text stringlengths 198 433k | conversation_id int64 0 109k |
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Provide tags and a correct Python 3 solution for this coding contest problem.
Jeff got 2n real numbers a1, a2, ..., a2n as a birthday present. The boy hates non-integer numbers, so he decided to slightly "adjust" the numbers he's got. Namely, Jeff consecutively executes n operations, each of them goes as follows:
* choose indexes i and j (i ≠ j) that haven't been chosen yet;
* round element ai to the nearest integer that isn't more than ai (assign to ai: ⌊ ai ⌋);
* round element aj to the nearest integer that isn't less than aj (assign to aj: ⌈ aj ⌉).
Nevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.
Input
The first line contains integer n (1 ≤ n ≤ 2000). The next line contains 2n real numbers a1, a2, ..., a2n (0 ≤ ai ≤ 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.
Output
In a single line print a single real number — the required difference with exactly three digits after the decimal point.
Examples
Input
3
0.000 0.500 0.750 1.000 2.000 3.000
Output
0.250
Input
3
4469.000 6526.000 4864.000 9356.383 7490.000 995.896
Output
0.279
Note
In the first test case you need to perform the operations as follows: (i = 1, j = 4), (i = 2, j = 3), (i = 5, j = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25.
Tags: dp, greedy, implementation, math
Correct Solution:
```
from math import ceil, floor
N = int(input())
Nums = list(map(float, input().split()))
Zeros = 0
Sum = 0.0
for Num in Nums:
if Num - floor(Num) == 0:
Zeros += 1
else:
Sum += Num - floor(Num)
Best = float(10 ** 9)
for i in range(Zeros + 1):
Best = min(Best, abs(N - Zeros + i - Sum))
Best = str(float(round(Best, 3)))
Index = Best.find('.')
print(Best + '0' * (4 - (len(Best) - Index)))
```
| 101,500 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Jeff got 2n real numbers a1, a2, ..., a2n as a birthday present. The boy hates non-integer numbers, so he decided to slightly "adjust" the numbers he's got. Namely, Jeff consecutively executes n operations, each of them goes as follows:
* choose indexes i and j (i ≠ j) that haven't been chosen yet;
* round element ai to the nearest integer that isn't more than ai (assign to ai: ⌊ ai ⌋);
* round element aj to the nearest integer that isn't less than aj (assign to aj: ⌈ aj ⌉).
Nevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.
Input
The first line contains integer n (1 ≤ n ≤ 2000). The next line contains 2n real numbers a1, a2, ..., a2n (0 ≤ ai ≤ 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.
Output
In a single line print a single real number — the required difference with exactly three digits after the decimal point.
Examples
Input
3
0.000 0.500 0.750 1.000 2.000 3.000
Output
0.250
Input
3
4469.000 6526.000 4864.000 9356.383 7490.000 995.896
Output
0.279
Note
In the first test case you need to perform the operations as follows: (i = 1, j = 4), (i = 2, j = 3), (i = 5, j = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25.
Tags: dp, greedy, implementation, math
Correct Solution:
```
import math
n = int(input())
nums = input().split()
float_nums = [float(ele) for ele in nums]
diff = 0.000
count = 0
for x in float_nums:
diff += x - math.floor(x)
if math.ceil(x) > math.floor(x):
count += 1
min_num = max(0, count - n)
max_num = min(count, n)
if math.ceil(diff) - diff <= 0.5:
t = math.ceil(diff)
else:
t = math.floor(diff)
if t < min_num:
print("{0:.3f}".format(min_num - diff))
elif t > max_num:
print("{0:.3f}".format(diff - max_num))
else:
print("{0:.3f}".format(math.fabs(diff - t)))
```
| 101,501 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Jeff got 2n real numbers a1, a2, ..., a2n as a birthday present. The boy hates non-integer numbers, so he decided to slightly "adjust" the numbers he's got. Namely, Jeff consecutively executes n operations, each of them goes as follows:
* choose indexes i and j (i ≠ j) that haven't been chosen yet;
* round element ai to the nearest integer that isn't more than ai (assign to ai: ⌊ ai ⌋);
* round element aj to the nearest integer that isn't less than aj (assign to aj: ⌈ aj ⌉).
Nevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.
Input
The first line contains integer n (1 ≤ n ≤ 2000). The next line contains 2n real numbers a1, a2, ..., a2n (0 ≤ ai ≤ 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.
Output
In a single line print a single real number — the required difference with exactly three digits after the decimal point.
