 << (i + 1), flush=True)
v = input()
i += 1
if i == 0:
print('!', 1, flush=True)
else:
lo, hi = (1 << (i - 1)) + 1, (1 << i)
while lo < hi:
mi = (lo + hi) // 2
print('?', (1 << (i - 1)), mi, flush=True)
if input() == 'x':
hi = mi
else:
lo = mi + 1
print('!', lo, flush=True)
s = input()
return
if __name__ == '__main__':
main()
``` | output | 1 | 73,358 | 20 | 146,717 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1.
Submitted Solution:
```
while(True):
a=input()
if (a!="start"):
break
d=1
low=-1
high=-1
print ("? 0 1")
o=input()
if (o=="x"):
print("! 1")
continue
while(1):
print ("?",d,2*d)
o=input()
if (o=="x"):
low=d+1
high=2*d
break
else:
d=d*2
while(low<high):
mid=(low+high)//2
print ("?",mid,high)
o=input()
if (o=="x"):
low=mid+1
else:
high=mid
print ("!",high)
``` | instruction | 0 | 73,359 | 20 | 146,718 |
Yes | output | 1 | 73,359 | 20 | 146,719 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1.
Submitted Solution:
```
from sys import stdout
def ask(x,y) :
print('?',x,y)
stdout.flush()
return input() == 'x'
def work() :
if ask(0, 1) : return 1
l = 1
while ask(l*2,l) : l*=2
r = min(1000000000, l*2+1)
l += 1
while r > l :
mid=(l+r)//2
if ask(mid, (mid+1)//2) :
l=mid+1
else :
r=mid
return l
while input()=='start' :
print('!',work())
stdout.flush()
``` | instruction | 0 | 73,360 | 20 | 146,720 |
Yes | output | 1 | 73,360 | 20 | 146,721 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1.
Submitted Solution:
```
import sys
def ask(x, y):
print("?", x, y)
return input() == "y"
while input() == "start":
if not ask(0, 1):
print("! 1")
continue
d = 1
while ask(d, d * 2):
d *= 2
r = d
l = d // 2
while l + 1 < r:
m = (l + r) // 2
if ask(m, m * 2):
l = m
else:
r = m
print("!", r * 2 if not ask(r * 2 - 1, r * 2) else r * 2 - 1)
``` | instruction | 0 | 73,361 | 20 | 146,722 |
Yes | output | 1 | 73,361 | 20 | 146,723 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1.
Submitted Solution:
```
#begin = input()
#x = 2*10**9
def f(a=-1):
s = input()
if s == 'end':
return False
y,x = 1,2
count = 0
def oracle(x,y):
nonlocal count
count += 1
if a == -1:
print('?',x,y)
return input()
else:
if x%a >= y%a:
return 'x'
else:
return 'y'
while True:
if y>2*10**9 or x>2*10**9:
print('!',1)
return True
s = oracle(x,y)
if s == 'x':
# x >= y
pass
x *= 2
y *= 2
else:
# x < y
#print(y,x)
break
# within [y,x]
while y<x-1:
m = (y+x)//2
s = oracle(m,y)
if s == 'x':
# m >= y
y = m
else:
# m < y
x = m
#print(y,x,'rounds',count)
print('!',x)
return True
#f(int(input()))
while f(): pass
``` | instruction | 0 | 73,362 | 20 | 146,724 |
Yes | output | 1 | 73,362 | 20 | 146,725 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1.
Submitted Solution:
```
# -*- coding: utf-8 -*-
import sys
def rli():
return list(map(int, input().split()))
def guess(x, y):
print('? {} {}'.format(x, y))
sys.stdout.flush()
res = input()
return res
def solve():
st, ed = 1, 2
if guess(1, 2) == 'x' and guess(2, 3) == 'x':
print('! 1')
return
while st != ed:
ans = guess(st, ed)
if ans == 'y':
st, ed = ed, ed + ed
else:
ed = int((st + ed) // 2)
while guess(st, st + 1) == 'x':
st += 1
print('! {}'.format(st))
def main():
while True:
s = input()
if s == 'start':
solve()
else:
break
if __name__ == '__main__':
main()
``` | instruction | 0 | 73,363 | 20 | 146,726 |
No | output | 1 | 73,363 | 20 | 146,727 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1.
