message stringlengths 2 44.5k | message_type stringclasses 2
values | message_id int64 0 1 | conversation_id int64 42 109k | cluster float64 5 5 | __index_level_0__ int64 84 217k |
|---|---|---|---|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b. Print a+b.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given as a line of two integers a and b (-1000 ≤ a, b ≤ 1000).
Output
Print t integers — the required numbers a+b.
Example
Input
4
1 5
314 15
-99 99
123 987
Output
6
329
0
1110
Submitted Solution:
```
t = int(input())
for _ in range(t):
s = ''
s = input()
a = s.split(" ")
print(int(a[0])+int(a[1]))
``` | instruction | 0 | 61,628 | 5 | 123,256 |
Yes | output | 1 | 61,628 | 5 | 123,257 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b. Print a+b.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given as a line of two integers a and b (-1000 ≤ a, b ≤ 1000).
Output
Print t integers — the required numbers a+b.
Example
Input
4
1 5
314 15
-99 99
123 987
Output
6
329
0
1110
Submitted Solution:
```
t = int(input())
for _ in range(t):
print(sum(map(int, input().split())))
``` | instruction | 0 | 61,629 | 5 | 123,258 |
Yes | output | 1 | 61,629 | 5 | 123,259 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b. Print a+b.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given as a line of two integers a and b (-1000 ≤ a, b ≤ 1000).
Output
Print t integers — the required numbers a+b.
Example
Input
4
1 5
314 15
-99 99
123 987
Output
6
329
0
1110
Submitted Solution:
```
k=int(input())
result=[]
for i in range(0,k):
a,b=input().split()
c=int(a)+int(b)
result.append(c)
for i in result:
print(i)
``` | instruction | 0 | 61,630 | 5 | 123,260 |
Yes | output | 1 | 61,630 | 5 | 123,261 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b. Print a+b.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given as a line of two integers a and b (-1000 ≤ a, b ≤ 1000).
Output
Print t integers — the required numbers a+b.
Example
Input
4
1 5
314 15
-99 99
123 987
Output
6
329
0
1110
Submitted Solution:
```
def solve():
n1,k1 = map(int,input().split())
print(n1+k1)
tests = int(input())
while tests:
tests-=1
print(solve())
``` | instruction | 0 | 61,631 | 5 | 123,262 |
No | output | 1 | 61,631 | 5 | 123,263 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b. Print a+b.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given as a line of two integers a and b (-1000 ≤ a, b ≤ 1000).
Output
Print t integers — the required numbers a+b.
Example
Input
4
1 5
314 15
-99 99
123 987
Output
6
329
0
1110
Submitted Solution:
```
for _ in range(int(input())):
a,b=input().split()
print(int(a),int(b))
``` | instruction | 0 | 61,632 | 5 | 123,264 |
No | output | 1 | 61,632 | 5 | 123,265 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b. Print a+b.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given as a line of two integers a and b (-1000 ≤ a, b ≤ 1000).
Output
Print t integers — the required numbers a+b.
Example
Input
4
1 5
314 15
-99 99
123 987
Output
6
329
0
1110
Submitted Solution:
```
s=int(input())
a,b=map(int,input().split())
print(a+b)
``` | instruction | 0 | 61,633 | 5 | 123,266 |
No | output | 1 | 61,633 | 5 | 123,267 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given two integers a and b. Print a+b.
Input
The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.
Each test case is given as a line of two integers a and b (-1000 ≤ a, b ≤ 1000).
Output
Print t integers — the required numbers a+b.
Example
Input
4
1 5
314 15
-99 99
123 987
Output
6
329
0
1110
Submitted Solution:
```
print(1)
``` | instruction | 0 | 61,634 | 5 | 123,268 |
No | output | 1 | 61,634 | 5 | 123,269 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer m, and a list of n distinct integers between 0 and m - 1.
You would like to construct a sequence satisfying the properties:
* Each element is an integer between 0 and m - 1, inclusive.
* All prefix products of the sequence modulo m are distinct.
* No prefix product modulo m appears as an element of the input list.
* The length of the sequence is maximized.
Construct any sequence satisfying the properties above.
Input
The first line of input contains two integers n and m (0 ≤ n < m ≤ 200 000) — the number of forbidden prefix products and the modulus.
If n is non-zero, the next line of input contains n distinct integers between 0 and m - 1, the forbidden prefix products. If n is zero, this line doesn't exist.
Output
On the first line, print the number k, denoting the length of your sequence.
On the second line, print k space separated integers, denoting your sequence.
Examples
Input
0 5
Output
5
1 2 4 3 0
Input
3 10
2 9 1
Output
6
3 9 2 9 8 0
Note
For the first case, the prefix products of this sequence modulo m are [1, 2, 3, 4, 0].
For the second case, the prefix products of this sequence modulo m are [3, 7, 4, 6, 8, 0].
Submitted Solution:
```
import math
def gcdExtended(a, b):
# Base Case
if a == 0 :
return b, 0, 1
gcd, x1, y1 = gcdExtended(b%a, a)
# Update x and y using results of recursive
# call
x = y1 - (b//a) * x1
y = x1
return gcd, x, y
def rev_elem(x, m):
return (gcdExtended(x, m)[1] + m) % m
n, m = map(int, input().split())
a = []
if n > 0:
a = [int(i) for i in input().split()]
banned = [False] * (m + 5)
for i in a:
banned[i] = True
cycle = [[] for i in range(m + 5)]
d, dp, p = [], [], []
for i in range(m):
cycle[math.gcd(m, i)].append(i)
cycle = [[i for i in j if not banned[i]] for j in cycle]
d = [i for i in range(1, m + 1) if m % i == 0]
dp = [len(cycle[i]) for i in d]
p = [-1 for i in d]
ans, lst = -1, -1
for i in range(len(d)):
if dp[i] > ans:
ans, lst = dp[i], i
for j in range(i + 1, len(d)):
if d[j] % d[i] != 0 or dp[j] > dp[i] + len(cycle[d[j]]):
continue
dp[j] = dp[i] + len(cycle[d[j]])
p[j] = i
print(ans)
pos, dpos, pref = [], [], []
cur = lst
while cur != -1:
dpos.append(d[cur])
cur = p[cur]
dpos.reverse()
for i in dpos:
pref += cycle[i]
cur = 1
for i in pref:
ad = 1
if math.gcd(i, m) != math.gcd(cur, m):
ad = ((cur * math.gcd(i, m) // math.gcd(cur, math.gcd(i, m))) // cur) % m
cur = (cur * ad) % m
if i != cur:
ad *= (i // math.gcd(i, cur)) * rev_elem(cur // math.gcd(i, cur), m)
ad %= m
cur = (cur * ad) % m
pos.append(ad)
print(*pos)
``` | instruction | 0 | 61,950 | 5 | 123,900 |
No | output | 1 | 61,950 | 5 | 123,901 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer m, and a list of n distinct integers between 0 and m - 1.