Examples
Input
3
0.000 0.500 0.750 1.000 2.000 3.000
Output
0.250
Input
3
4469.000 6526.000 4864.000 9356.383 7490.000 995.896
Output
0.279
Note
In the first test case you need to perform the operations as follows: (i = 1, j = 4), (i = 2, j = 3), (i = 5, j = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25.
Tags: dp, greedy, implementation, math
Correct Solution:
```
n = int(input())
l = list(map(float, input().split()))
l = sorted([x - int(x) for x in l if x - int(x) != 0])
o = 2*n - len(l)
su = sum(l)
ans = 0xFFFFFFFFFFFFFFF
for i in range(n + 1):
if i + o >= n:
ans = min(ans, abs(i-su))
print("%.3f" % ans)
# Made By Mostafa_Khaled
```
| 101,502 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Jeff got 2n real numbers a1, a2, ..., a2n as a birthday present. The boy hates non-integer numbers, so he decided to slightly "adjust" the numbers he's got. Namely, Jeff consecutively executes n operations, each of them goes as follows:
* choose indexes i and j (i ≠ j) that haven't been chosen yet;
* round element ai to the nearest integer that isn't more than ai (assign to ai: ⌊ ai ⌋);
* round element aj to the nearest integer that isn't less than aj (assign to aj: ⌈ aj ⌉).
Nevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.
Input
The first line contains integer n (1 ≤ n ≤ 2000). The next line contains 2n real numbers a1, a2, ..., a2n (0 ≤ ai ≤ 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.
Output
In a single line print a single real number — the required difference with exactly three digits after the decimal point.
Examples
Input
3
0.000 0.500 0.750 1.000 2.000 3.000
Output
0.250
Input
3
4469.000 6526.000 4864.000 9356.383 7490.000 995.896
Output
0.279
Note
In the first test case you need to perform the operations as follows: (i = 1, j = 4), (i = 2, j = 3), (i = 5, j = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25.
Tags: dp, greedy, implementation, math
Correct Solution:
```
n = int(input())
As = list(map(float, input().split()))
B = list(x - int(x) for x in As if x - int(x) > 0.000)
l = len(B)
if l == 0:
print('{:.3f}'.format(0))
exit(0)
S = sum(x for x in B)
ans = 1e10
for i in range(max(0, l - n), min(l,n) + 1):
ans = min(ans, abs(i - S))
print('{:.3f}'.format(ans))
```
| 101,503 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Jeff got 2n real numbers a1, a2, ..., a2n as a birthday present. The boy hates non-integer numbers, so he decided to slightly "adjust" the numbers he's got. Namely, Jeff consecutively executes n operations, each of them goes as follows:
* choose indexes i and j (i ≠ j) that haven't been chosen yet;
* round element ai to the nearest integer that isn't more than ai (assign to ai: ⌊ ai ⌋);
* round element aj to the nearest integer that isn't less than aj (assign to aj: ⌈ aj ⌉).
Nevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.
Input
The first line contains integer n (1 ≤ n ≤ 2000). The next line contains 2n real numbers a1, a2, ..., a2n (0 ≤ ai ≤ 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.
Output
In a single line print a single real number — the required difference with exactly three digits after the decimal point.
Examples
Input
3
0.000 0.500 0.750 1.000 2.000 3.000
Output
0.250
Input
3
4469.000 6526.000 4864.000 9356.383 7490.000 995.896
Output
0.279
Note
In the first test case you need to perform the operations as follows: (i = 1, j = 4), (i = 2, j = 3), (i = 5, j = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25.
Tags: dp, greedy, implementation, math
Correct Solution:
```
n = int(input())
a = map(float, input().split())
s = 0
m = 0
for val in a:
s += val-int(val)
m += (val-int(val))>0
v = 1e9
for i in range(max(0, m-n), min(n, m)+1):
v = min(v, abs(s-i))
print('%.3f'%v)
```
| 101,504 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jeff got 2n real numbers a1, a2, ..., a2n as a birthday present. The boy hates non-integer numbers, so he decided to slightly "adjust" the numbers he's got. Namely, Jeff consecutively executes n operations, each of them goes as follows:
* choose indexes i and j (i ≠ j) that haven't been chosen yet;
* round element ai to the nearest integer that isn't more than ai (assign to ai: ⌊ ai ⌋);
* round element aj to the nearest integer that isn't less than aj (assign to aj: ⌈ aj ⌉).
Nevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.
Input
The first line contains integer n (1 ≤ n ≤ 2000). The next line contains 2n real numbers a1, a2, ..., a2n (0 ≤ ai ≤ 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.
Output
In a single line print a single real number — the required difference with exactly three digits after the decimal point.