Submitted Solution:
```
from sys import stdout
powoftwo = [1]
pow = 0
while 1:
n = input()
if n == 'start':
i = 1
ans = -1
while ans != 'x':
print ('?', i, 2*i)
stdout.flush()
i = i*2
powoftwo.append(i)
pow += 1
ans = input()
if i == 2:
print('?', 2,3)
stdout.flush()
ans = input()
if ans == 'x':
print('!',1)
stdout.flush()
else:
print ('!',2)
stdout.flush()
else:
upper = powoftwo[pow]
lower = powoftwo[pow-1]
mid = (upper+lower)/2
while upper-lower > 1:
print('?',mid, 2*mid)
stdout.flush()
ans = input()
if ans == 'x':
lower = mid
else:
upper = mid
print (lower,upper)
stdout.flush()
ans = input()
if ans == 'y':
print('!', lower)
stdout.flush()
else:
print('!', upper)
stdout.flush()
else:
break
``` | instruction | 0 | 73,364 | 20 | 146,728 |
No | output | 1 | 73,364 | 20 | 146,729 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1.
Submitted Solution:
```
import sys
v = sys.stdin.readline().strip()
while v == "start":
print("? 0 1")
sys.stdout.flush()
ans = sys.stdin.readline().strip()
if ans == "x":
print("! 1")
sys.stdout.flush()
else:
i = 1
j = 2
while ans == "y":
print("? " + str(i) + " " + str(j))
sys.stdout.flush()
i = i * 2
j = j * 2
ans = sys.stdin.readline().strip()
i = i // 2
j = j // 2
while i != j:
print("? " + str(i) + " " + str((j + i) // 2))
sys.stdout.flush()
ans = sys.stdin.readline().strip()
if ans == "x":
j = (i + j) // 2
else:
i = (i + j) // 2
print("! " + str(i + 1))
sys.stdout.flush()
v = sys.stdin.readline().strip()
``` | instruction | 0 | 73,365 | 20 | 146,730 |
No | output | 1 | 73,365 | 20 | 146,731 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
This is an interactive problem.
Vasya and Petya are going to play the following game: Petya has some positive integer number a. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers (x, y). Petya will answer him:
* "x", if (x mod a) ≥ (y mod a).
* "y", if (x mod a) < (y mod a).
We define (x mod a) as a remainder of division x by a.
Vasya should guess the number a using no more, than 60 questions.
It's guaranteed that Petya has a number, that satisfies the inequality 1 ≤ a ≤ 10^9.
Help Vasya playing this game and write a program, that will guess the number a.
Interaction
Your program should play several games.
Before the start of any game your program should read the string:
* "start" (without quotes) — the start of the new game.
* "mistake" (without quotes) — in the previous game, you found the wrong answer. Your program should terminate after reading this string and it will get verdict "Wrong answer".
* "end" (without quotes) — all games finished. Your program should terminate after reading this string.
After reading the string "start" (without quotes) the new game starts.
At the beginning, your program should ask several questions about pairs of non-negative integer numbers (x, y). You can only ask the numbers, that satisfy the inequalities 0 ≤ x, y ≤ 2 ⋅ 10^9. To ask a question print "? x y" (without quotes). As the answer, you should read one symbol:
* "x" (without quotes), if (x mod a) ≥ (y mod a).
* "y" (without quotes), if (x mod a) < (y mod a).
* "e" (without quotes) — you asked more than 60 questions. Your program should terminate after reading this string and it will get verdict "Wrong answer".
After your program asked several questions your program should print the answer in form "! a" (without quotes). You should print the number a satisfying the inequalities 1 ≤ a ≤ 10^9. It's guaranteed that Petya's number a satisfied this condition. After that, the current game will finish.
We recall that your program can't ask more than 60 questions during one game.
If your program doesn't terminate after reading "mistake" (without quotes), "end" (without quotes) or "e" (without quotes), it can get any verdict, because it will continue reading from closed input. Also, if your program prints answer or question in the incorrect format it can get any verdict, too. Be careful.
