message stringlengths 2 65.1k | message_type stringclasses 2
values | message_id int64 0 1 | conversation_id int64 0 108k | cluster float64 14 14 | __index_level_0__ int64 0 217k |
|---|---|---|---|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
The Berland University is preparing to celebrate the 256-th anniversary of its founding! A specially appointed Vice Rector for the celebration prepares to decorate the campus. In the center of the campus n ice sculptures were erected. The sculptures are arranged in a circle at equal distances from each other, so they form a regular n-gon. They are numbered in clockwise order with numbers from 1 to n.
The site of the University has already conducted a voting that estimated each sculpture's characteristic of ti — the degree of the sculpture's attractiveness. The values of ti can be positive, negative or zero.
When the university rector came to evaluate the work, he said that this might be not the perfect arrangement. He suggested to melt some of the sculptures so that:
* the remaining sculptures form a regular polygon (the number of vertices should be between 3 and n),
* the sum of the ti values of the remaining sculptures is maximized.
Help the Vice Rector to analyze the criticism — find the maximum value of ti sum which can be obtained in this way. It is allowed not to melt any sculptures at all. The sculptures can not be moved.
Input
The first input line contains an integer n (3 ≤ n ≤ 20000) — the initial number of sculptures. The second line contains a sequence of integers t1, t2, ..., tn, ti — the degree of the i-th sculpture's attractiveness ( - 1000 ≤ ti ≤ 1000). The numbers on the line are separated by spaces.
Output
Print the required maximum sum of the sculptures' attractiveness.
Examples
Input
8
1 2 -3 4 -5 5 2 3
Output
14
Input
6
1 -2 3 -4 5 -6
Output
9
Input
6
1 2 3 4 5 6
Output
21
Note
In the first sample it is best to leave every second sculpture, that is, leave sculptures with attractivenesses: 2, 4, 5 и 3. | instruction | 0 | 44,076 | 14 | 88,152 |
Tags: *special, brute force, number theory
Correct Solution:
```
# https://codeforces.com/problemset/problem/158/D?locale=ru
n = int(input())
t = list(map(int, input().split()))
def divs(n):
d=1
while d*d<n:
if n%d == 0:
yield d
yield n//d
d+=1
if n%d == 0:
yield d
print(max(sum(t[r::d]) for d in divs(n) if d<=n//3 for r in range(d)))
``` | output | 1 | 44,076 | 14 | 88,153 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Berland University is preparing to celebrate the 256-th anniversary of its founding! A specially appointed Vice Rector for the celebration prepares to decorate the campus. In the center of the campus n ice sculptures were erected. The sculptures are arranged in a circle at equal distances from each other, so they form a regular n-gon. They are numbered in clockwise order with numbers from 1 to n.
The site of the University has already conducted a voting that estimated each sculpture's characteristic of ti — the degree of the sculpture's attractiveness. The values of ti can be positive, negative or zero.
When the university rector came to evaluate the work, he said that this might be not the perfect arrangement. He suggested to melt some of the sculptures so that:
* the remaining sculptures form a regular polygon (the number of vertices should be between 3 and n),
* the sum of the ti values of the remaining sculptures is maximized.
Help the Vice Rector to analyze the criticism — find the maximum value of ti sum which can be obtained in this way. It is allowed not to melt any sculptures at all. The sculptures can not be moved.
Input
The first input line contains an integer n (3 ≤ n ≤ 20000) — the initial number of sculptures. The second line contains a sequence of integers t1, t2, ..., tn, ti — the degree of the i-th sculpture's attractiveness ( - 1000 ≤ ti ≤ 1000). The numbers on the line are separated by spaces.
Output
Print the required maximum sum of the sculptures' attractiveness.
Examples
Input
8
1 2 -3 4 -5 5 2 3
Output
14
Input
6
1 -2 3 -4 5 -6
Output
9
Input
6
1 2 3 4 5 6
Output
21
Note
In the first sample it is best to leave every second sculpture, that is, leave sculptures with attractivenesses: 2, 4, 5 и 3. | instruction | 0 | 44,077 | 14 | 88,154 |
Tags: *special, brute force, number theory
Correct Solution:
```
import math as m
def su(s,n):
max = -1000*20000
for i in range(len(s)//n):
sum = 0
for j in range(i,len(s),len(s) // n,):
sum += s[j]
if max < sum:
max = sum
return max
def main():
n = int(input())
s = list(map(int, input().split()))
MIN = sum(s)
i = 2
while i <= m.sqrt(n):
if n % i == 0:
if n // i != 2:
MIN = max(MIN, su(s, n // i))
if i != 2:
MIN = max(MIN, su(s, i))
i += 1
print(MIN)
if __name__ == '__main__':
main()
``` | output | 1 | 44,077 | 14 | 88,155 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Berland University is preparing to celebrate the 256-th anniversary of its founding! A specially appointed Vice Rector for the celebration prepares to decorate the campus. In the center of the campus n ice sculptures were erected. The sculptures are arranged in a circle at equal distances from each other, so they form a regular n-gon. They are numbered in clockwise order with numbers from 1 to n.
The site of the University has already conducted a voting that estimated each sculpture's characteristic of ti — the degree of the sculpture's attractiveness. The values of ti can be positive, negative or zero.
When the university rector came to evaluate the work, he said that this might be not the perfect arrangement. He suggested to melt some of the sculptures so that:
* the remaining sculptures form a regular polygon (the number of vertices should be between 3 and n),
* the sum of the ti values of the remaining sculptures is maximized.
Help the Vice Rector to analyze the criticism — find the maximum value of ti sum which can be obtained in this way. It is allowed not to melt any sculptures at all. The sculptures can not be moved.
Input
The first input line contains an integer n (3 ≤ n ≤ 20000) — the initial number of sculptures. The second line contains a sequence of integers t1, t2, ..., tn, ti — the degree of the i-th sculpture's attractiveness ( - 1000 ≤ ti ≤ 1000). The numbers on the line are separated by spaces.
Output
Print the required maximum sum of the sculptures' attractiveness.
Examples
Input
8
1 2 -3 4 -5 5 2 3
Output
14
Input
6
1 -2 3 -4 5 -6
Output
9
Input
6
1 2 3 4 5 6
Output
21
Note
In the first sample it is best to leave every second sculpture, that is, leave sculptures with attractivenesses: 2, 4, 5 и 3. | instruction | 0 | 44,078 | 14 | 88,156 |
Tags: *special, brute force, number theory
Correct Solution:
```
# _
#####################################################################################################################
from math import sqrt, ceil
def factorsOf(n):
yield 1
squareRoot_n = sqrt(n)
limit = ceil(squareRoot_n)
if n%2:
step = 2
else:
yield 2
step = 1
for value in range(3, limit, step):
if not n%value:
yield value
yield n//value
if squareRoot_n == limit:
yield limit
def maxAttractiveness(nSculptures, sculptures_attractiveness):
if nSculptures < 6:
return sum(sculptures_attractiveness)
return max(max(sum(sculptures_attractiveness[iFirst: nSculptures: i])
for iFirst in range(i))
for i in factorsOf(nSculptures))
print(maxAttractiveness(int(input()), list(map(int, input().split()))))
``` | output | 1 | 44,078 | 14 | 88,157 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Berland University is preparing to celebrate the 256-th anniversary of its founding! A specially appointed Vice Rector for the celebration prepares to decorate the campus. In the center of the campus n ice sculptures were erected. The sculptures are arranged in a circle at equal distances from each other, so they form a regular n-gon. They are numbered in clockwise order with numbers from 1 to n.
The site of the University has already conducted a voting that estimated each sculpture's characteristic of ti — the degree of the sculpture's attractiveness. The values of ti can be positive, negative or zero.
When the university rector came to evaluate the work, he said that this might be not the perfect arrangement. He suggested to melt some of the sculptures so that:
* the remaining sculptures form a regular polygon (the number of vertices should be between 3 and n),
* the sum of the ti values of the remaining sculptures is maximized.
Help the Vice Rector to analyze the criticism — find the maximum value of ti sum which can be obtained in this way. It is allowed not to melt any sculptures at all. The sculptures can not be moved.
Input
The first input line contains an integer n (3 ≤ n ≤ 20000) — the initial number of sculptures. The second line contains a sequence of integers t1, t2, ..., tn, ti — the degree of the i-th sculpture's attractiveness ( - 1000 ≤ ti ≤ 1000). The numbers on the line are separated by spaces.