Examples
Input
3
0.000 0.500 0.750 1.000 2.000 3.000
Output
0.250
Input
3
4469.000 6526.000 4864.000 9356.383 7490.000 995.896
Output
0.279
Note
In the first test case you need to perform the operations as follows: (i = 1, j = 4), (i = 2, j = 3), (i = 5, j = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25.
Submitted Solution:
```
N=int(input())
n=N
A=list(map(float,input().strip().split(' ')))
z=0
for i in range(len(A)):
A[i]=round(A[i],3)-int(A[i])
if A[i]==0:
z+=1
#print(A)
ANS=sum(A)
#print(ANS)
ans=10**10
for j in range(n-z,n+1):
ans=min(ans,abs(ANS-j))
print("%.3f"%ans)
```
Yes
| 101,505 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jeff got 2n real numbers a1, a2, ..., a2n as a birthday present. The boy hates non-integer numbers, so he decided to slightly "adjust" the numbers he's got. Namely, Jeff consecutively executes n operations, each of them goes as follows:
* choose indexes i and j (i ≠ j) that haven't been chosen yet;
* round element ai to the nearest integer that isn't more than ai (assign to ai: ⌊ ai ⌋);
* round element aj to the nearest integer that isn't less than aj (assign to aj: ⌈ aj ⌉).
Nevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.
Input
The first line contains integer n (1 ≤ n ≤ 2000). The next line contains 2n real numbers a1, a2, ..., a2n (0 ≤ ai ≤ 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.
Output
In a single line print a single real number — the required difference with exactly three digits after the decimal point.
Examples
Input
3
0.000 0.500 0.750 1.000 2.000 3.000
Output
0.250
Input
3
4469.000 6526.000 4864.000 9356.383 7490.000 995.896
Output
0.279
Note
In the first test case you need to perform the operations as follows: (i = 1, j = 4), (i = 2, j = 3), (i = 5, j = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25.
Submitted Solution:
```
n = int(input())
l = list(map(float, input().split()))
l = sorted([x - int(x) for x in l if x - int(x) != 0])
o = 2*n - len(l)
su = sum(l)
ans = 0xFFFFFFFFFFFFFFF
for i in range(n + 1):
if i + o >= n:
ans = min(ans, abs(i-su))
print("%.3f" % ans)
```
Yes
| 101,506 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jeff got 2n real numbers a1, a2, ..., a2n as a birthday present. The boy hates non-integer numbers, so he decided to slightly "adjust" the numbers he's got. Namely, Jeff consecutively executes n operations, each of them goes as follows:
* choose indexes i and j (i ≠ j) that haven't been chosen yet;
* round element ai to the nearest integer that isn't more than ai (assign to ai: ⌊ ai ⌋);
* round element aj to the nearest integer that isn't less than aj (assign to aj: ⌈ aj ⌉).
Nevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.
Input
The first line contains integer n (1 ≤ n ≤ 2000). The next line contains 2n real numbers a1, a2, ..., a2n (0 ≤ ai ≤ 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.
Output
In a single line print a single real number — the required difference with exactly three digits after the decimal point.
Examples
Input
3
0.000 0.500 0.750 1.000 2.000 3.000
Output
0.250
Input
3
4469.000 6526.000 4864.000 9356.383 7490.000 995.896
Output
0.279
Note
In the first test case you need to perform the operations as follows: (i = 1, j = 4), (i = 2, j = 3), (i = 5, j = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25.
Submitted Solution:
```
from sys import *
s1=stdin.readline().strip()
n=int(s1)
s1=stdin.readline().strip()
a=list(map(float,s1.split()))
b=[]
for i in range (2*n):
if int(a[i])!=a[i]:
b.append(round(1000*(a[i]-int(a[i]))))
m=len(b)
r=0
for i in range (m):
r=r+b[i]
if m<=n:
if r>=1000*m:
r=r-1000*m
else:
r=min(r-1000*(r//1000),1000-r+1000*(r//1000))
else:
if r>=n*1000:
r=r-1000*n
else:
if r<=1000*(m-n):
r=1000*(m-n)-r
else:
r=min(r-1000*(r//1000),1000-r+1000*(r//1000))
r=r/1000
print("%.3f"%r)
```
Yes
| 101,507 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jeff got 2n real numbers a1, a2, ..., a2n as a birthday present. The boy hates non-integer numbers, so he decided to slightly "adjust" the numbers he's got. Namely, Jeff consecutively executes n operations, each of them goes as follows:
* choose indexes i and j (i ≠ j) that haven't been chosen yet;
* round element ai to the nearest integer that isn't more than ai (assign to ai: ⌊ ai ⌋);
* round element aj to the nearest integer that isn't less than aj (assign to aj: ⌈ aj ⌉).
Nevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.
Input
The first line contains integer n (1 ≤ n ≤ 2000). The next line contains 2n real numbers a1, a2, ..., a2n (0 ≤ ai ≤ 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.
Output
In a single line print a single real number — the required difference with exactly three digits after the decimal point.
Examples
Input
3
0.000 0.500 0.750 1.000 2.000 3.000
Output
0.250
Input
3
4469.000 6526.000 4864.000 9356.383 7490.000 995.896
Output
0.279
Note
In the first test case you need to perform the operations as follows: (i = 1, j = 4), (i = 2, j = 3), (i = 5, j = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25.
Submitted Solution:
```
n = int(input())
arr = list(map(float, input().split()))
arr = sorted([x - int(x) for x in arr if x - int(x) != 0])
o = 2 * n - len(arr)
arr_sum = sum(arr)
res = int(2e9)
for i in range(n + 1):
if i + o >= n:
res = min(res, abs(i - arr_sum))
print("%.3f" % res)
```
Yes
| 101,508 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jeff got 2n real numbers a1, a2, ..., a2n as a birthday present. The boy hates non-integer numbers, so he decided to slightly "adjust" the numbers he's got. Namely, Jeff consecutively executes n operations, each of them goes as follows:
* choose indexes i and j (i ≠ j) that haven't been chosen yet;
* round element ai to the nearest integer that isn't more than ai (assign to ai: ⌊ ai ⌋);
* round element aj to the nearest integer that isn't less than aj (assign to aj: ⌈ aj ⌉).
Nevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.
Input
The first line contains integer n (1 ≤ n ≤ 2000). The next line contains 2n real numbers a1, a2, ..., a2n (0 ≤ ai ≤ 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.
Output
In a single line print a single real number — the required difference with exactly three digits after the decimal point.
Examples
Input
3
0.000 0.500 0.750 1.000 2.000 3.000
Output
0.250
Input
3
4469.000 6526.000 4864.000 9356.383 7490.000 995.896
Output
0.279
Note
In the first test case you need to perform the operations as follows: (i = 1, j = 4), (i = 2, j = 3), (i = 5, j = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25.
Submitted Solution:
```
from sys import *
import math
def numline(f = int):
return map(f, input().split())
n = int(input())
a = list(filter(lambda x: x != 0, numline(lambda s: int(s.split('.')[1]))))
c0 = min(2 * n - len(a), len(a))
ans = sum(a) - 1000 * min(n, len(a))
while c0 > 0 and abs(ans) > 1000:
c0 -= 1
if ans > 0:
ans -= 1000
else:
ans += 1000
if c0 > 0:
if ans > 0:
ans = min(ans, abs(1000 - ans))
else:
ans = min(abs(ans), abs(ans + 1000))
ans = abs(ans)
print('{}.{:0>3}'.format(ans // 1000, ans % 1000))
```
No
| 101,509 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jeff got 2n real numbers a1, a2, ..., a2n as a birthday present. The boy hates non-integer numbers, so he decided to slightly "adjust" the numbers he's got. Namely, Jeff consecutively executes n operations, each of them goes as follows:
* choose indexes i and j (i ≠ j) that haven't been chosen yet;
* round element ai to the nearest integer that isn't more than ai (assign to ai: ⌊ ai ⌋);
* round element aj to the nearest integer that isn't less than aj (assign to aj: ⌈ aj ⌉).
Nevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.
Input
The first line contains integer n (1 ≤ n ≤ 2000). The next line contains 2n real numbers a1, a2, ..., a2n (0 ≤ ai ≤ 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.
Output
In a single line print a single real number — the required difference with exactly three digits after the decimal point.
Examples
Input
3
0.000 0.500 0.750 1.000 2.000 3.000
Output
0.250
Input
3
4469.000 6526.000 4864.000 9356.383 7490.000 995.896
Output
0.279
Note
In the first test case you need to perform the operations as follows: (i = 1, j = 4), (i = 2, j = 3), (i = 5, j = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25.