You would like to construct a sequence satisfying the properties:
* Each element is an integer between 0 and m - 1, inclusive.
* All prefix products of the sequence modulo m are distinct.
* No prefix product modulo m appears as an element of the input list.
* The length of the sequence is maximized.
Construct any sequence satisfying the properties above.
Input
The first line of input contains two integers n and m (0 ≤ n < m ≤ 200 000) — the number of forbidden prefix products and the modulus.
If n is non-zero, the next line of input contains n distinct integers between 0 and m - 1, the forbidden prefix products. If n is zero, this line doesn't exist.
Output
On the first line, print the number k, denoting the length of your sequence.
On the second line, print k space separated integers, denoting your sequence.
Examples
Input
0 5
Output
5
1 2 4 3 0
Input
3 10
2 9 1
Output
6
3 9 2 9 8 0
Note
For the first case, the prefix products of this sequence modulo m are [1, 2, 3, 4, 0].
For the second case, the prefix products of this sequence modulo m are [3, 7, 4, 6, 8, 0].
Submitted Solution:
```
import math
def gcdExtended(a, b):
# Base Case
if a == 0 :
return b, 0, 1
gcd, x1, y1 = gcdExtended(b%a, a)
# Update x and y using results of recursive
# call
x = y1 - (b//a) * x1
y = x1
return gcd, x, y
def rev_elem(x, m):
return (gcdExtended(x, m)[1] + m) % m
n, m = map(int, input().split())
a = []
if n > 0:
a = [int(i) for i in input().split()]
banned = [False] * (m + 5)
for i in a:
banned[i] = True
cycle = [[] for i in range(m + 5)]
d, dp, p = [], [], []
for i in range(m):
cycle[math.gcd(m, i)].append(i)
cycle = [[i for i in j if not banned[i]] for j in cycle]
d = [i for i in range(1, m + 1) if m % i == 0]
dp = [len(cycle[i]) for i in d]
p = [-1 for i in d]
ans, lst = -1, -1
for i in range(len(d)):
if dp[i] > ans:
ans, lst = dp[i], i
for j in range(i + 1, len(d)):
if d[j] % d[i] != 0 or dp[j] > dp[i] + len(cycle[d[j]]):
continue
dp[j] = dp[i] + len(cycle[d[j]])
p[j] = i
print(ans)
pos, dpos, pref = [], [], []
cur = lst
while cur != -1:
dpos.append(d[cur])
cur = p[cur]
dpos.reverse()
for i in dpos:
pref += cycle[i]
cur = 1
for i in pref:
ad = 1
if math.gcd(i, m) != math.gcd(cur, m):
ad = ((cur * math.gcd(i, m) // math.gcd(cur, math.gcd(i, m))) // cur) % m
cur = (cur * ad) % m
ad *= (i // math.gcd(i, m)) * rev_elem(cur // math.gcd(i, m), m)
ad %= m
cur = (cur * ad) % m
pos.append(ad)
print(*pos)
``` | instruction | 0 | 61,951 | 5 | 123,902 |
No | output | 1 | 61,951 | 5 | 123,903 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer m, and a list of n distinct integers between 0 and m - 1.
You would like to construct a sequence satisfying the properties:
* Each element is an integer between 0 and m - 1, inclusive.
* All prefix products of the sequence modulo m are distinct.
* No prefix product modulo m appears as an element of the input list.
* The length of the sequence is maximized.
Construct any sequence satisfying the properties above.
Input
The first line of input contains two integers n and m (0 ≤ n < m ≤ 200 000) — the number of forbidden prefix products and the modulus.
If n is non-zero, the next line of input contains n distinct integers between 0 and m - 1, the forbidden prefix products. If n is zero, this line doesn't exist.
Output
On the first line, print the number k, denoting the length of your sequence.
On the second line, print k space separated integers, denoting your sequence.
Examples
Input
0 5
Output
5
1 2 4 3 0
Input
3 10
2 9 1
Output
6
3 9 2 9 8 0
Note
For the first case, the prefix products of this sequence modulo m are [1, 2, 3, 4, 0].
For the second case, the prefix products of this sequence modulo m are [3, 7, 4, 6, 8, 0].
Submitted Solution:
```
def invm(m, n):
nn = n
x = 0
y = 1
while m != 0:
x, y = y, x - (n // m) * y
n, m = m, n % m
while x < 0:
x += nn
return x
def gcd(m, n):
while n:
m, n = n, m % n
return m
n, m = map(int, input().split())
if n:
data = set(map(int, input().split()))
else:
data = set()
res = []
cur = 1
gc = 1
while True:
gn = None
for i in range(gc, m, gc):
g = gcd(i,m)
if g == gc:
if i not in data:
next = invm(cur, m) * i % m
res.append(next)
cur = cur * next % m
elif gn is None:
gn = g
if gn:
gc = gn
else:
break
res.append(0)
print(len(res))
print(*res)
``` | instruction | 0 | 61,952 | 5 | 123,904 |
No | output | 1 | 61,952 | 5 | 123,905 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an integer m, and a list of n distinct integers between 0 and m - 1.
You would like to construct a sequence satisfying the properties:
* Each element is an integer between 0 and m - 1, inclusive.
* All prefix products of the sequence modulo m are distinct.
* No prefix product modulo m appears as an element of the input list.
* The length of the sequence is maximized.
Construct any sequence satisfying the properties above.
Input
The first line of input contains two integers n and m (0 ≤ n < m ≤ 200 000) — the number of forbidden prefix products and the modulus.