Don't forget to flush the output after printing questions and answers.
To flush the output, you can use:
* fflush(stdout) in C++.
* System.out.flush() in Java.
* stdout.flush() in Python.
* flush(output) in Pascal.
* See the documentation for other languages.
It's guaranteed that you should play at least 1 and no more than 100 games.
Hacks:
In hacks, you can use only one game. To hack a solution with Petya's number a (1 ≤ a ≤ 10^9) in the first line you should write a single number 1 and in the second line you should write a single number a.
Example
Input
start
x
x
start
x
x
y
start
x
x
y
y
end
Output
? 0 0
? 10 1
! 1
? 0 0
? 3 4
? 2 5
! 2
? 2 4
? 2 5
? 3 10
? 9 1
! 3
Note
In the first test, you should play 3 games with Petya's numbers 1, 2 and 3.
In the first game, Petya will answer "x" (without quotes) to any question, because (x mod 1) = 0 for any integer x.
In the second game, if you will ask pair (0, 0), the answer will be "x" (without quotes), because (0 mod 2) ≥ (0 mod 2). But if you will ask pair (2, 5), the answer will be "y" (without quotes), because (2 mod 2) < (5 mod 2), because (2 mod 2) = 0 and (5 mod 2) = 1.
Submitted Solution:
```
while True:
if input() == "end":
break
x = 0
y = 2
print("?", x, y)
if input() == "x":
print("?", 0, 1)
if input() == "x":
print("!", 1)
else:
print("!", 2)
break
else:
x = y
y *= 2
while True:
print("?", x, y)
if input() == "x":
break
x = y
y *= 2
l = x
r = y
while True:
if r-l == 1:
print("!", r)
break
print("?", r, l+r)
if input() == "x":
r = (l+r) // 2
else:
l = (l+r) // 2
``` | instruction | 0 | 73,366 | 20 | 146,732 |
No | output | 1 | 73,366 | 20 | 146,733 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes to play very much. And most of all he likes to play the following game:
He is given a sequence of N integer numbers. At each step it is allowed to increase the value of any number by 1 or to decrease it by 1. The goal of the game is to make the sequence non-decreasing with the smallest number of steps. Petya is not good at math, so he asks for your help.
The sequence a is called non-decreasing if a1 ≤ a2 ≤ ... ≤ aN holds, where N is the length of the sequence.
Input
The first line of the input contains single integer N (1 ≤ N ≤ 5000) — the length of the initial sequence. The following N lines contain one integer each — elements of the sequence. These numbers do not exceed 109 by absolute value.
Output
Output one integer — minimum number of steps required to achieve the goal.
Examples
Input
5
3 2 -1 2 11
Output
4
Input
5
2 1 1 1 1
Output
1
Submitted Solution:
```
n = int(input())
a = [*map(int, input().split())]
best_ans = 10**9
for i in range(n):
acopy = a.copy()
ans = 0
for j in range(i - 1, -1, -1):
if acopy[j] < acopy[j + 1]:
continue
ans += acopy[j] - acopy[j + 1]
acopy[j] = acopy[j + 1]
for j in range(i + 1, n):
if acopy[j] > acopy[j - 1]:
continue
ans += acopy[j - 1] - acopy[j]
acopy[j] = acopy[j - 1]
best_ans = min(ans, best_ans)
print(best_ans)
``` | instruction | 0 | 73,524 | 20 | 147,048 |
No | output | 1 | 73,524 | 20 | 147,049 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes to play very much. And most of all he likes to play the following game:
He is given a sequence of N integer numbers. At each step it is allowed to increase the value of any number by 1 or to decrease it by 1. The goal of the game is to make the sequence non-decreasing with the smallest number of steps. Petya is not good at math, so he asks for your help.
The sequence a is called non-decreasing if a1 ≤ a2 ≤ ... ≤ aN holds, where N is the length of the sequence.
Input
The first line of the input contains single integer N (1 ≤ N ≤ 5000) — the length of the initial sequence. The following N lines contain one integer each — elements of the sequence. These numbers do not exceed 109 by absolute value.