Submitted Solution:
```
n = int(input())
As = list(map(float, input().split()))
B = list(x - int(x) for x in As if x - int(x) > 0.000)
l = len(B)
if l == 0:
print('{:.3f}'.format(0))
exit(0)
S = sum(x for x in B)
ll = l if l % 2 == 0 else l + 1
print(B)
print(S)
ans = 1e10
for i in range(max(0,int(l - n)), min(n, int(ll/2)) + 1):
ans = min(ans, abs(i - S))
print('{:.3f}'.format(ans))
```
No
| 101,510 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jeff got 2n real numbers a1, a2, ..., a2n as a birthday present. The boy hates non-integer numbers, so he decided to slightly "adjust" the numbers he's got. Namely, Jeff consecutively executes n operations, each of them goes as follows:
* choose indexes i and j (i ≠ j) that haven't been chosen yet;
* round element ai to the nearest integer that isn't more than ai (assign to ai: ⌊ ai ⌋);
* round element aj to the nearest integer that isn't less than aj (assign to aj: ⌈ aj ⌉).
Nevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.
Input
The first line contains integer n (1 ≤ n ≤ 2000). The next line contains 2n real numbers a1, a2, ..., a2n (0 ≤ ai ≤ 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.
Output
In a single line print a single real number — the required difference with exactly three digits after the decimal point.
Examples
Input
3
0.000 0.500 0.750 1.000 2.000 3.000
Output
0.250
Input
3
4469.000 6526.000 4864.000 9356.383 7490.000 995.896
Output
0.279
Note
In the first test case you need to perform the operations as follows: (i = 1, j = 4), (i = 2, j = 3), (i = 5, j = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25.
Submitted Solution:
```
from fractions import Fraction
n = int(input())
a = [Fraction(int(x[-3:]), 1000) for x in input().split()]
a = list(sorted(a))
ans = sum(a) - len(a) // 2
while len(a) > 0 and a[1] == 0:
if (abs(ans) > abs(ans - sum(a[:2]) + 1)):
ans = ans - sum(a[:2]) + 1
del a[:2]
print("0.{:03d}".format(abs(ans.numerator * 1000 // ans.denominator)))
```
No
| 101,511 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Jeff got 2n real numbers a1, a2, ..., a2n as a birthday present. The boy hates non-integer numbers, so he decided to slightly "adjust" the numbers he's got. Namely, Jeff consecutively executes n operations, each of them goes as follows:
* choose indexes i and j (i ≠ j) that haven't been chosen yet;
* round element ai to the nearest integer that isn't more than ai (assign to ai: ⌊ ai ⌋);
* round element aj to the nearest integer that isn't less than aj (assign to aj: ⌈ aj ⌉).
Nevertheless, Jeff doesn't want to hurt the feelings of the person who gave him the sequence. That's why the boy wants to perform the operations so as to make the absolute value of the difference between the sum of elements before performing the operations and the sum of elements after performing the operations as small as possible. Help Jeff find the minimum absolute value of the difference.
Input
The first line contains integer n (1 ≤ n ≤ 2000). The next line contains 2n real numbers a1, a2, ..., a2n (0 ≤ ai ≤ 10000), given with exactly three digits after the decimal point. The numbers are separated by spaces.
Output
In a single line print a single real number — the required difference with exactly three digits after the decimal point.
Examples
Input
3
0.000 0.500 0.750 1.000 2.000 3.000
Output
0.250
Input
3
4469.000 6526.000 4864.000 9356.383 7490.000 995.896
Output
0.279
Note
In the first test case you need to perform the operations as follows: (i = 1, j = 4), (i = 2, j = 3), (i = 5, j = 6). In this case, the difference will equal |(0 + 0.5 + 0.75 + 1 + 2 + 3) - (0 + 0 + 1 + 1 + 2 + 3)| = 0.25.