Output
Print the required maximum sum of the sculptures' attractiveness.
Examples
Input
8
1 2 -3 4 -5 5 2 3
Output
14
Input
6
1 -2 3 -4 5 -6
Output
9
Input
6
1 2 3 4 5 6
Output
21
Note
In the first sample it is best to leave every second sculpture, that is, leave sculptures with attractivenesses: 2, 4, 5 и 3. | instruction | 0 | 44,079 | 14 | 88,158 |
Tags: *special, brute force, number theory
Correct Solution:
```
import math as m
def sum(s,n):
max = -1000*20000
for i in range(len(s)//n):
sum = 0
for j in range(i,len(s),len(s) // n,):
sum += s[j]
if max < sum:
max = sum
return max
def main():
n = int(input())
s = list(map(int, input().split()))
MIN = sum(s,n)
i = 2
while i <= m.sqrt(n):
if n % i == 0:
if n // i != 2:
k = sum(s, n // i)
if MIN < k:
MIN = k
if i != 2:
k = sum(s, i)
if MIN < k:
MIN = k
i += 1
print(MIN)
if __name__ == '__main__':
main()
``` | output | 1 | 44,079 | 14 | 88,159 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Berland University is preparing to celebrate the 256-th anniversary of its founding! A specially appointed Vice Rector for the celebration prepares to decorate the campus. In the center of the campus n ice sculptures were erected. The sculptures are arranged in a circle at equal distances from each other, so they form a regular n-gon. They are numbered in clockwise order with numbers from 1 to n.
The site of the University has already conducted a voting that estimated each sculpture's characteristic of ti — the degree of the sculpture's attractiveness. The values of ti can be positive, negative or zero.
When the university rector came to evaluate the work, he said that this might be not the perfect arrangement. He suggested to melt some of the sculptures so that:
* the remaining sculptures form a regular polygon (the number of vertices should be between 3 and n),
* the sum of the ti values of the remaining sculptures is maximized.
Help the Vice Rector to analyze the criticism — find the maximum value of ti sum which can be obtained in this way. It is allowed not to melt any sculptures at all. The sculptures can not be moved.
Input
The first input line contains an integer n (3 ≤ n ≤ 20000) — the initial number of sculptures. The second line contains a sequence of integers t1, t2, ..., tn, ti — the degree of the i-th sculpture's attractiveness ( - 1000 ≤ ti ≤ 1000). The numbers on the line are separated by spaces.
Output
Print the required maximum sum of the sculptures' attractiveness.
Examples
Input
8
1 2 -3 4 -5 5 2 3
Output
14
Input
6
1 -2 3 -4 5 -6
Output
9
Input
6
1 2 3 4 5 6
Output
21
Note
In the first sample it is best to leave every second sculpture, that is, leave sculptures with attractivenesses: 2, 4, 5 и 3. | instruction | 0 | 44,080 | 14 | 88,160 |
Tags: *special, brute force, number theory
Correct Solution:
```
n = int(input())
l = list(map(int,input().split()))
ans = sum(l)
x=[]
for i in range(3,n):
if n%i==0:
x.append(i)
for i in x:
for j in range(n//i):
ans = max(ans,sum(l[j::n//i]))
print(ans)
``` | output | 1 | 44,080 | 14 | 88,161 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Berland University is preparing to celebrate the 256-th anniversary of its founding! A specially appointed Vice Rector for the celebration prepares to decorate the campus. In the center of the campus n ice sculptures were erected. The sculptures are arranged in a circle at equal distances from each other, so they form a regular n-gon. They are numbered in clockwise order with numbers from 1 to n.
The site of the University has already conducted a voting that estimated each sculpture's characteristic of ti — the degree of the sculpture's attractiveness. The values of ti can be positive, negative or zero.
When the university rector came to evaluate the work, he said that this might be not the perfect arrangement. He suggested to melt some of the sculptures so that:
* the remaining sculptures form a regular polygon (the number of vertices should be between 3 and n),
* the sum of the ti values of the remaining sculptures is maximized.
Help the Vice Rector to analyze the criticism — find the maximum value of ti sum which can be obtained in this way. It is allowed not to melt any sculptures at all. The sculptures can not be moved.
Input
The first input line contains an integer n (3 ≤ n ≤ 20000) — the initial number of sculptures. The second line contains a sequence of integers t1, t2, ..., tn, ti — the degree of the i-th sculpture's attractiveness ( - 1000 ≤ ti ≤ 1000). The numbers on the line are separated by spaces.
Output
Print the required maximum sum of the sculptures' attractiveness.
Examples
Input
8
1 2 -3 4 -5 5 2 3
Output
14
Input
6
1 -2 3 -4 5 -6
Output
9
Input
6
1 2 3 4 5 6
Output
21
Note
In the first sample it is best to leave every second sculpture, that is, leave sculptures with attractivenesses: 2, 4, 5 и 3. | instruction | 0 | 44,081 | 14 | 88,162 |
Tags: *special, brute force, number theory
Correct Solution:
```
def primes(n):
p = []
for i in range(2, n):
if n % i == 0:
p.append(i)
return p
def spec_sum(s, d):
c = 0
q = 0
for i in range(0, len(s), d):
c += s[i]
for j in range(1, d):
for i in range(j, len(s), d):
q += s[i]
if q > c:
c = q
q = 0
return c
n = int(input())
s = list(map(int, input().split(' ')))
max = spec_sum(s, 1)
for div in primes(n):
if n // div < 3:
continue
q = spec_sum(s, div)
if q > max:
max = q
print(max)
``` | output | 1 | 44,081 | 14 | 88,163 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Berland University is preparing to celebrate the 256-th anniversary of its founding! A specially appointed Vice Rector for the celebration prepares to decorate the campus. In the center of the campus n ice sculptures were erected. The sculptures are arranged in a circle at equal distances from each other, so they form a regular n-gon. They are numbered in clockwise order with numbers from 1 to n.
The site of the University has already conducted a voting that estimated each sculpture's characteristic of ti — the degree of the sculpture's attractiveness. The values of ti can be positive, negative or zero.
When the university rector came to evaluate the work, he said that this might be not the perfect arrangement. He suggested to melt some of the sculptures so that:
* the remaining sculptures form a regular polygon (the number of vertices should be between 3 and n),
* the sum of the ti values of the remaining sculptures is maximized.
Help the Vice Rector to analyze the criticism — find the maximum value of ti sum which can be obtained in this way. It is allowed not to melt any sculptures at all. The sculptures can not be moved.
Input
The first input line contains an integer n (3 ≤ n ≤ 20000) — the initial number of sculptures. The second line contains a sequence of integers t1, t2, ..., tn, ti — the degree of the i-th sculpture's attractiveness ( - 1000 ≤ ti ≤ 1000). The numbers on the line are separated by spaces.
Output
Print the required maximum sum of the sculptures' attractiveness.
Examples
Input
8
1 2 -3 4 -5 5 2 3
Output
14
Input
6
1 -2 3 -4 5 -6
Output
9
Input
6
1 2 3 4 5 6
Output
21
Note
In the first sample it is best to leave every second sculpture, that is, leave sculptures with attractivenesses: 2, 4, 5 и 3. | instruction | 0 | 44,082 | 14 | 88,164 |
Tags: *special, brute force, number theory
Correct Solution:
```
# _
#####################################################################################################################
from math import sqrt, ceil
def factorsOf(n):
yield 1
factorsStorage, squareRoot_n = [], sqrt(n)
limit = ceil(squareRoot_n)
if n%2:
step = 2
else:
yield 2
step = 1
for value in range(3, limit, step):
if not n%value:
yield value
yield n//value
if squareRoot_n == limit:
yield limit
def maxAttractiveness(nSculptures, sculptures_attractiveness):
if nSculptures < 6:
return sum(sculptures_attractiveness)
return max(max(sum(sculptures_attractiveness[x]
for x in range(iFirst, nSculptures, i))
for iFirst in range(i))
for i in factorsOf(nSculptures))
print(maxAttractiveness(int(input()), list(map(int, input().split()))))
``` | output | 1 | 44,082 | 14 | 88,165 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The Berland University is preparing to celebrate the 256-th anniversary of its founding! A specially appointed Vice Rector for the celebration prepares to decorate the campus. In the center of the campus n ice sculptures were erected. The sculptures are arranged in a circle at equal distances from each other, so they form a regular n-gon. They are numbered in clockwise order with numbers from 1 to n.