If n is non-zero, the next line of input contains n distinct integers between 0 and m - 1, the forbidden prefix products. If n is zero, this line doesn't exist.
Output
On the first line, print the number k, denoting the length of your sequence.
On the second line, print k space separated integers, denoting your sequence.
Examples
Input
0 5
Output
5
1 2 4 3 0
Input
3 10
2 9 1
Output
6
3 9 2 9 8 0
Note
For the first case, the prefix products of this sequence modulo m are [1, 2, 3, 4, 0].
For the second case, the prefix products of this sequence modulo m are [3, 7, 4, 6, 8, 0].
Submitted Solution:
```
import math
def gcdExtended(a, b):
# Base Case
if a == 0 :
return b, 0, 1
gcd, x1, y1 = gcdExtended(b%a, a)
# Update x and y using results of recursive
# call
x = y1 - (b//a) * x1
y = x1
return gcd, x, y
def rev_elem(x, m):
return (gcdExtended(x, m)[1] % m + m) % m
n, m = map(int, input().split())
a = []
if n > 0:
a = [int(i) for i in input().split()]
banned = [False] * (m + 5)
for i in a:
banned[i] = True
cycle = [[] for i in range(m + 5)]
d, dp, p = [], [], []
for i in range(m):
cycle[math.gcd(m, i)].append(i)
cycle = [[i for i in j if not banned[i]] for j in cycle]
d = [i for i in range(1, m + 1) if m % i == 0]
dp = [len(cycle[i]) for i in d]
p = [-1 for i in d]
ans, lst = -1, -1
for i in range(len(d)):
if dp[i] > ans:
ans, lst = dp[i], i
for j in range(i + 1, len(d)):
if d[j] % d[i] != 0 or dp[j] > dp[i] + len(cycle[d[j]]):
continue
dp[j] = dp[i] + len(cycle[d[j]])
p[j] = i
print(ans)
pos, dpos, pref = [], [], []
cur = lst
while cur != -1:
dpos.append(d[cur])
cur = p[cur]
dpos.reverse()
for i in dpos:
pref += cycle[i]
cur = 1
for i in pref:
ad = 1
if math.gcd(i, m) != math.gcd(cur, m):
ad = ((cur * math.gcd(i, m) // math.gcd(cur, math.gcd(i, m))) // cur) % m
cur = (cur * ad) % m
ad *= i * rev_elem(cur // math.gcd(i, m), m)
ad %= m
cur = (cur * ad) % m
pos.append(ad)
print(*pos)
``` | instruction | 0 | 61,953 | 5 | 123,906 |
No | output | 1 | 61,953 | 5 | 123,907 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n integers. You have to process q queries to this array; each query is given as four numbers l, r, x and y, denoting that for every i such that l ≤ i ≤ r and ai = x you have to set ai equal to y.
Print the array after all queries are processed.
Input
The first line contains one integer n (1 ≤ n ≤ 200000) — the size of array a.
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 100) — the elements of array a.
The third line contains one integer q (1 ≤ q ≤ 200000) — the number of queries you have to process.
Then q lines follow. i-th line contains four integers l, r, x and y denoting i-th query (1 ≤ l ≤ r ≤ n, 1 ≤ x, y ≤ 100).
Output
Print n integers — elements of array a after all changes are made.
Example
Input
5
1 2 3 4 5
3
3 5 3 5
1 5 5 1
1 5 1 5
Output
5 2 5 4 5
Submitted Solution:
```
import sys
input_ = sys.stdin.read()
input_ = input_.split('\n')[:-1]
arr = [x for x in input_[1].split()]
print(arr)
``` | instruction | 0 | 62,006 | 5 | 124,012 |
No | output | 1 | 62,006 | 5 | 124,013 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n integers. You have to process q queries to this array; each query is given as four numbers l, r, x and y, denoting that for every i such that l ≤ i ≤ r and ai = x you have to set ai equal to y.
Print the array after all queries are processed.
Input
The first line contains one integer n (1 ≤ n ≤ 200000) — the size of array a.
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 100) — the elements of array a.
The third line contains one integer q (1 ≤ q ≤ 200000) — the number of queries you have to process.
Then q lines follow. i-th line contains four integers l, r, x and y denoting i-th query (1 ≤ l ≤ r ≤ n, 1 ≤ x, y ≤ 100).
Output
Print n integers — elements of array a after all changes are made.
Example
Input
5
1 2 3 4 5
3
3 5 3 5
1 5 5 1
1 5 1 5
Output
5 2 5 4 5
Submitted Solution:
```
n = input()
arr = list(map(int, input().split()))
q = int(input())
for t in range(q):
l, r, x, y = map(int, input().split())
for i in range(l-1,r):
if(arr[i] == x):
arr[i]=y
print(arr)
``` | instruction | 0 | 62,007 | 5 | 124,014 |
No | output | 1 | 62,007 | 5 | 124,015 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n integers. You have to process q queries to this array; each query is given as four numbers l, r, x and y, denoting that for every i such that l ≤ i ≤ r and ai = x you have to set ai equal to y.
Print the array after all queries are processed.
Input
The first line contains one integer n (1 ≤ n ≤ 200000) — the size of array a.
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 100) — the elements of array a.
The third line contains one integer q (1 ≤ q ≤ 200000) — the number of queries you have to process.
Then q lines follow. i-th line contains four integers l, r, x and y denoting i-th query (1 ≤ l ≤ r ≤ n, 1 ≤ x, y ≤ 100).
Output
Print n integers — elements of array a after all changes are made.
Example
Input
5
1 2 3 4 5
3
3 5 3 5
1 5 5 1
1 5 1 5
Output
5 2 5 4 5
Submitted Solution:
```
import sys
input_ = sys.stdin.readlines()
print(input_)
``` | instruction | 0 | 62,008 | 5 | 124,016 |
No | output | 1 | 62,008 | 5 | 124,017 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are given an array a consisting of n integers. You have to process q queries to this array; each query is given as four numbers l, r, x and y, denoting that for every i such that l ≤ i ≤ r and ai = x you have to set ai equal to y.
Print the array after all queries are processed.
Input
The first line contains one integer n (1 ≤ n ≤ 200000) — the size of array a.