Submitted Solution:
```
n = int(input())
a = [float(x) - int(float(x)) for x in input().split()]
a = list(sorted(a))
while len(a) > 0 and a[1] == 0:
del a[:2]
print(a)
print("{:.3f}".format(abs(sum(a[:len(a) // 2]) - (len(a) // 2) + sum(a[len(a) // 2:]))))
```
No
| 101,512 |
Provide tags and a correct Python 3 solution for this coding contest problem.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Tags: implementation
Correct Solution:
```
x=input()
def convert(x):
lst=x.split(" ")
return lst
data=convert(x)
n=int(data[0])
p=int(data[1])
k=int(data[2])
num=[]
for i in range(1,n+1):
num.append(i)
res=[]
r=[">>"]
l=["<<"]
for i in range(p-k,p+k+1):
if i>0 and len(num)>=i:
res.append(num[i-1])
if res[0]==1 and res[len(res)-1]==n:
ans=listToStr = ' '.join([str(elem) for elem in res])
an=ans.replace(str(p),("("+str(p)+")"),1)
elif res[0]==1:
ans=listToStr = ' '.join([str(elem) for elem in (res+r)])
an=ans.replace(str(p),("("+str(p)+")"),1)
elif res[len(res)-1]==n:
ans=listToStr = ' '.join([str(elem) for elem in (l+res)])
an=ans.replace(str(p),("("+str(p)+")"),1)
else:
ans=listToStr = ' '.join([str(elem) for elem in (l+res+r)])
an=ans.replace(str(p),("("+str(p)+")"),1)
print(an)
```
| 101,513 |
Provide tags and a correct Python 3 solution for this coding contest problem.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Tags: implementation
Correct Solution:
```
n, p, k = list(map(int,input().split()))
if(p - k > 1):
print("<< ",end="")
for i in range(k):
if(p - k + i >= 1):
print(p - k + i,end=" ")
print("(",end="")
print(p,end=") ")
for i in range(k):
if(p + i + 1 <= n):
print(p + i + 1,end=" ")
if(p + k < n):
print(">>")
```
| 101,514 |
Provide tags and a correct Python 3 solution for this coding contest problem.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Tags: implementation
Correct Solution:
```
n, p, k = list(map(int, input().split()))
l = []
i = 0
e = 0
while (i <= k*2 and e<n):
e = p-k+i
if e > 0:
l.append(e)
i = i+1
if l[0] > 1:
print('<<', end = ' ')
for i in l:
if i == p:
i = '('+str(i)+')'
print(i, end = ' ')
if l[len(l)-1] < n:
print('>>')
```
| 101,515 |
Provide tags and a correct Python 3 solution for this coding contest problem.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Tags: implementation
Correct Solution:
```
def pages(n,p,k):
output = ""
if p<1 or p>n :
return output
if p-k > 1 :
output += "<< "
for i in range(p-k, p+k+1):
if i <= n and i >= 1:
if i == p:
output += "(" + str(i) + ") "
else:
output += str(i) + " "
if p+k < n:
output += ">>"
return output
n,p,k = map(int, input().split())
print(pages(n, p, k))
```
| 101,516 |
Provide tags and a correct Python 3 solution for this coding contest problem.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Tags: implementation
Correct Solution:
```
# cook your dish here
p,n,k=map(int,input().split())
u=1
d=p+1
if n-k<=1:
ans=[]
else:
ans=["<<"]
if n+k+1<=p:
d=n+k+1
if n-k>0:
u=n-k
for i in range(u,d):
if i==n:
ans.append("("+str(n)+")")
else:
ans.append(i)
if n<p-k:
ans.append(">>")
ans=str(ans).replace(","," ")
ans=ans.replace("'","")
print(ans[1:-1])
```
| 101,517 |
Provide tags and a correct Python 3 solution for this coding contest problem.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Tags: implementation
Correct Solution:
```
entrada=input()
numbers=entrada.split()
n=int(numbers[0])
p=int(numbers[1])
k=int(numbers[2])
if p+k>=n and p-k<=1:
for i in range (1, n+1):
if i==p:
print("(" + str(p) + ")", end=" ")
else:
print(i,end=" ")
if p+k>=n and p-k>1:
print("<<", end=" ")
for i in range (p-k, n+1):
if i==p:
print("(" + str(p) + ")", end=" ")
else:
print(i,end=" ")
if p+k<n and p-k<=1:
for i in range (1, p+k+1):
if i==p:
print("(" + str(p) + ")", end=" ")
else:
print(i,end=" ")
print(">>")
if p+k<n and p-k>1:
print("<<", end=" ")
for i in range (p-k, p+k+1):
if i==p:
print("(" + str(p) + ")", end=" ")
else:
print(i,end=" ")
print(">>")
```
| 101,518 |
Provide tags and a correct Python 3 solution for this coding contest problem.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Tags: implementation
Correct Solution:
```
class Solution:
def navigation(self, n, p, k):
start = max(1, p-k)
end = min(p+k, n)
pagination = ""
if start > 1:
pagination += "<< "
while start <= end:
if start == p:
pagination += "(" + str(start) + ") "
else:
pagination += str(start) + " "
start += 1
if end < n:
pagination += ">>"
return pagination
sol = Solution()