The site of the University has already conducted a voting that estimated each sculpture's characteristic of ti — the degree of the sculpture's attractiveness. The values of ti can be positive, negative or zero.
When the university rector came to evaluate the work, he said that this might be not the perfect arrangement. He suggested to melt some of the sculptures so that:
* the remaining sculptures form a regular polygon (the number of vertices should be between 3 and n),
* the sum of the ti values of the remaining sculptures is maximized.
Help the Vice Rector to analyze the criticism — find the maximum value of ti sum which can be obtained in this way. It is allowed not to melt any sculptures at all. The sculptures can not be moved.
Input
The first input line contains an integer n (3 ≤ n ≤ 20000) — the initial number of sculptures. The second line contains a sequence of integers t1, t2, ..., tn, ti — the degree of the i-th sculpture's attractiveness ( - 1000 ≤ ti ≤ 1000). The numbers on the line are separated by spaces.
Output
Print the required maximum sum of the sculptures' attractiveness.
Examples
Input
8
1 2 -3 4 -5 5 2 3
Output
14
Input
6
1 -2 3 -4 5 -6
Output
9
Input
6
1 2 3 4 5 6
Output
21
Note
In the first sample it is best to leave every second sculpture, that is, leave sculptures with attractivenesses: 2, 4, 5 и 3. | instruction | 0 | 44,083 | 14 | 88,166 |
Tags: *special, brute force, number theory
Correct Solution:
```
import math
n = int(input())
a = [int(x) for x in input().split()]
#print(a)
maxNum = -10000000001
for i in range(1, math.ceil(math.sqrt(n))+1):
if n % i == 0:
t = n // i
if t > 2:
for j in range(i):
k = 0
num = 0
#b = []
while k < n:
num += a[k+j]
#b.append(a[k+j])
k += i
#print(i, b)
#print(num)
maxNum = max(maxNum, num)
if i > 2:
for j in range(t):
k = 0
num = 0
#b = []
while k < n:
num += a[k+j]
#b.append(a[k+j])
k += t
maxNum = max(maxNum, num)
#print(t, b)
#print(num)
print(maxNum)
``` | output | 1 | 44,083 | 14 | 88,167 |
Provide tags and a correct Python 3 solution for this coding contest problem.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish. | instruction | 0 | 44,130 | 14 | 88,260 |
Tags: constructive algorithms, greedy
Correct Solution:
```
n,m,k=map(int,input().split())
Alice=list(map(int,input().split()))
Bob=list(map(int,input().split()))
SA={}
SB={}
for item in Alice:
if(item in SA):
SA[item]+=1
continue
SA[item]=1
SB[item]=0
for item in Bob:
if(item in SB):
SB[item]+=1
continue
SB[item]=1
SA[item]=0
x=sorted(list(set(Alice+Bob)),reverse=True)
n=len(x)
done=False
i=0
needed=0
while(i<n):
if(SA[x[i]]-SB[x[i]]>needed):
print("YES")
done=True
break
needed+=SB[x[i]]-SA[x[i]]
i+=1
if(not done):
print("NO")
``` | output | 1 | 44,130 | 14 | 88,261 |
Provide tags and a correct Python 3 solution for this coding contest problem.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish. | instruction | 0 | 44,131 | 14 | 88,262 |
Tags: constructive algorithms, greedy
Correct Solution:
```
from sys import stdin,stdout
nmbr = lambda: int(stdin.readline())
lst = lambda: list(map(int,stdin.readline().split()))
for _ in range(1):#nmbr()):
n,m,k=lst()
f=0
a=sorted(lst(),reverse=1)
b=sorted(lst(),reverse=1)
p=p1=0
while p<n and p1<m:
if a[p]>b[p1]:
f=1
break
p+=1
p1+=1
if p<n and p1>=m:
f=1
print('YES' if f else 'NO')
``` | output | 1 | 44,131 | 14 | 88,263 |
Provide tags and a correct Python 3 solution for this coding contest problem.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish. | instruction | 0 | 44,132 | 14 | 88,264 |
Tags: constructive algorithms, greedy
Correct Solution:
```
n,m,k=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
a.sort(key=lambda x:-x)
b.sort(key=lambda x: -x)
t=False
n1=min(m,n)
if n>m:
t=True
else:
for i in range (n1):
if a[i]>b[i]:
t=True
if t:
print('YES')
else:
print('NO')
# Made By Mostafa_Khaled
``` | output | 1 | 44,132 | 14 | 88,265 |
Provide tags and a correct Python 3 solution for this coding contest problem.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish. | instruction | 0 | 44,133 | 14 | 88,266 |
Tags: constructive algorithms, greedy
Correct Solution:
```
rd = lambda: list(map(int, input().split()))
rd()
a = sorted(rd(), reverse=True)
b = sorted(rd(), reverse=True)
if len(a) > len(b): print("YES"); exit()
for i in range(len(a)):
if a[i] > b[i]: print("YES"); exit()
print("NO")
``` | output | 1 | 44,133 | 14 | 88,267 |
Provide tags and a correct Python 3 solution for this coding contest problem.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish. | instruction | 0 | 44,134 | 14 | 88,268 |
Tags: constructive algorithms, greedy
Correct Solution:
```
n,m,k=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
a.sort(key=lambda x:-x)
b.sort(key=lambda x: -x)
t=False
n1=min(m,n)
if n>m:
t=True
else:
for i in range (n1):
if a[i]>b[i]:
t=True
if t:
print('YES')
else:
print('NO')
``` | output | 1 | 44,134 | 14 | 88,269 |
Provide tags and a correct Python 3 solution for this coding contest problem.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish. | instruction | 0 | 44,135 | 14 | 88,270 |
Tags: constructive algorithms, greedy
Correct Solution:
```
n,m,k=list(map(int,input().split()))
a=sorted(list(map(int,input().split())))
b=sorted(list(map(int,input().split())))
for i in range(n):
if a[-i-1]>int(b[-i-1] if i<m else 0):
print('YES')
break
else:
print('NO')
``` | output | 1 | 44,135 | 14 | 88,271 |
Provide tags and a correct Python 3 solution for this coding contest problem.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish. | instruction | 0 | 44,136 | 14 | 88,272 |
Tags: constructive algorithms, greedy
Correct Solution:
```
n,m,k = map(int,input().split())
a = sorted(map(int,input().split()),reverse=True)
b = sorted(map(int,input().split()),reverse=True)
cou=ind=0
l=min(m,n)
aa=max(b)
for i in range(l):
if a[i]>b[i]:
cou+=1
ind=max(ind,a[i])
if m>=n and cou>0:
print("YES")
elif m<n:
print("YES")
else:
print("NO")
``` | output | 1 | 44,136 | 14 | 88,273 |
Provide tags and a correct Python 3 solution for this coding contest problem.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish. | instruction | 0 | 44,137 | 14 | 88,274 |
Tags: constructive algorithms, greedy
Correct Solution:
```
import copy
import itertools
import string
import sys
###
def powmod(x, p, m):
if p <= 0:
return 1
if p <= 1:
return x%m
return powmod(x*x%m, p//2, m) * (x%m)**(p%2) % m
###
def to_basex(num, x):
while num > 0:
yield num % x
num //= x
def from_basex(it, x):
ret = 0
p = 1
for d in it:
ret += d*p
p *= x
return ret
###
def core():
_ = input()
a = [int(x) for x in input().split()]
r = [int(x) for x in input().split()]
a.sort()
r.sort()
# print(a)
# print(r)
while (
len(a) > 0 and
len(r) > 0 and
r[-1] >= a[-1]
):
a.pop()
r.pop()
ans = "YES" if len(a) > 0 else "NO"
print(ans)
core()
``` | output | 1 | 44,137 | 14 | 88,275 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish.
Submitted Solution:
```
n, m, k = [int(x) for x in input().split()]
alice = [int(x) for x in input().split()]
bob = [int(x) for x in input().split()]
alice.sort()
bob.sort()
balance = 0
i = n - 1
j = m - 1
while i >= 0 and j >= 0:
if alice[i] > bob[j]:
balance += 1
i -= 1
elif alice[i] < bob[j]:
balance -= 1
j -= 1
else:
i -= 1
j -= 1
if balance > 0:
break
if i + 1 + balance > 0:
print('YES')
else:
print('NO')
``` | instruction | 0 | 44,138 | 14 | 88,276 |
Yes | output | 1 | 44,138 | 14 | 88,277 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish.