Output
Output one integer — minimum number of steps required to achieve the goal.
Examples
Input
5
3 2 -1 2 11
Output
4
Input
5
2 1 1 1 1
Output
1
Submitted Solution:
```
import sys
sys.setrecursionlimit(999999999)
Abs = abs
Min = min
siz = int(input())
arr = [int(i) for i in input().split()]
sor = sorted(arr)
mem = dict([])
def past(n, k):
return get(n, k-1) + Abs(sor[n] - arr[k]);
def get(n, k):
if(k == -1 or n == -1):
return 0
if((n, k) in mem):
return mem[(n, k)]
if(n == 0):
mem[(n, k)] = past(n, k)
return mem[(n, k)]
else:
mem[(n, k)] = Min(get(n-1, k), past(n, k))
return mem[(n, k)]
get(siz-1, siz-1)
``` | instruction | 0 | 73,525 | 20 | 147,050 |
No | output | 1 | 73,525 | 20 | 147,051 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes to play very much. And most of all he likes to play the following game:
He is given a sequence of N integer numbers. At each step it is allowed to increase the value of any number by 1 or to decrease it by 1. The goal of the game is to make the sequence non-decreasing with the smallest number of steps. Petya is not good at math, so he asks for your help.
The sequence a is called non-decreasing if a1 ≤ a2 ≤ ... ≤ aN holds, where N is the length of the sequence.
Input
The first line of the input contains single integer N (1 ≤ N ≤ 5000) — the length of the initial sequence. The following N lines contain one integer each — elements of the sequence. These numbers do not exceed 109 by absolute value.
Output
Output one integer — minimum number of steps required to achieve the goal.
Examples
Input
5
3 2 -1 2 11
Output
4
Input
5
2 1 1 1 1
Output
1
Submitted Solution:
```
def first(numbers, size):
previous = numbers[0]
ans = 0
for i in range(1,size,1):
if numbers[i] < previous:
ans += abs(previous - numbers[i])
else:
previous = numbers[i]
return ans
def last(numbers, size):
previous = numbers[-1]
ans = 0
for i in range(-2, -(size + 1), -1):
if numbers[i] > previous:
ans += abs(previous - numbers[i])
else:
previous = numbers[i]
return ans
def before(numbers, position):
#print("Inicia")
previous = numbers[position]
ans = 0
for i in range(position - 1, -1, -1):
if numbers[i] > previous:
#print("first", i, numbers[i], previous)
ans += abs(previous - numbers[i])
else:
#print("second", i, numbers[i], previous)
previous = numbers[i]
#print("Termina")
return ans
def after(numbers, position, size):
#print("Inicia")
previous = numbers[position]
ans = 0
for i in range(position + 1, size, 1):
if numbers[i] < previous:
#print("first", i, numbers[i], previous)
ans += abs(previous - numbers[i])
else:
#print("second", i, numbers[i], previous)
previous = numbers[i]
#print("Termina")
return ans
size = int( input() )
arg = input()
arg = arg.split(" ")
numbers = []
for num in arg:
numbers.append( int(num) )
steps = []
ans = 1000000000
size = len(numbers)
for i in range( len(numbers) ):
if i is 0:
ans = min(ans, first(numbers, size))
#print(first(numbers, size))
elif i == size - 1:
ans = min(ans, last(numbers, size))
#print(last(numbers, size))
else:
ans = min(ans, before(numbers, i) + after(numbers, i, size))
#print(before(numbers, i) + after(numbers, i, size))
print(ans)
``` | instruction | 0 | 73,526 | 20 | 147,052 |
No | output | 1 | 73,526 | 20 | 147,053 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Little Petya likes to play very much. And most of all he likes to play the following game:
He is given a sequence of N integer numbers. At each step it is allowed to increase the value of any number by 1 or to decrease it by 1. The goal of the game is to make the sequence non-decreasing with the smallest number of steps. Petya is not good at math, so he asks for your help.
The sequence a is called non-decreasing if a1 ≤ a2 ≤ ... ≤ aN holds, where N is the length of the sequence.