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 100) — the elements of array a.
The third line contains one integer q (1 ≤ q ≤ 200000) — the number of queries you have to process.
Then q lines follow. i-th line contains four integers l, r, x and y denoting i-th query (1 ≤ l ≤ r ≤ n, 1 ≤ x, y ≤ 100).
Output
Print n integers — elements of array a after all changes are made.
Example
Input
5
1 2 3 4 5
3
3 5 3 5
1 5 5 1
1 5 1 5
Output
5 2 5 4 5
Submitted Solution:
```
import sys
input_ = sys.stdin.read()
print(input_)
``` | instruction | 0 | 62,009 | 5 | 124,018 |
No | output | 1 | 62,009 | 5 | 124,019 |
Provide a correct Python 3 solution for this coding contest problem.
Given is a positive integer N.
We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.
* Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.
In how many choices of K will N become 1 in the end?
Constraints
* 2 \leq N \leq 10^{12}
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the number of choices of K in which N becomes 1 in the end.
Examples
Input
6
Output
3
Input
3141
Output
13
Input
314159265358
Output
9 | instruction | 0 | 62,048 | 5 | 124,096 |
"Correct Solution:
```
def factor(N):
arr=[]
for i in range(1,int(N**0.5)+1):
if(N%i==0):
arr.append(i)
if(N//i!=i):
arr.append(N//i)
return arr
N=int(input())
li=factor(N)
fac=factor(N-1)
res=len(fac)-1
for i in range(len(li)):
if(li[i]==1):
continue
tmp=N
while(tmp%li[i]==0):
tmp//=li[i]
if(tmp%li[i]==1):
res+=1
print(res)
``` | output | 1 | 62,048 | 5 | 124,097 |
Provide a correct Python 3 solution for this coding contest problem.
Given is a positive integer N.
We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.
* Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.
In how many choices of K will N become 1 in the end?
Constraints
* 2 \leq N \leq 10^{12}
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the number of choices of K in which N becomes 1 in the end.
Examples
Input
6
Output
3
Input
3141
Output
13
Input
314159265358
Output
9 | instruction | 0 | 62,049 | 5 | 124,098 |
"Correct Solution:
```
n,a=int(input()),1
for i in range(2,int(n**.5)+1):
a+=-~(~-n//i>i)*(~-n%i<1)
if n%i<1:
m=n
while m%i<1:m//=i
a+=m%i<2
print(a+(n>2))
``` | output | 1 | 62,049 | 5 | 124,099 |
Provide a correct Python 3 solution for this coding contest problem.
Given is a positive integer N.
We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.
* Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.
In how many choices of K will N become 1 in the end?
Constraints
* 2 \leq N \leq 10^{12}
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the number of choices of K in which N becomes 1 in the end.
Examples
Input
6
Output
3
Input
3141
Output
13
Input
314159265358
Output
9 | instruction | 0 | 62,050 | 5 | 124,100 |
"Correct Solution:
```
n = int(input());div=[];ans=[]
for i in range(1,int(n**0.5)+2):
if n%i == 0:
div.append(i);div.append(n//i)
for i in div:
if i == 1:
continue
tmp = n
while tmp % i == 0:
tmp //= i
if tmp % i ==1:
ans.append(i)
n -= 1
for i in range(1,int(n**0.5)+2):
if n%i == 0:
ans.append(i);ans.append(n//i)
print(len(set(ans))-1)
``` | output | 1 | 62,050 | 5 | 124,101 |
Provide a correct Python 3 solution for this coding contest problem.
Given is a positive integer N.
We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.
* Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.
In how many choices of K will N become 1 in the end?
Constraints
* 2 \leq N \leq 10^{12}
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the number of choices of K in which N becomes 1 in the end.
Examples
Input
6
Output
3
Input
3141
Output
13
Input
314159265358
Output
9 | instruction | 0 | 62,052 | 5 | 124,104 |
"Correct Solution:
```
def check(i):
tot=k
while(tot%i==0):
tot//=i
if(tot%i==1):
setl.add(i)
import math
k=int(input())
setl = set()
setl.add(k); setl.add(k-1)
for x in range(2,int(math.sqrt(k))+1):
check(x)
check(k//x)
if(setl.__contains__(1)):
setl.remove(1)
print(len(setl))
``` | output | 1 | 62,052 | 5 | 124,105 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is a positive integer N.
We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.
* Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.
In how many choices of K will N become 1 in the end?
Constraints
* 2 \leq N \leq 10^{12}
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the number of choices of K in which N becomes 1 in the end.
Examples
Input
6
Output
3
Input
3141
Output
13
Input
314159265358
Output
9
Submitted Solution:
```
N = int(input())
ans = set()
def check(N, k):
if k<2:
return False
N //= k
while N:
if (N-1)%k==0:
return True
if N%k:
return False
N //= k
for k in range(1, int(N**0.5)+1):
if (N-1)%k==0:
ans.add(k)
ans.add((N-1)//k)
if N%k==0:
if check(N, k):
ans.add(k)
if check(N, N//k):
ans.add(N//k)
ans.remove(1)
print(len(ans))
``` | instruction | 0 | 62,055 | 5 | 124,110 |
Yes | output | 1 | 62,055 | 5 | 124,111 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is a positive integer N.
We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.
* Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.
In how many choices of K will N become 1 in the end?
Constraints
* 2 \leq N \leq 10^{12}
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the number of choices of K in which N becomes 1 in the end.
Examples
Input
6
Output
3
Input
3141
Output
13
Input
314159265358
Output
9
Submitted Solution:
```
import math
def main():
N = int(input())
cnt = 0
N1 = N - 1
cnt = 2
for i in range(2, int(math.sqrt(N1)) + 1):
if N1 % i == 0:
cnt += 2
for i in range(2, int(math.sqrt(N)) + 1):
if N % i != 0:
continue
m = N // i
n = m
while n % i == 0:
n //= i
if n % i == 1:
cnt += 1
n = N // m
i = m
while n % i == 0:
n //= i
if n % i == 1:
cnt += 1
print(cnt)
main()
``` | instruction | 0 | 62,059 | 5 | 124,118 |
No | output | 1 | 62,059 | 5 | 124,119 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Given is a positive integer N.
We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.
* Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.