Submitted Solution:
```
n, m, k = map(int, input().split())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
if n > m:
print('YES')
else:
a.sort()
b.sort()
b = b[-n:]
ans = 'NO'
for i in range(n):
if a[i] > b[i]:
ans = 'YES'
print(ans)
``` | instruction | 0 | 44,139 | 14 | 88,278 |
Yes | output | 1 | 44,139 | 14 | 88,279 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish.
Submitted Solution:
```
import sys
from math import gcd,sqrt,ceil
from collections import defaultdict,Counter,deque
from bisect import bisect_left,bisect_right
import math
from itertools import permutations
# input=sys.stdin.readline
# def print(x):
# sys.stdout.write(str(x)+"\n")
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# import sys
# import io, os
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def get_sum(bit,i):
s = 0
i+=1
while i>0:
s+=bit[i]
i-=i&(-i)
return s
def update(bit,n,i,v):
i+=1
while i<=n:
bit[i]+=v
i+=i&(-i)
def modInverse(b,m):
g = math.gcd(b, m)
if (g != 1):
return -1
else:
return pow(b, m - 2, m)
def primeFactors(n):
sa = set()
sa.add(n)
while n % 2 == 0:
sa.add(2)
n = n // 2
for i in range(3,int(math.sqrt(n))+1,2):
while n % i== 0:
sa.add(i)
n = n // i
# sa.add(n)
return sa
def seive(n):
pri = [True]*(n+1)
p = 2
while p*p<=n:
if pri[p] == True:
for i in range(p*p,n+1,p):
pri[i] = False
p+=1
return pri
def check_prim(n):
if n<0:
return False
for i in range(2,int(sqrt(n))+1):
if n%i == 0:
return False
return True
n,m,k = map(int,input().split())
hash1 = defaultdict(int)
hash2 = defaultdict(int)
l1 = list(map(int,input().split()))
l2 = list(map(int,input().split()))
w = defaultdict(lambda : 1)
ha = set()
for i in l1:
hash1[i]+=1
ha.add(i)
for i in l2:
hash2[i]+=1
ha.add(i)
w1,w2 = 0,0
ha = list(ha)
ha.sort()
prev = 1
for i in ha:
z1,z2 = hash1[i],hash2[i]
if hash2[i]>=hash1[i]:
w[i] = prev
else:
if w1>=w2:
w[i] = prev+1
else:
w[i] = w2-w1 + 2
w1+=hash1[i]*w[i]
w2+=hash2[i]*w[i]
prev = w[i]
if w1>w2:
print('YES')
else:
print('NO')
``` | instruction | 0 | 44,140 | 14 | 88,280 |
Yes | output | 1 | 44,140 | 14 | 88,281 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish.
Submitted Solution:
```
import sys
input=sys.stdin.readline
n,m,k=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
a.sort(reverse=True)
b.sort(reverse=True)
for i in range(n):
bb=b[i] if i<m else 0
if a[i]>bb:
print("YES")
exit()
print("NO")
``` | instruction | 0 | 44,141 | 14 | 88,282 |
Yes | output | 1 | 44,141 | 14 | 88,283 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish.
Submitted Solution:
```
n,m,k=map(int,input().split())
Alice=list(map(int,input().split()))
Bob=list(map(int,input().split()))
SA={}
SB={}
for item in Alice:
if(item in SA):
SA[item]+=1
continue
SA[item]=0
SB[item]=0
for item in Bob:
if(item in SB):
SB[item]+=1
continue
SB[item]=0
SA[item]=0
x=sorted(list(set(Alice+Bob)),reverse=True)
n=len(x)
done=False
i=0
needed=0
while(i<n):
if(SA[x[i]]-SB[x[i]]>needed):
print("YES")
done=True
break
needed+=SB[x[i]]-SA[x[i]]
i+=1
if(not done):
print("NO")
``` | instruction | 0 | 44,142 | 14 | 88,284 |
No | output | 1 | 44,142 | 14 | 88,285 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish.
Submitted Solution:
```
import sys
input=sys.stdin.readline
n,m,k=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
a.sort(reverse=True)
b.sort(reverse=True)
for i in range(n):
if i<m and a[i]>b[i]:
print("YES")
exit()
elif i>=m:
break
print("NO")
``` | instruction | 0 | 44,143 | 14 | 88,286 |
No | output | 1 | 44,143 | 14 | 88,287 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish.
Submitted Solution:
```
import sys
from math import gcd,sqrt,ceil
from collections import defaultdict,Counter,deque
from bisect import bisect_left,bisect_right
import math
from itertools import permutations
# input=sys.stdin.readline
# def print(x):
# sys.stdout.write(str(x)+"\n")
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# import sys
# import io, os
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def get_sum(bit,i):
s = 0
i+=1
while i>0:
s+=bit[i]
i-=i&(-i)
return s
def update(bit,n,i,v):
i+=1
while i<=n:
bit[i]+=v
i+=i&(-i)
def modInverse(b,m):
g = math.gcd(b, m)
if (g != 1):
return -1
else:
return pow(b, m - 2, m)
def primeFactors(n):
sa = set()
sa.add(n)
while n % 2 == 0:
sa.add(2)
n = n // 2
for i in range(3,int(math.sqrt(n))+1,2):
while n % i== 0:
sa.add(i)
n = n // i
# sa.add(n)
return sa
def seive(n):
pri = [True]*(n+1)
p = 2
while p*p<=n:
if pri[p] == True:
for i in range(p*p,n+1,p):
pri[i] = False
p+=1
return pri
def check_prim(n):
if n<0:
return False
for i in range(2,int(sqrt(n))+1):
if n%i == 0:
return False
return True
n,m,k = map(int,input().split())
hash1 = defaultdict(int)
hash2 = defaultdict(int)
l1 = list(map(int,input().split()))
l2 = list(map(int,input().split()))
w = defaultdict(lambda : 1)
ha = set()
for i in l1:
hash1[i]+=1
ha.add(i)
for i in l2:
hash2[i]+=1
ha.add(i)
w1,w2 = 0,0
ha = list(ha)
ha.sort()
for i in ha:
z1,z2 = hash1[i],hash2[i]
if hash2[i]>=hash1[i]:
w[i] = w[i-1]
else:
if w1>=w2:
w[i] = w[i-1]+1
else:
w[i] = w2-w1 + 2
w1+=hash1[i]*w[i]
w2+=hash2[i]*w[i]
if w1>w2:
print('YES')
else:
print('NO')
``` | instruction | 0 | 44,144 | 14 | 88,288 |
No | output | 1 | 44,144 | 14 | 88,289 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk holds.
Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights wi (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?
Input
The first line contains three integers n, m, k (1 ≤ n, m ≤ 105, 1 ≤ k ≤ 109) — the number of fish caught by Alice and Bob respectively, and the number of fish species.
The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.
Note that one may have caught more than one fish for a same species.
Output
Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.
Examples
Input
3 3 3
2 2 2
1 1 3
Output
YES
Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7
Output
NO
Note
In the first sample, if w1 = 1, w2 = 2, w3 = 2.5, then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.
In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish.
Submitted Solution:
```
n,m,k = map(int,input().split())
a = sorted(map(int,input().split()))
b = sorted(map(int,input().split()))
cou=ind=0
l=min(m,n)
aa=max(b)
for i in range(l):
if a[i]>b[i]:
cou+=1
ind=a[i]
if m>n and aa < ind:
print("YES")
if m==n and cou>0:
print("YES")
elif m<n:
print("YES")
else:
print("NO")
``` | instruction | 0 | 44,145 | 14 | 88,290 |
No | output | 1 | 44,145 | 14 | 88,291 |
Provide tags and a correct Python 3 solution for this coding contest problem.
One Big Software Company has n employees numbered from 1 to n. The director is assigned number 1. Every employee of the company except the director has exactly one immediate superior. The director, of course, doesn't have a superior.
We will call person a a subordinates of another person b, if either b is an immediate supervisor of a, or the immediate supervisor of a is a subordinate to person b. In particular, subordinates of the head are all other employees of the company.
To solve achieve an Important Goal we need to form a workgroup. Every person has some efficiency, expressed by a positive integer ai, where i is the person's number. The efficiency of the workgroup is defined as the total efficiency of all the people included in it.