# array = [11, 12, 1, 2, 13, 14, 3, 4]
# print(sol.thanosSort(array))
[n, p, k] = list(map(int, input().strip().split()))
print(sol.navigation(n, p, k))
```
| 101,519 |
Provide tags and a correct Python 3 solution for this coding contest problem.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Tags: implementation
Correct Solution:
```
a, b, c = map(int, input().split(" "))
# a → limit b→now c → range
ll = max(1, b-c)
rl = min(a, b + c )
left = [i for i in range(b - 1, ll-1, -1)]
right = [i for i in range(b + 1, rl + 1)]
l_bar = "<< "
if ll == 1:
l_bar = ""
r_bar = " >>"
if rl == a:
r_bar = ""
left.reverse()
print(l_bar, *(left), "({})".format(b), *(right), r_bar)
```
| 101,520 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Submitted Solution:
```
x,y,z=map(int,input().split())
ok=1
ko=1
if 1>=y-z :
ok=0
if x<=y+z :
ko=0
if ok==1 :
print("<<",end=' ')
for i in range(max(1,y-z),min(x,y+z)+1) :
if i == y :
print('(',end='')
print(i,end='')
print(')',end=' ')
else:
print(i,end=' ')
if ko == 1:
print(">>")
```
Yes
| 101,521 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Submitted Solution:
```
n = list(map(lambda x: int(x), input().split(' ')))
n, p, k = n[0], n[1], n[2]
pages = []
for i in range(-k, k+1):
if p + i == p:
pages.append(f'({p})')
elif p + i > 0 and p + i < n + 1:
pages.append(str(p+i))
if '1' not in pages and '(1)' not in pages:
pages.insert(0, '<<')
if str(n) not in pages and f'({n})' not in pages:
pages.append('>>')
print(str(' '.join(pages)))
```
Yes
| 101,522 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Submitted Solution:
```
a,b,k = map(int,input().split(" "))
flag1 = True
flag2 = True
if b-k > 1:
print("<<",end=" ")
for i in range(b-k,b+k+1):
if i > a:
break
if i > 0:
if i == b:
print("("+str(i)+")",end=" ")
else:
print(i,end=" ")
if b+k < a:
print(">>")
```
Yes
| 101,523 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Submitted Solution:
```
# cook your dish here
n,p,k = map(int,(input()).split())
result_list = ['({p})'.format(p=p)]
end=beg=p
if p<n:
for i in range(k):
if end>=n:
break
end+=1
result_list.append(end)
if end<n:
result_list.append('>>')
if p>1:
for i in range(k):
if beg<=1:
break
beg-=1
result_list.insert(0,beg)
if beg>1:
result_list.insert(0,'<<')
for i in result_list:
print(i,end=' ')
```
Yes
| 101,524 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Submitted Solution:
```
output=''
n, p , k = input().split()
n = int(n)
p=int(p)
k = int(k)
for i in range(p-k,p+k+1):
if i <=0:
pass
elif i == p:
output+= '(' + str(i) + ') '
elif i == n:
output+= str(i) + ' '
break
else:
output+= str(i) + ' '
if output[0:2]== '1 ' or output[0]== '(':
pass
else:
output = '<< ' + output
if output[-2] == str(n) or output[-2] == ')':
pass
else:
output = output + '>>'
print(output)
```
No
| 101,525 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Submitted Solution:
```
n, p, k = map(int, input().split())
if (p - k > 1) and (p + k < n):
print("<< ", end="")
for c in range(p - k, p + k + 1):
if c == p:
print('(' + str(p) + ')', end=" ")
else:
print(str(c) + " ", end="")
print(">>")
elif p - k <= 1:
for c in range(1, p + k + 1):
if c == p:
print('(' + str(p) + ')', end=" ")
else:
print(str(c) + " ", end="")
print(">>")
else:
print("<< ", end="")
for c in range(p - k, n + 1):
if c == p:
print('(' + str(p) + ')', end=" ")
else:
print(str(c) + " ", end="")
```
No
| 101,526 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Submitted Solution:
```
n, p, k = map(int, input().split())
mas = []
for i in range(p , p - k - 1,-1):
if i == 1:
mas.append(i)
break
else:
mas.append(i)
mas.reverse()
for i in range(p + 1, p + k + 1):
if i == n:
mas.append(i)
break
else:
mas.append(i)
if mas[0] != 1:
print("<<", end = " ")
for i in mas:
if i == p:
print("({})".format(i), end = " ")
else:
print(i, end = " ")
if mas[-1] != n:
print(">>")
```
No
| 101,527 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this:
<< p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >>
When someone clicks the button "<<" he is redirected to page 1, and when someone clicks the button ">>" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.
There are some conditions in the navigation:
* If page 1 is in the navigation, the button "<<" must not be printed.
* If page n is in the navigation, the button ">>" must not be printed.
* If the page number is smaller than 1 or greater than n, it must not be printed.
You can see some examples of the navigations. Make a program that prints the navigation.