In how many choices of K will N become 1 in the end?
Constraints
* 2 \leq N \leq 10^{12}
* N is an integer.
Input
Input is given from Standard Input in the following format:
N
Output
Print the number of choices of K in which N becomes 1 in the end.
Examples
Input
6
Output
3
Input
3141
Output
13
Input
314159265358
Output
9
Submitted Solution:
```
N = int(input())
def check(p):
_N = N
while _N%p == 0:
_N //= p
return ((_N-1)%p == 0) or (_N == 1)
n = int(N**0.5)
P0 = [N]
P1 = [N-1]
for i in range(2, n+1):
if (N-1)%i == 0:
P1 += [i, (N-1)//i]
if N%i == 0:
P0 += [i, N//i]
ans = len(P1)
for p in P0:
ans += check(p)
print(ans)
``` | instruction | 0 | 62,060 | 5 | 124,120 |
No | output | 1 | 62,060 | 5 | 124,121 |
Provide a correct Python 3 solution for this coding contest problem.
A group of people played a game. All players had distinct scores, which are positive integers.
Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i.
Find the maximum possible number of players in the game.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9(1\leq i\leq N)
* 0 \leq B_i \leq 10^9(1\leq i\leq N)
* If i ≠j, A_i ≠A_j.
* There exists a possible outcome of the game that are consistent with the facts.
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Outputs
Print the maximum possible number of players in the game.
Examples
Input
3
4 7
2 9
6 2
Output
8
Input
5
1 10
3 6
5 2
4 4
2 8
Output
7
Input
2
1 1000000000
1000000000 1
Output
1000000001 | instruction | 0 | 62,141 | 5 | 124,282 |
"Correct Solution:
```
n = int(input())
AB = [list(map(int,input().split())) for i in range(n)]
AB.sort(reverse=True)
print(AB[0][0]+AB[0][1])
``` | output | 1 | 62,141 | 5 | 124,283 |
Provide a correct Python 3 solution for this coding contest problem.
A group of people played a game. All players had distinct scores, which are positive integers.
Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i.
Find the maximum possible number of players in the game.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9(1\leq i\leq N)
* 0 \leq B_i \leq 10^9(1\leq i\leq N)
* If i ≠j, A_i ≠A_j.
* There exists a possible outcome of the game that are consistent with the facts.
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Outputs
Print the maximum possible number of players in the game.
Examples
Input
3
4 7
2 9
6 2
Output
8
Input
5
1 10
3 6
5 2
4 4
2 8
Output
7
Input
2
1 1000000000
1000000000 1
Output
1000000001 | instruction | 0 | 62,143 | 5 | 124,286 |
"Correct Solution:
```
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N)]
sAB = sorted(AB, key=lambda x: - x[0])
print(sum(sAB[0]))
``` | output | 1 | 62,143 | 5 | 124,287 |
Provide a correct Python 3 solution for this coding contest problem.
A group of people played a game. All players had distinct scores, which are positive integers.
Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i.
Find the maximum possible number of players in the game.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9(1\leq i\leq N)
* 0 \leq B_i \leq 10^9(1\leq i\leq N)
* If i ≠j, A_i ≠A_j.
* There exists a possible outcome of the game that are consistent with the facts.
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Outputs
Print the maximum possible number of players in the game.
Examples
Input
3
4 7
2 9
6 2
Output
8
Input
5
1 10
3 6
5 2
4 4
2 8
Output
7
Input
2
1 1000000000
1000000000 1
Output
1000000001 | instruction | 0 | 62,144 | 5 | 124,288 |
"Correct Solution:
```
N=int(input())
maxA=0
minB=10**9
for _ in range(N):
A,B=map(int,input().split())
if maxA<A:
maxA=A
minB=B
print(maxA+minB)
``` | output | 1 | 62,144 | 5 | 124,289 |
Provide a correct Python 3 solution for this coding contest problem.
A group of people played a game. All players had distinct scores, which are positive integers.
Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i.
Find the maximum possible number of players in the game.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9(1\leq i\leq N)
* 0 \leq B_i \leq 10^9(1\leq i\leq N)
* If i ≠j, A_i ≠A_j.
* There exists a possible outcome of the game that are consistent with the facts.
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Outputs
Print the maximum possible number of players in the game.
Examples
Input
3
4 7
2 9
6 2
Output
8
Input
5
1 10
3 6
5 2
4 4
2 8
Output
7
Input
2
1 1000000000
1000000000 1
Output
1000000001 | instruction | 0 | 62,145 | 5 | 124,290 |
"Correct Solution:
```
N = int(input())
AB = [list(map(int, input().split())) for _ in range(N)]
ab = sorted(AB)
print(sum(ab[-1]))
``` | output | 1 | 62,145 | 5 | 124,291 |
Provide a correct Python 3 solution for this coding contest problem.
A group of people played a game. All players had distinct scores, which are positive integers.
Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i.
Find the maximum possible number of players in the game.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9(1\leq i\leq N)
* 0 \leq B_i \leq 10^9(1\leq i\leq N)
* If i ≠j, A_i ≠A_j.
* There exists a possible outcome of the game that are consistent with the facts.
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Outputs
Print the maximum possible number of players in the game.
Examples
Input
3
4 7
2 9
6 2
Output
8
Input
5
1 10
3 6
5 2
4 4
2 8
Output
7
Input
2
1 1000000000
1000000000 1
Output
1000000001 | instruction | 0 | 62,146 | 5 | 124,292 |
"Correct Solution:
```
n = int(input())
a,b = [],[]
for i in range(n):
aa, bb = map(int, input().split())
a.append(aa)
b.append(bb)
print (max(a)+min(b))
``` | output | 1 | 62,146 | 5 | 124,293 |
Provide a correct Python 3 solution for this coding contest problem.
A group of people played a game. All players had distinct scores, which are positive integers.
Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i.
Find the maximum possible number of players in the game.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9(1\leq i\leq N)
* 0 \leq B_i \leq 10^9(1\leq i\leq N)
* If i ≠j, A_i ≠A_j.
* There exists a possible outcome of the game that are consistent with the facts.
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Outputs
Print the maximum possible number of players in the game.