Input
The first line of the input contains single integer N (1 ≤ N ≤ 5000) — the length of the initial sequence. The following N lines contain one integer each — elements of the sequence. These numbers do not exceed 109 by absolute value.
Output
Output one integer — minimum number of steps required to achieve the goal.
Examples
Input
5
3 2 -1 2 11
Output
4
Input
5
2 1 1 1 1
Output
1
Submitted Solution:
```
n = int(input())
data = list(map(int,input().split()))
answer = 0
prev = None
for el in data:
if prev == None:
prev = el
else:
answer += max(0, el - prev)
prev = max(prev, el)
print(answer)
``` | instruction | 0 | 73,527 | 20 | 147,054 |
No | output | 1 | 73,527 | 20 | 147,055 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A number is called 2050-number if it is 2050, 20500, ..., (2050 ⋅ 10^k for integer k ≥ 0).
Given a number n, you are asked to represent n as the sum of some (not necessarily distinct) 2050-numbers. Compute the minimum number of 2050-numbers required for that.
Input
The first line contains a single integer T (1≤ T≤ 1 000) denoting the number of test cases.
The only line of each test case contains a single integer n (1≤ n≤ 10^{18}) denoting the number to be represented.
Output
For each test case, output the minimum number of 2050-numbers in one line.
If n cannot be represented as the sum of 2050-numbers, output -1 instead.
Example
Input
6
205
2050
4100
20500
22550
25308639900
Output
-1
1
2
1
2
36
Note
In the third case, 4100 = 2050 + 2050.
In the fifth case, 22550 = 20500 + 2050. | instruction | 0 | 73,576 | 20 | 147,152 |
Tags: greedy, math
Correct Solution:
```
for _ in range(int(input())):
n=int(input())
ans=0
if((n%2050)!=0):
print(-1)
continue
n=n//2050
rem=0
while(n>0):
rem=n%10
ans+=rem
n//=10
print(ans)
``` | output | 1 | 73,576 | 20 | 147,153 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A number is called 2050-number if it is 2050, 20500, ..., (2050 ⋅ 10^k for integer k ≥ 0).
Given a number n, you are asked to represent n as the sum of some (not necessarily distinct) 2050-numbers. Compute the minimum number of 2050-numbers required for that.
Input
The first line contains a single integer T (1≤ T≤ 1 000) denoting the number of test cases.
The only line of each test case contains a single integer n (1≤ n≤ 10^{18}) denoting the number to be represented.
Output
For each test case, output the minimum number of 2050-numbers in one line.
If n cannot be represented as the sum of 2050-numbers, output -1 instead.
Example
Input
6
205
2050
4100
20500
22550
25308639900
Output
-1
1
2
1
2
36
Note
In the third case, 4100 = 2050 + 2050.
In the fifth case, 22550 = 20500 + 2050. | instruction | 0 | 73,577 | 20 | 147,154 |
Tags: greedy, math
Correct Solution:
```
for _ in ' '*int(input()):
n = int(input())
c = n%2050==0
print(int(c*(sum(list(map(lambda x: int(x), list(str(n//2050)))))))+ int((not c)*(-1)))
``` | output | 1 | 73,577 | 20 | 147,155 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A number is called 2050-number if it is 2050, 20500, ..., (2050 ⋅ 10^k for integer k ≥ 0).
Given a number n, you are asked to represent n as the sum of some (not necessarily distinct) 2050-numbers. Compute the minimum number of 2050-numbers required for that.
Input
The first line contains a single integer T (1≤ T≤ 1 000) denoting the number of test cases.
The only line of each test case contains a single integer n (1≤ n≤ 10^{18}) denoting the number to be represented.
Output
For each test case, output the minimum number of 2050-numbers in one line.
If n cannot be represented as the sum of 2050-numbers, output -1 instead.
Example
Input
6
205
2050
4100
20500
22550
25308639900
Output
-1
1
2
1
2
36
Note
In the third case, 4100 = 2050 + 2050.