The employees of the big software company are obsessed with modern ways of work process organization. Today pair programming is at the peak of popularity, so the workgroup should be formed with the following condition. Each person entering the workgroup should be able to sort all of his subordinates who are also in the workgroup into pairs. In other words, for each of the members of the workgroup the number of his subordinates within the workgroup should be even.
Your task is to determine the maximum possible efficiency of the workgroup formed at observing the given condition. Any person including the director of company can enter the workgroup.
Input
The first line contains integer n (1 ≤ n ≤ 2·105) — the number of workers of the Big Software Company.
Then n lines follow, describing the company employees. The i-th line contains two integers pi, ai (1 ≤ ai ≤ 105) — the number of the person who is the i-th employee's immediate superior and i-th employee's efficiency. For the director p1 = - 1, for all other people the condition 1 ≤ pi < i is fulfilled.
Output
Print a single integer — the maximum possible efficiency of the workgroup.
Examples
Input
7
-1 3
1 2
1 1
1 4
4 5
4 3
5 2
Output
17
Note
In the sample test the most effective way is to make a workgroup from employees number 1, 2, 4, 5, 6. | instruction | 0 | 44,233 | 14 | 88,466 |
Tags: dfs and similar, dp, graphs, strings, trees
Correct Solution:
```
n = int(input())
t = [list(map(int, input().split())) for q in range(n)]
n += 1
u = [-1e7] * n
v = [0] * n
for i, (j, a) in list(enumerate(t, 1))[::-1]:
u[i] = max(u[i], v[i] + a)
v[j], u[j] = max(v[j] + v[i], u[j] + u[i]), max(v[j] + u[i], u[j] + v[i])
print(u[1])
``` | output | 1 | 44,233 | 14 | 88,467 |
Provide tags and a correct Python 3 solution for this coding contest problem.
One Big Software Company has n employees numbered from 1 to n. The director is assigned number 1. Every employee of the company except the director has exactly one immediate superior. The director, of course, doesn't have a superior.
We will call person a a subordinates of another person b, if either b is an immediate supervisor of a, or the immediate supervisor of a is a subordinate to person b. In particular, subordinates of the head are all other employees of the company.
To solve achieve an Important Goal we need to form a workgroup. Every person has some efficiency, expressed by a positive integer ai, where i is the person's number. The efficiency of the workgroup is defined as the total efficiency of all the people included in it.
The employees of the big software company are obsessed with modern ways of work process organization. Today pair programming is at the peak of popularity, so the workgroup should be formed with the following condition. Each person entering the workgroup should be able to sort all of his subordinates who are also in the workgroup into pairs. In other words, for each of the members of the workgroup the number of his subordinates within the workgroup should be even.
Your task is to determine the maximum possible efficiency of the workgroup formed at observing the given condition. Any person including the director of company can enter the workgroup.
Input
The first line contains integer n (1 ≤ n ≤ 2·105) — the number of workers of the Big Software Company.
Then n lines follow, describing the company employees. The i-th line contains two integers pi, ai (1 ≤ ai ≤ 105) — the number of the person who is the i-th employee's immediate superior and i-th employee's efficiency. For the director p1 = - 1, for all other people the condition 1 ≤ pi < i is fulfilled.
Output
Print a single integer — the maximum possible efficiency of the workgroup.
Examples
Input
7
-1 3
1 2
1 1
1 4
4 5
4 3
5 2
Output
17
Note
In the sample test the most effective way is to make a workgroup from employees number 1, 2, 4, 5, 6. | instruction | 0 | 44,234 | 14 | 88,468 |
Tags: dfs and similar, dp, graphs, strings, trees
Correct Solution:
```
n = int(input())
t = [list(map(int, input().split())) for q in range(n)]
t[0][0] = 0
n += 1
u = [-1e7] * n
v = [0] * n
for i, (j, a) in list(enumerate(t, 1))[::-1]:
u[i] = max(u[i], v[i] + a)
v[j], u[j] = max(v[j] + v[i], u[j] + u[i]), max(v[j] + u[i], u[j] + v[i])
print(u[1])
``` | output | 1 | 44,234 | 14 | 88,469 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One Big Software Company has n employees numbered from 1 to n. The director is assigned number 1. Every employee of the company except the director has exactly one immediate superior. The director, of course, doesn't have a superior.
We will call person a a subordinates of another person b, if either b is an immediate supervisor of a, or the immediate supervisor of a is a subordinate to person b. In particular, subordinates of the head are all other employees of the company.
To solve achieve an Important Goal we need to form a workgroup. Every person has some efficiency, expressed by a positive integer ai, where i is the person's number. The efficiency of the workgroup is defined as the total efficiency of all the people included in it.
The employees of the big software company are obsessed with modern ways of work process organization. Today pair programming is at the peak of popularity, so the workgroup should be formed with the following condition. Each person entering the workgroup should be able to sort all of his subordinates who are also in the workgroup into pairs. In other words, for each of the members of the workgroup the number of his subordinates within the workgroup should be even.
Your task is to determine the maximum possible efficiency of the workgroup formed at observing the given condition. Any person including the director of company can enter the workgroup.
Input
The first line contains integer n (1 ≤ n ≤ 2·105) — the number of workers of the Big Software Company.
Then n lines follow, describing the company employees. The i-th line contains two integers pi, ai (1 ≤ ai ≤ 105) — the number of the person who is the i-th employee's immediate superior and i-th employee's efficiency. For the director p1 = - 1, for all other people the condition 1 ≤ pi < i is fulfilled.
Output
Print a single integer — the maximum possible efficiency of the workgroup.
Examples
Input
7
-1 3
1 2
1 1
1 4
4 5
4 3
5 2
Output
17
Note
In the sample test the most effective way is to make a workgroup from employees number 1, 2, 4, 5, 6.
Submitted Solution:
```
import math
n = int(input())
superior = []
costs=[]
cost_total=0
for i in range(n):
a, b = map(int, input().split())
superior.append(a)
costs.append(b)
hijos = [[] for _ in range(n+1)]
for i in range(n):
if superior[i]==-1:
cost_total+=costs[i]
else:
hijos[superior[i]].append(i+1)
for i in range (n):
menor = math.inf
if len(hijos[i]) > 1 :
if len(hijos[i]) % 2 == 0:
for j in hijos[i]:
cost_total+=costs[j-1]
else :
for j in hijos[i]:
if costs[j-1] < menor:
menor = j
for j in hijos[i]:
if j != menor:
cost_total+=costs[j-1]
print(cost_total)
``` | instruction | 0 | 44,235 | 14 | 88,470 |
No | output | 1 | 44,235 | 14 | 88,471 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One Big Software Company has n employees numbered from 1 to n. The director is assigned number 1. Every employee of the company except the director has exactly one immediate superior. The director, of course, doesn't have a superior.
We will call person a a subordinates of another person b, if either b is an immediate supervisor of a, or the immediate supervisor of a is a subordinate to person b. In particular, subordinates of the head are all other employees of the company.
To solve achieve an Important Goal we need to form a workgroup. Every person has some efficiency, expressed by a positive integer ai, where i is the person's number. The efficiency of the workgroup is defined as the total efficiency of all the people included in it.
The employees of the big software company are obsessed with modern ways of work process organization. Today pair programming is at the peak of popularity, so the workgroup should be formed with the following condition. Each person entering the workgroup should be able to sort all of his subordinates who are also in the workgroup into pairs. In other words, for each of the members of the workgroup the number of his subordinates within the workgroup should be even.
Your task is to determine the maximum possible efficiency of the workgroup formed at observing the given condition. Any person including the director of company can enter the workgroup.
Input
The first line contains integer n (1 ≤ n ≤ 2·105) — the number of workers of the Big Software Company.
Then n lines follow, describing the company employees. The i-th line contains two integers pi, ai (1 ≤ ai ≤ 105) — the number of the person who is the i-th employee's immediate superior and i-th employee's efficiency. For the director p1 = - 1, for all other people the condition 1 ≤ pi < i is fulfilled.
Output
Print a single integer — the maximum possible efficiency of the workgroup.
Examples
Input
7
-1 3
1 2
1 1
1 4
4 5
4 3
5 2
Output
17
Note
In the sample test the most effective way is to make a workgroup from employees number 1, 2, 4, 5, 6.