Examples
Input
3
4 7
2 9
6 2
Output
8
Input
5
1 10
3 6
5 2
4 4
2 8
Output
7
Input
2
1 1000000000
1000000000 1
Output
1000000001 | instruction | 0 | 62,147 | 5 | 124,294 |
"Correct Solution:
```
n = int(input())
In = sorted([list(map(int,input().split())) for i in range(n)])
print(In[-1][0]+In[-1][1])
``` | output | 1 | 62,147 | 5 | 124,295 |
Provide a correct Python 3 solution for this coding contest problem.
A group of people played a game. All players had distinct scores, which are positive integers.
Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i.
Find the maximum possible number of players in the game.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9(1\leq i\leq N)
* 0 \leq B_i \leq 10^9(1\leq i\leq N)
* If i ≠j, A_i ≠A_j.
* There exists a possible outcome of the game that are consistent with the facts.
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Outputs
Print the maximum possible number of players in the game.
Examples
Input
3
4 7
2 9
6 2
Output
8
Input
5
1 10
3 6
5 2
4 4
2 8
Output
7
Input
2
1 1000000000
1000000000 1
Output
1000000001 | instruction | 0 | 62,148 | 5 | 124,296 |
"Correct Solution:
```
N=int(input())
A=[list(map(int,input().split())) for _ in range(N)]
AA=sorted(A)
print(AA[-1][0]+AA[-1][1])
``` | output | 1 | 62,148 | 5 | 124,297 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A group of people played a game. All players had distinct scores, which are positive integers.
Takahashi knows N facts on the players' scores. The i-th fact is as follows: the A_i-th highest score among the players is B_i.
Find the maximum possible number of players in the game.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq A_i \leq 10^9(1\leq i\leq N)
* 0 \leq B_i \leq 10^9(1\leq i\leq N)
* If i ≠j, A_i ≠A_j.
* There exists a possible outcome of the game that are consistent with the facts.
* All input values are integers.
Inputs
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Outputs
Print the maximum possible number of players in the game.
Examples
Input
3
4 7
2 9
6 2
Output
8
Input
5
1 10
3 6
5 2
4 4
2 8
Output
7
Input
2
1 1000000000
1000000000 1
Output
1000000001
Submitted Solution:
```
n=int(input())
a=0
ans=0
for i in range(n):
x,y=map(int,input().split())
if a<x:
ans=x+y-1
a=x
print(ans)
``` | instruction | 0 | 62,156 | 5 | 124,312 |
No | output | 1 | 62,156 | 5 | 124,313 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below.
A image of angles
Constraints
The input satisfies the following conditions.
* Angle is expressed in degrees
* 0 ≤ θ1, θ2 <360
* θ1 and θ2 are integers
* | θ1 − θ2 | ≠180
* No input is given that gives the answer [0,0.0001] or [359.999,360)
Input
The input is given in the following format.
θ1
θ2
Output
Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001.
Examples
Input
10
20
Output
15.0
Input
20
350
Output
5.0 | instruction | 0 | 62,228 | 5 | 124,456 |
"Correct Solution:
```
a = int(input())
b = int(input())
a = a % 360
b = b % 360
if a > b :
a, b = b, a
if b - a > 180 :
a += 360
t = abs((a - b) / 2)
ans = min(a, b) + t
ans = ans % 360
print('{:6f}'.format(ans))
``` | output | 1 | 62,228 | 5 | 124,457 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below.
A image of angles
Constraints
The input satisfies the following conditions.
* Angle is expressed in degrees
* 0 ≤ θ1, θ2 <360
* θ1 and θ2 are integers
* | θ1 − θ2 | ≠180
* No input is given that gives the answer [0,0.0001] or [359.999,360)
Input
The input is given in the following format.
θ1
θ2
Output
Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001.
Examples
Input
10
20
Output
15.0
Input
20
350
Output
5.0 | instruction | 0 | 62,229 | 5 | 124,458 |
"Correct Solution:
```
a = int(input())
b = int(input())
a, b = min(a, b), max(a, b)
if b - a <= 180:
print((a+b) / 2)
else:
print(((a+b+360) % 720) / 2)
``` | output | 1 | 62,229 | 5 | 124,459 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below.
A image of angles
Constraints
The input satisfies the following conditions.
* Angle is expressed in degrees
* 0 ≤ θ1, θ2 <360
* θ1 and θ2 are integers
* | θ1 − θ2 | ≠180
* No input is given that gives the answer [0,0.0001] or [359.999,360)
Input
The input is given in the following format.
θ1
θ2
Output
Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001.
Examples
Input
10
20
Output
15.0
Input
20
350
Output
5.0 | instruction | 0 | 62,230 | 5 | 124,460 |
"Correct Solution:
```
a, b = int(input()), int(input())
print((a + b) / 2 % 360 if abs (a - b) % 360 < 180 else (a + b + 360) / 2 % 360)
``` | output | 1 | 62,230 | 5 | 124,461 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below.
A image of angles
Constraints
The input satisfies the following conditions.
* Angle is expressed in degrees
* 0 ≤ θ1, θ2 <360
* θ1 and θ2 are integers
* | θ1 − θ2 | ≠180
* No input is given that gives the answer [0,0.0001] or [359.999,360)
Input
The input is given in the following format.
θ1
θ2
Output
Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001.
Examples
Input
10
20
Output
15.0
Input
20
350
Output
5.0 | instruction | 0 | 62,231 | 5 | 124,462 |
"Correct Solution:
```
s1 = int(input())
s2 = int(input())
a = min(s1,s2)
b = max(s1,s2)
if b-a>180:
print((b+(360-b+a)/2)%360)
else:
print((a+b)/2)
``` | output | 1 | 62,231 | 5 | 124,463 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below.
A image of angles
Constraints
The input satisfies the following conditions.
* Angle is expressed in degrees
* 0 ≤ θ1, θ2 <360
* θ1 and θ2 are integers
* | θ1 − θ2 | ≠180
* No input is given that gives the answer [0,0.0001] or [359.999,360)
Input
The input is given in the following format.
θ1
θ2
Output
Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001.