In the fifth case, 22550 = 20500 + 2050. | instruction | 0 | 73,578 | 20 | 147,156 |
Tags: greedy, math
Correct Solution:
```
def biggestlessthan(a):
if (int("2050"+"0"*(len(str(a))-4))<=a):
return int("2050"+"0"*(len(str(a))-4))
return int("2050"+"0"*(len(str(a))-5))
def solve():
count=0
a=int(input())
while a>=2050:
a-=biggestlessthan(a)
count+=1
if a!=0:
return -1
return count
def main():
for i in range (int(input())):
print (solve())
#print(biggestlessthan(20499))
main()
``` | output | 1 | 73,578 | 20 | 147,157 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A number is called 2050-number if it is 2050, 20500, ..., (2050 ⋅ 10^k for integer k ≥ 0).
Given a number n, you are asked to represent n as the sum of some (not necessarily distinct) 2050-numbers. Compute the minimum number of 2050-numbers required for that.
Input
The first line contains a single integer T (1≤ T≤ 1 000) denoting the number of test cases.
The only line of each test case contains a single integer n (1≤ n≤ 10^{18}) denoting the number to be represented.
Output
For each test case, output the minimum number of 2050-numbers in one line.
If n cannot be represented as the sum of 2050-numbers, output -1 instead.
Example
Input
6
205
2050
4100
20500
22550
25308639900
Output
-1
1
2
1
2
36
Note
In the third case, 4100 = 2050 + 2050.
In the fifth case, 22550 = 20500 + 2050. | instruction | 0 | 73,579 | 20 | 147,158 |
Tags: greedy, math
Correct Solution:
```
for _ in range(int(input())):
n = int(input())
if n%2050==0:
arr = list(map(int, list(str(int(n//2050)))))
print(sum(arr))
else:
print(-1)
``` | output | 1 | 73,579 | 20 | 147,159 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A number is called 2050-number if it is 2050, 20500, ..., (2050 ⋅ 10^k for integer k ≥ 0).
Given a number n, you are asked to represent n as the sum of some (not necessarily distinct) 2050-numbers. Compute the minimum number of 2050-numbers required for that.
Input
The first line contains a single integer T (1≤ T≤ 1 000) denoting the number of test cases.
The only line of each test case contains a single integer n (1≤ n≤ 10^{18}) denoting the number to be represented.
Output
For each test case, output the minimum number of 2050-numbers in one line.
If n cannot be represented as the sum of 2050-numbers, output -1 instead.
Example
Input
6
205
2050
4100
20500
22550
25308639900
Output
-1
1
2
1
2
36
Note
In the third case, 4100 = 2050 + 2050.
In the fifth case, 22550 = 20500 + 2050. | instruction | 0 | 73,580 | 20 | 147,160 |
Tags: greedy, math
Correct Solution:
```
t=int(input())
while(t!=0):
t=t-1
s="2050"
n=int(input())
if(n%2050!=0):
print(-1)
else:
c=0
while(n!=0):
le=len(str(n))-4
for i in range(le):
s=s+'0'
if(int(s)>n):
s=s[:-1]
#print(n,s)
n=n-int(s)
s="2050"
c=c+1
print(c)
``` | output | 1 | 73,580 | 20 | 147,161 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A number is called 2050-number if it is 2050, 20500, ..., (2050 ⋅ 10^k for integer k ≥ 0).
Given a number n, you are asked to represent n as the sum of some (not necessarily distinct) 2050-numbers. Compute the minimum number of 2050-numbers required for that.
Input
The first line contains a single integer T (1≤ T≤ 1 000) denoting the number of test cases.
The only line of each test case contains a single integer n (1≤ n≤ 10^{18}) denoting the number to be represented.
Output
For each test case, output the minimum number of 2050-numbers in one line.
If n cannot be represented as the sum of 2050-numbers, output -1 instead.
Example
Input
6
205
2050
4100
20500
22550
25308639900
Output
-1
1
2
1
2
36
Note
In the third case, 4100 = 2050 + 2050.