Submitted Solution:
```
n = int(input())
t = [list(map(int, input().split())) for q in range(n)]
t[0][0] = 0
n += 1
u = [0] * n
v = [0] * n
for i, (j, a) in list(enumerate([(0, 0)] + t))[::-1]:
u[i] = max(u[i], v[i] + a)
v[j], u[j] = max(v[j] + v[i], u[j] + u[i]), max(v[j] + u[i], u[j] + v[i])
print(v[1])
``` | instruction | 0 | 44,236 | 14 | 88,472 |
No | output | 1 | 44,236 | 14 | 88,473 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One Big Software Company has n employees numbered from 1 to n. The director is assigned number 1. Every employee of the company except the director has exactly one immediate superior. The director, of course, doesn't have a superior.
We will call person a a subordinates of another person b, if either b is an immediate supervisor of a, or the immediate supervisor of a is a subordinate to person b. In particular, subordinates of the head are all other employees of the company.
To solve achieve an Important Goal we need to form a workgroup. Every person has some efficiency, expressed by a positive integer ai, where i is the person's number. The efficiency of the workgroup is defined as the total efficiency of all the people included in it.
The employees of the big software company are obsessed with modern ways of work process organization. Today pair programming is at the peak of popularity, so the workgroup should be formed with the following condition. Each person entering the workgroup should be able to sort all of his subordinates who are also in the workgroup into pairs. In other words, for each of the members of the workgroup the number of his subordinates within the workgroup should be even.
Your task is to determine the maximum possible efficiency of the workgroup formed at observing the given condition. Any person including the director of company can enter the workgroup.
Input
The first line contains integer n (1 ≤ n ≤ 2·105) — the number of workers of the Big Software Company.
Then n lines follow, describing the company employees. The i-th line contains two integers pi, ai (1 ≤ ai ≤ 105) — the number of the person who is the i-th employee's immediate superior and i-th employee's efficiency. For the director p1 = - 1, for all other people the condition 1 ≤ pi < i is fulfilled.
Output
Print a single integer — the maximum possible efficiency of the workgroup.
Examples
Input
7
-1 3
1 2
1 1
1 4
4 5
4 3
5 2
Output
17
Note
In the sample test the most effective way is to make a workgroup from employees number 1, 2, 4, 5, 6.
Submitted Solution:
```
"""import sys
try:
FILE = open(str(sys.argv[1]), "r")
except IOError:
print("IOError")
sys.exit(0)
except IndexError:
print("IndexError")
sys.exit(0)
NUM = int(FILE.readline())
"""
NUM = int(input())
class Emp:
"""employee class"""
def __init__(self, employee_num, efficiency):
self.empnum = int(1 if employee_num == -1 else employee_num + 1)
self.eff = int(efficiency)
def print_items(self):
print(self.empnum, self.eff)
def as_list(self):
return [self.empnum, self.eff]
# Input
employees = list()
# change "input()" to "FILE.readline()"
for i in range(NUM):
inp = [int(i) for i in input().split()]
employees.append(Emp(inp[0], inp[1]))
"""
the number of his subordinates within the workgroup should be even.
"""
#print("Output:\n")
graded = list() # 員工分級層列表
# Organizing
for i in range(1, NUM):
graded.append([j for j in employees if j.empnum == i])
"""
print("graded:")
for i in graded:
print([j.as_list() for j in i])
"""
#print("\nlevel pruning")
for i in graded:
try:
#print(i[0].print_items())
if i[0].empnum == 1:
#print("-> manager")
continue
except:
#print("level is empty")
continue
if len(i) % 2 == 1:
#print("--> start pruning")
i.sort(key = lambda ahaha: ahaha.eff, reverse = True)
i.pop()
"""
print("graded:")
for i in graded:
print([j.as_list() for j in i])
"""
sum = 0
for i in graded:
for j in i:
sum+=j.eff
print(sum)
``` | instruction | 0 | 44,237 | 14 | 88,474 |
No | output | 1 | 44,237 | 14 | 88,475 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
One Big Software Company has n employees numbered from 1 to n. The director is assigned number 1. Every employee of the company except the director has exactly one immediate superior. The director, of course, doesn't have a superior.
We will call person a a subordinates of another person b, if either b is an immediate supervisor of a, or the immediate supervisor of a is a subordinate to person b. In particular, subordinates of the head are all other employees of the company.
To solve achieve an Important Goal we need to form a workgroup. Every person has some efficiency, expressed by a positive integer ai, where i is the person's number. The efficiency of the workgroup is defined as the total efficiency of all the people included in it.
The employees of the big software company are obsessed with modern ways of work process organization. Today pair programming is at the peak of popularity, so the workgroup should be formed with the following condition. Each person entering the workgroup should be able to sort all of his subordinates who are also in the workgroup into pairs. In other words, for each of the members of the workgroup the number of his subordinates within the workgroup should be even.
Your task is to determine the maximum possible efficiency of the workgroup formed at observing the given condition. Any person including the director of company can enter the workgroup.
Input
The first line contains integer n (1 ≤ n ≤ 2·105) — the number of workers of the Big Software Company.
Then n lines follow, describing the company employees. The i-th line contains two integers pi, ai (1 ≤ ai ≤ 105) — the number of the person who is the i-th employee's immediate superior and i-th employee's efficiency. For the director p1 = - 1, for all other people the condition 1 ≤ pi < i is fulfilled.
Output
Print a single integer — the maximum possible efficiency of the workgroup.
Examples
Input
7
-1 3
1 2
1 1
1 4
4 5
4 3
5 2
Output
17
Note
In the sample test the most effective way is to make a workgroup from employees number 1, 2, 4, 5, 6.
Submitted Solution:
```
from operator import itemgetter
def match_subs(tree):
for i, v in enumerate(tree):
if v[0] > 0:
tree[v[0] - 1][2].append(i + 1)
tree[v[0] - 1][3] += 1
def explore_tree(tree):
to_visit = [(tree[0][4], 0)]
while to_visit:
visiting = to_visit.pop(0)
level = visiting[1]
visiting = tree[visiting[0]]
to_visit += [(x - 1, level + 1) for x in tree[visiting[4]][2]]
tree[visiting[4]][5] = level
#print(visiting[4])
#print(to_visit)
class CodeforcesTask533BSolution:
def __init__(self):
self.result = ''
self.workers_count = 0
self.workers = []
def read_input(self):
self.workers_count = int(input())
for x in range(self.workers_count):
self.workers.append([int(x) for x in input().split(" ")] + [[], 0, x, 0, [], 0])
def process_task(self):
match_subs(self.workers)
#print(self.workers)
explore_tree(self.workers)
tree2 = self.workers.copy()
tree2.sort(key=itemgetter(5), reverse=True)
for v in tree2:
if v[6]:
if len(v[6]) % 2:
v[6].sort(reverse=True)
v[7] = sum(v[6][:-1])
else:
v[7] = sum(v[6])
if v[0] > 0:
self.workers[v[0] - 1][6].append(v[7] + v[1])
self.result = str(self.workers[0][7] + self.workers[0][1])
def get_result(self):
return self.result
if __name__ == "__main__":
Solution = CodeforcesTask533BSolution()
Solution.read_input()
Solution.process_task()
print(Solution.get_result())
``` | instruction | 0 | 44,238 | 14 | 88,476 |
No | output | 1 | 44,238 | 14 | 88,477 |
Provide a correct Python 3 solution for this coding contest problem.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25. | instruction | 0 | 44,385 | 14 | 88,770 |
"Correct Solution:
```
def min(a, b):
if a >= b:
return b
else:
return a
b = 0
n = int(input())
a = input().split()
for i in range(len(a)):
a[i] = int(a[i])
for i in range(n):
if a[i] % 2 == 0:
b += 1
c = n - b
ans = min(b, c)
if b < c:
ans += ((c - b) // 3)
print(ans)
``` | output | 1 | 44,385 | 14 | 88,771 |
Provide a correct Python 3 solution for this coding contest problem.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25. | instruction | 0 | 44,386 | 14 | 88,772 |
"Correct Solution:
```
s=0;
q=0;
n = int(input());
qq=0;
w = str(input());
w1=w.split()