Examples
Input
10
20
Output
15.0
Input
20
350
Output
5.0 | instruction | 0 | 62,232 | 5 | 124,464 |
"Correct Solution:
```
s1 = int(input())
s2 = int(input())
if s1 > s2:
s1, s2 = s2, s1
if s2 - s1 < 180:
print((s1+s2)/2)
elif (s1+s2)/2 +180 < 360:
print((s1+s2)/2 +180)
else:
print((s1 + s2) / 2 - 180)
``` | output | 1 | 62,232 | 5 | 124,465 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below.
A image of angles
Constraints
The input satisfies the following conditions.
* Angle is expressed in degrees
* 0 ≤ θ1, θ2 <360
* θ1 and θ2 are integers
* | θ1 − θ2 | ≠180
* No input is given that gives the answer [0,0.0001] or [359.999,360)
Input
The input is given in the following format.
θ1
θ2
Output
Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001.
Examples
Input
10
20
Output
15.0
Input
20
350
Output
5.0 | instruction | 0 | 62,234 | 5 | 124,468 |
"Correct Solution:
```
angs = [int(input()), int(input())]
angs.sort()
if angs[1] - angs[0] > 180:
ans = sum(angs) / 2 + 180
if ans >= 360:
ans -= 360
print(ans)
else:
print(sum(angs) / 2)
``` | output | 1 | 62,234 | 5 | 124,469 |
Provide a correct Python 3 solution for this coding contest problem.
Problem
Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below.
A image of angles
Constraints
The input satisfies the following conditions.
* Angle is expressed in degrees
* 0 ≤ θ1, θ2 <360
* θ1 and θ2 are integers
* | θ1 − θ2 | ≠180
* No input is given that gives the answer [0,0.0001] or [359.999,360)
Input
The input is given in the following format.
θ1
θ2
Output
Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001.
Examples
Input
10
20
Output
15.0
Input
20
350
Output
5.0 | instruction | 0 | 62,235 | 5 | 124,470 |
"Correct Solution:
```
t1 = int(input())
t2 = int(input())
x = (t2-t1)/2
a = x
for i in range(-2,3):
t = x + i*180
if abs(a) > abs(t):
a = t
ans = t1+a
while ans < 0:
ans += 360
while ans > 360:
ans -= 360
print(ans)
``` | output | 1 | 62,235 | 5 | 124,471 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Problem
Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below.
A image of angles
Constraints
The input satisfies the following conditions.
* Angle is expressed in degrees
* 0 ≤ θ1, θ2 <360
* θ1 and θ2 are integers
* | θ1 − θ2 | ≠180
* No input is given that gives the answer [0,0.0001] or [359.999,360)
Input
The input is given in the following format.
θ1
θ2
Output
Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001.
Examples
Input
10
20
Output
15.0
Input
20
350
Output
5.0
Submitted Solution:
```
a,b=int(input()),int(input())
print((a+b+360*(abs(a-b)>180))/2%360)
``` | instruction | 0 | 62,236 | 5 | 124,472 |
Yes | output | 1 | 62,236 | 5 | 124,473 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Problem
Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below.
A image of angles
Constraints
The input satisfies the following conditions.
* Angle is expressed in degrees
* 0 ≤ θ1, θ2 <360
* θ1 and θ2 are integers
* | θ1 − θ2 | ≠180
* No input is given that gives the answer [0,0.0001] or [359.999,360)
Input
The input is given in the following format.
θ1
θ2
Output
Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001.
Examples
Input
10
20
Output
15.0
Input
20
350
Output
5.0
Submitted Solution:
```
a = float(input())
b = float(input())
if a>b: a,b=b,a
ansa = (a+b)/2
ta = abs(a-ansa)
if ansa<0: ansa+=360.0
ansb = (a+b-360)/2
tb = abs(a-ansb)
if ansb<0: ansb+=360.0
if ta<tb: print(ansa)
else: print(ansb)
``` | instruction | 0 | 62,237 | 5 | 124,474 |
Yes | output | 1 | 62,237 | 5 | 124,475 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Problem
Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below.
A image of angles
Constraints
The input satisfies the following conditions.
* Angle is expressed in degrees
* 0 ≤ θ1, θ2 <360
* θ1 and θ2 are integers
* | θ1 − θ2 | ≠180
* No input is given that gives the answer [0,0.0001] or [359.999,360)
Input
The input is given in the following format.
θ1
θ2
Output
Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001.
Examples
Input
10
20
Output
15.0
Input
20
350
Output
5.0
Submitted Solution:
```
t1 = int(input())
t2 = int(input())
if not t1 < t2:
t1, t2 = t2, t1
if t2 - t1 <= 180:
print((t2 + t1)/2)
else:
print(((t2 + t1 + 360) % 720)/2)
``` | instruction | 0 | 62,238 | 5 | 124,476 |
Yes | output | 1 | 62,238 | 5 | 124,477 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Problem
Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below.
A image of angles
Constraints
The input satisfies the following conditions.
* Angle is expressed in degrees
* 0 ≤ θ1, θ2 <360
* θ1 and θ2 are integers
* | θ1 − θ2 | ≠180
* No input is given that gives the answer [0,0.0001] or [359.999,360)
Input
The input is given in the following format.
θ1
θ2
Output
Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001.
Examples
Input
10
20
Output
15.0
Input
20
350
Output
5.0
Submitted Solution:
```
a=int(input())
b=int(input())
if (a+b)/2<180:
print((a+b)/2)
else:
print(((a+b)/2)-180)
``` | instruction | 0 | 62,239 | 5 | 124,478 |
No | output | 1 | 62,239 | 5 | 124,479 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Problem
Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below.
A image of angles
Constraints
The input satisfies the following conditions.
* Angle is expressed in degrees
* 0 ≤ θ1, θ2 <360
* θ1 and θ2 are integers
* | θ1 − θ2 | ≠180
* No input is given that gives the answer [0,0.0001] or [359.999,360)
Input
The input is given in the following format.
θ1
θ2
Output
Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001.
Examples
Input
10
20
Output
15.0
Input
20
350
Output
5.0
Submitted Solution:
```
a = float(input())
b = float(input())
#if a>b: a,b=b,a
ansa = (a+b)/2
ta = abs(a-ansa)
if ansa<0: ansa+=360.0
ansb = (a+b-360)/2
tb = abs(a-ansb)
if ansb<0: ansb+=360.0
if ta<tb: print(ansa)
else: print(ansb)
``` | instruction | 0 | 62,240 | 5 | 124,480 |
No | output | 1 | 62,240 | 5 | 124,481 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Problem
Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below.