In the fifth case, 22550 = 20500 + 2050. | instruction | 0 | 73,581 | 20 | 147,162 |
Tags: greedy, math
Correct Solution:
```
t=int(input())
for i in range(t):
a=int(input())
i=16
s=0
while i>=0:
if a-2050*(10**i)>=0:
a-=2050*(10**i)
s+=1
else:
i-=1
if a>0:
print(-1)
else:
print(s)
``` | output | 1 | 73,581 | 20 | 147,163 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A number is called 2050-number if it is 2050, 20500, ..., (2050 ⋅ 10^k for integer k ≥ 0).
Given a number n, you are asked to represent n as the sum of some (not necessarily distinct) 2050-numbers. Compute the minimum number of 2050-numbers required for that.
Input
The first line contains a single integer T (1≤ T≤ 1 000) denoting the number of test cases.
The only line of each test case contains a single integer n (1≤ n≤ 10^{18}) denoting the number to be represented.
Output
For each test case, output the minimum number of 2050-numbers in one line.
If n cannot be represented as the sum of 2050-numbers, output -1 instead.
Example
Input
6
205
2050
4100
20500
22550
25308639900
Output
-1
1
2
1
2
36
Note
In the third case, 4100 = 2050 + 2050.
In the fifth case, 22550 = 20500 + 2050. | instruction | 0 | 73,582 | 20 | 147,164 |
Tags: greedy, math
Correct Solution:
```
import sys
r = sys.stdin.readline
for _ in range(int(r())):
N = int(r())
ans = 0
while 1:
s = 2050
if N == 0:
print(ans)
break
if N < 2050:
print(-1)
break
while N >= 10*s:
s *= 10
N -= s
ans += 1
``` | output | 1 | 73,582 | 20 | 147,165 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A number is called 2050-number if it is 2050, 20500, ..., (2050 ⋅ 10^k for integer k ≥ 0).
Given a number n, you are asked to represent n as the sum of some (not necessarily distinct) 2050-numbers. Compute the minimum number of 2050-numbers required for that.
Input
The first line contains a single integer T (1≤ T≤ 1 000) denoting the number of test cases.
The only line of each test case contains a single integer n (1≤ n≤ 10^{18}) denoting the number to be represented.
Output
For each test case, output the minimum number of 2050-numbers in one line.
If n cannot be represented as the sum of 2050-numbers, output -1 instead.
Example
Input
6
205
2050
4100
20500
22550
25308639900
Output
-1
1
2
1
2
36
Note
In the third case, 4100 = 2050 + 2050.
In the fifth case, 22550 = 20500 + 2050. | instruction | 0 | 73,583 | 20 | 147,166 |
Tags: greedy, math
Correct Solution:
```
import functools
tests = int(input())
m=2050
for case in range(tests):
n=int(input())
if n%m!=0:print(-1)
else: print(functools.reduce(lambda a,b:int(a)+int(b),str(int(n/m))))
``` | output | 1 | 73,583 | 20 | 147,167 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A number is called 2050-number if it is 2050, 20500, ..., (2050 ⋅ 10^k for integer k ≥ 0).
Given a number n, you are asked to represent n as the sum of some (not necessarily distinct) 2050-numbers. Compute the minimum number of 2050-numbers required for that.
Input
The first line contains a single integer T (1≤ T≤ 1 000) denoting the number of test cases.
The only line of each test case contains a single integer n (1≤ n≤ 10^{18}) denoting the number to be represented.
Output
For each test case, output the minimum number of 2050-numbers in one line.
If n cannot be represented as the sum of 2050-numbers, output -1 instead.
Example
Input
6
205
2050
4100
20500
22550
25308639900
Output
-1
1
2
1
2
36
Note
In the third case, 4100 = 2050 + 2050.
In the fifth case, 22550 = 20500 + 2050.
Submitted Solution:
```
import sys
input=sys.stdin.readline
from math import gcd
for _ in range(int(input().strip())):
#n,k=map(int,input().strip().split(" "))
#s=input().strip()
n=int(input().strip())
#a=list(map(int,input().strip().split(" ")))
if n%2050!=0:
print(-1)
continue
print(sum(map(int,list(str(n//2050)))))
``` | instruction | 0 | 73,584 | 20 | 147,168 |
Yes | output | 1 | 73,584 | 20 | 147,169 |
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