while qq<n:
qwe=int(w1[qq]);
if (qwe%2==0):
s=s+1;
else:
q=q+1
qq = qq + 1;
if q<=s:
print(q);
else:
print(s+(q-s)//3)
``` | output | 1 | 44,386 | 14 | 88,773 |
Provide a correct Python 3 solution for this coding contest problem.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25. | instruction | 0 | 44,387 | 14 | 88,774 |
"Correct Solution:
```
n = int(input())
f = input().split(" ")
a = 0
b = 0
for i in range(0, n):
g = int(f[i])
if( g % 2 == 0):
a += 1
else:
b += 1
if(a > b):
print(b)
else:
print(a + (b-a)//3)
``` | output | 1 | 44,387 | 14 | 88,775 |
Provide a correct Python 3 solution for this coding contest problem.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25. | instruction | 0 | 44,388 | 14 | 88,776 |
"Correct Solution:
```
n = int(input(""))
even = 0
odd = 0
ls = map(int, input("").split(' '))
for i in ls:
if i % 2 == 0:
even += 1
else:
odd += 1
ans = 0
while even > 0 and odd > 0:
ans += 1
even -= 1
odd -= 1
ans += int(odd / 3);
print(ans)
``` | output | 1 | 44,388 | 14 | 88,777 |
Provide a correct Python 3 solution for this coding contest problem.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25. | instruction | 0 | 44,389 | 14 | 88,778 |
"Correct Solution:
```
n = int(input())
arr = [int(z) for z in input().split()]
o, e = 0, 0
for i in arr:
if i % 2:
o += 1
else:
e += 1
b = min(o, e)
b += max(0, o - e) // 3
print(b)
``` | output | 1 | 44,389 | 14 | 88,779 |
Provide a correct Python 3 solution for this coding contest problem.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25. | instruction | 0 | 44,390 | 14 | 88,780 |
"Correct Solution:
```
n = (input())
kol_vo_chet = 0
kol_vo_nechet = 0
nb = input().split()
for i in nb:
if int(i, 10) % 2 == 0:
kol_vo_chet += 1
else:
kol_vo_nechet += 1
answ = 0
answ = min(kol_vo_nechet, kol_vo_chet)
kol_vo_nechet -= answ
if kol_vo_nechet !=0:
answ += kol_vo_nechet//3
print(answ)
``` | output | 1 | 44,390 | 14 | 88,781 |
Provide a correct Python 3 solution for this coding contest problem.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25. | instruction | 0 | 44,391 | 14 | 88,782 |
"Correct Solution:
```
n = int(input())
odd = 0
even = 0
t = input().split(' ')
for i in range(0, n):
x = int(t[i])
if x % 2 == 0:
even += 1
else:
odd += 1
ans = min(odd, even)
odd -= ans
ans += odd // 3
print(ans)
``` | output | 1 | 44,391 | 14 | 88,783 |
Provide a correct Python 3 solution for this coding contest problem.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25. | instruction | 0 | 44,392 | 14 | 88,784 |
"Correct Solution:
```
n = int(input())
a = [int(x) for x in input().split()]
x = 0
for i in range(0, n):
if a[i] % 2==1:
x = x + 1
cnt = n - x
if cnt > x:
cnt=x
x = x - (n - x)
if x > 0:
cnt += int(x / 3)
print (cnt)
``` | output | 1 | 44,392 | 14 | 88,785 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25.
Submitted Solution:
```
n = int(input())
a = [int(i) for i in input().split()]
nechet = [i % 2 for i in a].count(True)
chet = n - nechet
first = min(nechet, chet)
diff = nechet-chet
diff = diff // 3 if diff > 0 else 0
print(first + diff)
``` | instruction | 0 | 44,393 | 14 | 88,786 |
Yes | output | 1 | 44,393 | 14 | 88,787 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25.
Submitted Solution:
```
n = input()
a = input().split()
odd = 0
even = 0
for i in a:
if int(i)%2 == 1:
odd = odd + 1
else:
even = even + 1
ans = min( odd, even)
odd = odd - ans;
if odd >= 3:
ans = ans + int(odd/3)
print(ans)
``` | instruction | 0 | 44,394 | 14 | 88,788 |
Yes | output | 1 | 44,394 | 14 | 88,789 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25.
Submitted Solution:
```
nec=c=ans=0
def Sort(x):
global c, nec
s = int(x) % 2 == 0
if s: c += 1
else: nec += 1
return s
a = input()
List=list(map(Sort,input().split()))
if nec:
if not c:
print(nec//3)
else:
n = min(nec, c)
ans += n
nec -= n
c -= n
if nec:
ans += nec//3
print(ans)
else:
print(ans)
else:
print(0)
``` | instruction | 0 | 44,395 | 14 | 88,790 |
Yes | output | 1 | 44,395 | 14 | 88,791 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25.
Submitted Solution:
```
n=int (input())
a = list(map(int, input().split()))
k=0
d=0
for i in range(n):
if a[i]%2==1:
k+=1
else:
d+=1
if k<d:
ma=k
else:
ma=d
while (k>2):
k-=2
d+=1
if (k<d):
if k>ma:
ma=k
else:
if d>ma:
ma=d
print(ma)
``` | instruction | 0 | 44,396 | 14 | 88,792 |
Yes | output | 1 | 44,396 | 14 | 88,793 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25.
Submitted Solution:
```
s = input().split(" ")
a = 0
for i in s:
if (int(i)%2 == 1):
a+=1
print(a)
``` | instruction | 0 | 44,397 | 14 | 88,794 |
No | output | 1 | 44,397 | 14 | 88,795 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25.
Submitted Solution:
```
n = int(input())
arr = list(map(int,input().split()))
even = 0
odd = 0
for i in arr:
if i%2==0:
even+=1
else:
odd+=1
if odd==0:
print(0)
elif odd < even:
print(odd)
elif odd==even:
print(odd)
else:
print (even + int(odd//3))
``` | instruction | 0 | 44,398 | 14 | 88,796 |
No | output | 1 | 44,398 | 14 | 88,797 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25.
Submitted Solution:
```
n = int(input())
m = list(map(int, input().split()))
c = 0
for i in m:
if i % 2:
c += 1
if c < (n/2):
print(c)
exit()
uc = n - c
ans = 0
while c > uc:
c -=3
ans +=1
print((uc-c) // 3 + c)
``` | instruction | 0 | 44,399 | 14 | 88,798 |
No | output | 1 | 44,399 | 14 | 88,799 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A flower shop has got n bouquets, and the i-th bouquet consists of ai flowers. Vasya, the manager of the shop, decided to make large bouquets from these bouquets.
Vasya thinks that a bouquet is large if it is made of two or more initial bouquets, and there is a constraint: the total number of flowers in a large bouquet should be odd. Each of the initial bouquets can be a part of at most one large bouquet. If an initial bouquet becomes a part of a large bouquet, all its flowers are included in the large bouquet.
Determine the maximum possible number of large bouquets Vasya can make.
Input
The first line contains a single positive integer n (1 ≤ n ≤ 105) — the number of initial bouquets.
The second line contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 106) — the number of flowers in each of the initial bouquets.
Output
Print the maximum number of large bouquets Vasya can make.
Examples
Input
5
2 3 4 2 7
Output
2
Input
6
2 2 6 8 6 12
Output
0
Input
3
11 4 10
Output
1
Note
In the first example Vasya can make 2 large bouquets. For example, the first bouquet can contain the first and the fifth initial bouquets (the total number of flowers is then equal to 9), and the second bouquet can consist of the second and the third initial bouquets (the total number of flowers is then equal to 7). The fourth initial bouquet is unused in this scheme.
In the second example it is not possible to form a single bouquet with odd number of flowers.
In the third example Vasya can make one large bouquet. For example, he can make it using all three initial bouquets. The size of the large bouquet is then equal to 11 + 4 + 10 = 25.
Submitted Solution:
```
def is_odd(a):
return bool(a&1)
def main():
n = int(input())
even = 0
odd = 0
for a in map(int,input().split()):
if is_odd(a):
odd += 1
else:
even += 1
cnt = min(even,odd)
if odd>even:
cnt += odd/3
print(cnt)
main()
``` | instruction | 0 | 44,400 | 14 | 88,800 |
No | output | 1 | 44,400 | 14 | 88,801 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The only difference between easy and hard versions is the constraints.
Vova likes pictures with kittens. The news feed in the social network he uses can be represented as an array of n consecutive pictures (with kittens, of course). Vova likes all these pictures, but some are more beautiful than the others: the i-th picture has beauty a_i.
Vova wants to repost exactly x pictures in such a way that:
* each segment of the news feed of at least k consecutive pictures has at least one picture reposted by Vova;
* the sum of beauty values of reposted pictures is maximum possible.
For example, if k=1 then Vova has to repost all the pictures in the news feed. If k=2 then Vova can skip some pictures, but between every pair of consecutive pictures Vova has to repost at least one of them.