A image of angles
Constraints
The input satisfies the following conditions.
* Angle is expressed in degrees
* 0 ≤ θ1, θ2 <360
* θ1 and θ2 are integers
* | θ1 − θ2 | ≠180
* No input is given that gives the answer [0,0.0001] or [359.999,360)
Input
The input is given in the following format.
θ1
θ2
Output
Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001.
Examples
Input
10
20
Output
15.0
Input
20
350
Output
5.0
Submitted Solution:
```
s1 = int(input())
s2 = int(input())
d = s1 - s2
if abs(d) >= 180:
s1 = min(360-s1, s1)
s2 = min(360-s2, s2)
if s1 >= s2:
print(abs(s1-s2)/2)
else:
print(360-abs(s1-s2)/2)
else:
print(abs(d)/2 + min(s1, s2))
``` | instruction | 0 | 62,241 | 5 | 124,482 |
No | output | 1 | 62,241 | 5 | 124,483 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Problem
Find the angle between the two given angles θ1 and θ2. Here, the angle between them is defined as "θ1 & plus; t'when t'is the one with the smallest absolute value among the t satisfying θ1 & plus; t = θ2 − t" as shown in the figure below.
A image of angles
Constraints
The input satisfies the following conditions.
* Angle is expressed in degrees
* 0 ≤ θ1, θ2 <360
* θ1 and θ2 are integers
* | θ1 − θ2 | ≠180
* No input is given that gives the answer [0,0.0001] or [359.999,360)
Input
The input is given in the following format.
θ1
θ2
Output
Output the angle between θ1 and θ2 in one line in the range [0,360) in degrees. However, it must not include an error exceeding 0.0001.
Examples
Input
10
20
Output
15.0
Input
20
350
Output
5.0
Submitted Solution:
```
a=int(input())
b=int(input())
if a+b<360:
print((a+b)/2)
else:
print(((a+b)/2)-180)
``` | instruction | 0 | 62,242 | 5 | 124,484 |
No | output | 1 | 62,242 | 5 | 124,485 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x.
After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore.
Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve?
Input
A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above.
Output
Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0.
Examples
Input
4
Output
8
Input
6
Output
28
Input
2
Output
0
Note
In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2.
In the third example, it is impossible to perform even a single transformation. | instruction | 0 | 62,293 | 5 | 124,586 |
Tags: dfs and similar, graphs, implementation, math
Correct Solution:
```
import sys
input=sys.stdin.readline
n=int(input())
print(sum([sum([k//j for k in range(2*j,n+1,j)]) for j in range(2,n+1)])*4)
``` | output | 1 | 62,293 | 5 | 124,587 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x.
After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore.
Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve?
Input
A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above.
Output
Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0.
Examples
Input
4
Output
8
Input
6
Output
28
Input
2
Output
0
Note
In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2.
In the third example, it is impossible to perform even a single transformation. | instruction | 0 | 62,295 | 5 | 124,590 |
Tags: dfs and similar, graphs, implementation, math
Correct Solution:
```
n = int(input())
sum = 0
for i in range(2, n + 1):
j = 2
while(j * i <= n):
sum += i
j += 1
print(4 * sum)
``` | output | 1 | 62,295 | 5 | 124,591 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x.
After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore.
Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve?
Input
A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above.
Output
Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0.
Examples
Input
4
Output
8
Input
6
Output
28
Input
2
Output
0
Note
In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2.
In the third example, it is impossible to perform even a single transformation. | instruction | 0 | 62,296 | 5 | 124,592 |
Tags: dfs and similar, graphs, implementation, math
Correct Solution:
```
n=int(input())
ans=0
for i in range(2,n+1):
j=2
lead=2*i
while(lead<=n):
ans+=4*j
j+=1
lead+=i
print(ans)
``` | output | 1 | 62,296 | 5 | 124,593 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x.
After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore.
Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve?
Input
A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above.
Output
Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0.
Examples
Input
4
Output
8
Input
6
Output
28
Input
2
Output
0
Note
In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2.
In the third example, it is impossible to perform even a single transformation. | instruction | 0 | 62,297 | 5 | 124,594 |
Tags: dfs and similar, graphs, implementation, math
Correct Solution:
```
import sys
input=sys.stdin.readline
n=int(input())
ans=0
for i in range(2,n+1):
for j in range(i+i,n+1,i):
ans+=j//i
print(4*ans)
``` | output | 1 | 62,297 | 5 | 124,595 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x.
After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore.
Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve?
Input
A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above.
Output
Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0.
Examples
Input
4
Output
8
Input
6
Output
28
Input
2
Output
0
Note
In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2.
In the third example, it is impossible to perform even a single transformation. | instruction | 0 | 62,298 | 5 | 124,596 |
Tags: dfs and similar, graphs, implementation, math
Correct Solution:
```
n = int(input())
print(sum([(n//i -1)*i*4 for i in range(2,n+1)]))
``` | output | 1 | 62,298 | 5 | 124,597 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a positive integer n greater or equal to 2. For every pair of integers a and b (2 ≤ |a|, |b| ≤ n), you can transform a into b if and only if there exists an integer x such that 1 < |x| and (a ⋅ x = b or b ⋅ x = a), where |x| denotes the absolute value of x.
After such a transformation, your score increases by |x| points and you are not allowed to transform a into b nor b into a anymore.
Initially, you have a score of 0. You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve?
Input
A single line contains a single integer n (2 ≤ n ≤ 100 000) — the given integer described above.
Output
Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print 0.
Examples
Input
4
Output
8
Input
6
Output
28
Input
2
Output
0
Note
In the first example, the transformations are 2 → 4 → (-2) → (-4) → 2.
In the third example, it is impossible to perform even a single transformation. | instruction | 0 | 62,299 | 5 | 124,598 |
Tags: dfs and similar, graphs, implementation, math
Correct Solution:
```
n = int(input())
ans = 0
for i in range(2,n//2+1):
x = n // i
ans += ( x * (x+1) // 2 - 1 ) * 4
print(ans)
``` | output | 1 | 62,299 | 5 | 124,599 |
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