Your task is to calculate the maximum possible sum of values of reposted pictures if Vova follows conditions described above, or say that there is no way to satisfy all conditions.
Input
The first line of the input contains three integers n, k and x (1 ≤ k, x ≤ n ≤ 200) — the number of pictures in the news feed, the minimum length of segment with at least one repost in it and the number of pictures Vova is ready to repost.
The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the beauty of the i-th picture.
Output
Print -1 if there is no way to repost some pictures to satisfy all the conditions in the problem statement.
Otherwise print one integer — the maximum sum of values of reposted pictures if Vova follows conditions described in the problem statement.
Examples
Input
5 2 3
5 1 3 10 1
Output
18
Input
6 1 5
10 30 30 70 10 10
Output
-1
Input
4 3 1
1 100 1 1
Output
100 | instruction | 0 | 44,629 | 14 | 89,258 |
Tags: dp
Correct Solution:
```
import sys
S = sys.stdin.read()
S = list(map(lambda x: list(map(int, x)), list(map(lambda x: x.split(), [x for x in S.split('\n') if len(x) > 1]))))
n, k, x, B = S[0][0], S[0][1], S[0][2], S[1]
X = [[-1 for i in range(x+1)] for i in range(n+1)]
X[0][0] = 0
for i in range(1, n+1):
for j in range(1, x+1):
X[i][j] = max([X[i][j], max([-1] + [X[i-l][j-1]+B[i-1] for l in range(1, min([i, k])+1) if X[i-l][j-1] != -1])])
print(max(list(map(max, X[n-k+1:n+1]))))
``` | output | 1 | 44,629 | 14 | 89,259 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The only difference between easy and hard versions is the constraints.
Vova likes pictures with kittens. The news feed in the social network he uses can be represented as an array of n consecutive pictures (with kittens, of course). Vova likes all these pictures, but some are more beautiful than the others: the i-th picture has beauty a_i.
Vova wants to repost exactly x pictures in such a way that:
* each segment of the news feed of at least k consecutive pictures has at least one picture reposted by Vova;
* the sum of beauty values of reposted pictures is maximum possible.
For example, if k=1 then Vova has to repost all the pictures in the news feed. If k=2 then Vova can skip some pictures, but between every pair of consecutive pictures Vova has to repost at least one of them.
Your task is to calculate the maximum possible sum of values of reposted pictures if Vova follows conditions described above, or say that there is no way to satisfy all conditions.
Input
The first line of the input contains three integers n, k and x (1 ≤ k, x ≤ n ≤ 200) — the number of pictures in the news feed, the minimum length of segment with at least one repost in it and the number of pictures Vova is ready to repost.
The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the beauty of the i-th picture.
Output
Print -1 if there is no way to repost some pictures to satisfy all the conditions in the problem statement.
Otherwise print one integer — the maximum sum of values of reposted pictures if Vova follows conditions described in the problem statement.
Examples
Input
5 2 3
5 1 3 10 1
Output
18
Input
6 1 5
10 30 30 70 10 10
Output
-1
Input
4 3 1
1 100 1 1
Output
100 | instruction | 0 | 44,630 | 14 | 89,260 |
Tags: dp
Correct Solution:
```
import sys
from math import *
from collections import deque
def minp():
return sys.stdin.readline().strip()
def mint():
return int(minp())
def mints():
return map(int, minp().split())
def solve():
n, k, x = mints()
a = list(mints())
d = [-1e50]*n
p = [-1e50]*n
for i in range(0,k):
d[i] = a[i]
q = deque()
for xx in range(1,x):
d,p = p,d
q.clear()
for nn in range(xx-1,n):
while len(q) != 0 and q[0][1] < nn-k:
q.popleft()
if len(q):
d[nn] = q[0][0] + a[nn]
else:
d[nn] = -1e50
while len(q) and q[-1][0] <= p[nn]:
q.pop();
q.append((p[nn], nn))
m = -1
for i in range(n-k, n):
m = max(m, d[i])
print(m)
solve()
``` | output | 1 | 44,630 | 14 | 89,261 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The only difference between easy and hard versions is the constraints.
Vova likes pictures with kittens. The news feed in the social network he uses can be represented as an array of n consecutive pictures (with kittens, of course). Vova likes all these pictures, but some are more beautiful than the others: the i-th picture has beauty a_i.
Vova wants to repost exactly x pictures in such a way that:
* each segment of the news feed of at least k consecutive pictures has at least one picture reposted by Vova;
* the sum of beauty values of reposted pictures is maximum possible.
For example, if k=1 then Vova has to repost all the pictures in the news feed. If k=2 then Vova can skip some pictures, but between every pair of consecutive pictures Vova has to repost at least one of them.
Your task is to calculate the maximum possible sum of values of reposted pictures if Vova follows conditions described above, or say that there is no way to satisfy all conditions.
Input
The first line of the input contains three integers n, k and x (1 ≤ k, x ≤ n ≤ 200) — the number of pictures in the news feed, the minimum length of segment with at least one repost in it and the number of pictures Vova is ready to repost.
The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the beauty of the i-th picture.
Output
Print -1 if there is no way to repost some pictures to satisfy all the conditions in the problem statement.
Otherwise print one integer — the maximum sum of values of reposted pictures if Vova follows conditions described in the problem statement.
Examples
Input
5 2 3
5 1 3 10 1
Output
18
Input
6 1 5
10 30 30 70 10 10
Output
-1
Input
4 3 1
1 100 1 1
Output
100 | instruction | 0 | 44,631 | 14 | 89,262 |
Tags: dp
Correct Solution:
```
from math import ceil
n,jump,count=map(int,input().split())
a=[0]+list(map(int,input().split()))
dp=[[-1]*(count+1) for i in range(n+1) ]
dp[0][0]=0
for i in range(n):
for j in range(count):
if dp[i][j]>=0:
for k in range(1,min(jump,n-i)+1):
dp[i+k][j+1]=max(dp[i+k][j+1],dp[i][j]+a[i+k])
ans=0
for i in range(n-jump+1,n+1):
ans=max(ans,dp[i][count])
if n//jump>count:
print(-1)
else:
print(ans)
``` | output | 1 | 44,631 | 14 | 89,263 |
Provide tags and a correct Python 3 solution for this coding contest problem.
The only difference between easy and hard versions is the constraints.
Vova likes pictures with kittens. The news feed in the social network he uses can be represented as an array of n consecutive pictures (with kittens, of course). Vova likes all these pictures, but some are more beautiful than the others: the i-th picture has beauty a_i.
Vova wants to repost exactly x pictures in such a way that:
* each segment of the news feed of at least k consecutive pictures has at least one picture reposted by Vova;
* the sum of beauty values of reposted pictures is maximum possible.
For example, if k=1 then Vova has to repost all the pictures in the news feed. If k=2 then Vova can skip some pictures, but between every pair of consecutive pictures Vova has to repost at least one of them.
Your task is to calculate the maximum possible sum of values of reposted pictures if Vova follows conditions described above, or say that there is no way to satisfy all conditions.
Input
The first line of the input contains three integers n, k and x (1 ≤ k, x ≤ n ≤ 200) — the number of pictures in the news feed, the minimum length of segment with at least one repost in it and the number of pictures Vova is ready to repost.
The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the beauty of the i-th picture.
Output
Print -1 if there is no way to repost some pictures to satisfy all the conditions in the problem statement.
Otherwise print one integer — the maximum sum of values of reposted pictures if Vova follows conditions described in the problem statement.
Examples
Input
5 2 3
5 1 3 10 1
Output
18
Input
6 1 5
10 30 30 70 10 10
Output
-1
Input
4 3 1
1 100 1 1
Output
100 | instruction | 0 | 44,632 | 14 | 89,264 |
Tags: dp
Correct Solution:
```
# -*- coding: utf-8 -*-
import sys
def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
INF = 10 ** 18
MOD = 10 ** 9 + 7
N, K, X = MAP()
A = [0] + LIST()
dp = list2d(X+1, N+1, -1)
dp[0][0] = 0
for i in range(X):
for j in range(i, N):
if dp[i][j] == -1:
continue
for k in range(j+1, min(j+K+1, N+1)):
dp[i+1][k] = max(dp[i+1][k], dp[i][j] + A[k])
ans = max(dp[X][-K:])
print(ans)
``` | output | 1 | 44,632 | 14 | 89,265 |
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