Input
The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)
Output
Print the proper navigation. Follow the format of the output from the test samples.
Examples
Input
17 5 2
Output
<< 3 4 (5) 6 7 >>
Input
6 5 2
Output
<< 3 4 (5) 6
Input
6 1 2
Output
(1) 2 3 >>
Input
6 2 2
Output
1 (2) 3 4 >>
Input
9 6 3
Output
<< 3 4 5 (6) 7 8 9
Input
10 6 3
Output
<< 3 4 5 (6) 7 8 9 >>
Input
8 5 4
Output
1 2 3 4 (5) 6 7 8
Submitted Solution:
```
def solve():
n, p, k = map(int, input().split())
pages = range(1, n + 1)
result = []
if p - 1 - k > 1:
result.append('<<')
left_side = p - 1 - k
left_side = left_side if left_side > 0 else 0
result.extend(pages[left_side:p - 1])
result.append('({})'.format(pages[p - 1]))
result.extend(pages[p:p + k])
if p + k < n:
result.append('>>')
print(' '.join(map(str, result)))
```
No
| 101,528 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Tags: implementation
Correct Solution:
```
s = input()
if s == s[::-1] and not 'N' in s and not 'L' in s and not'G' in s and not 'F' in s and not 'R' in s and not 'S' in s and not 'C' in s and not 'Q' in s and not 'B' in s and not 'E' in s and not 'D' in s and not 'J' in s and not 'K' in s and not 'Z' in s and not 'P' in s:
print('YES')
else:
print('NO')
```
| 101,529 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Tags: implementation
Correct Solution:
```
cup = set('AHIMOTUVWXY')
s = input()
if not set(s).issubset(cup):
print('NO')
exit()
ls = list(s)
ls.reverse()
t = ''.join(ls)
if s == t:
print('YES')
else:
print('NO')
```
| 101,530 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Tags: implementation
Correct Solution:
```
def main():
name = input()
s = ('B', 'C', 'D', 'E', 'F', 'G', 'J', 'K', 'L', 'N', 'P', 'Q', 'R', 'S', 'Z')
for ch in s:
if ch in name:
print('NO')
return
if name[:len(name) // 2] != name[::-1][:len(name) // 2]:
print('NO')
return
print('YES')
main()
```
| 101,531 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Tags: implementation
Correct Solution:
```
class CodeforcesTask421BSolution:
def __init__(self):
self.result = ''
self.name = ''
def read_input(self):
self.name = input()
def process_task(self):
symetric = "AHIMOTUVWXY"
origin = self.name[len(self.name) // 2 + len(self.name) % 2 - 1:]
mirror = self.name[::-1][len(self.name) // 2 + len(self.name) % 2 - 1:]
#if "VAAOWHUOTHTHHYOAIAYUXI" in self.name:
# print(origin[:50], mirror[:50])
if origin != mirror:
self.result = "NO"
else:
can_ = True
for c in self.name:
if c not in symetric:
can_ = False
break
self.result = "YES" if can_ else "NO"
def get_result(self):
return self.result
if __name__ == "__main__":
Solution = CodeforcesTask421BSolution()
Solution.read_input()
Solution.process_task()
print(Solution.get_result())
```
| 101,532 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Tags: implementation
Correct Solution:
```
i=input()
n=len(i)
d="BCDEFGJKLNPQRSZ"
for x in i:
if x in d:
print("NO")
break
else:
for x in range(n // 2):
if i[x] != i[n - x - 1]:
print("NO")
break
else:
print("YES")
```
| 101,533 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Tags: implementation
Correct Solution:
```
l=input()
print(["NO","YES"][all([p in "AHIMOTUVWXY"for p in l])and l==l[::-1]])
# Made By Mostafa_Khaled
```
| 101,534 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Tags: implementation
Correct Solution:
```
# Name : Sachdev Hitesh
# College : GLSICA
user = input()
resu = user[::-1]
s = len(user)
#print(s)
c = 0
if user == resu:
for i in user:
if i == 'A' or i == 'H' or i == 'I' or i == 'O' or i == 'T' or i == 'V' or \
i == 'W' or i == 'X' or i == 'Y' or i == 'M' or i == 'U' :
c = c + 1
if c == s:
print("YES")
else:
print("NO")
```
| 101,535 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Tags: implementation
Correct Solution:
```
s = input()
l = {'A', 'H', 'I', 'M', 'O', 'T', 'U', 'V', 'W', 'X', 'Y'}
i = 0
j = len(s) - 1
y = True
while i <= j:
if s[i] != s[j] or s[i] not in l:
y = False
break
i += 1
j -= 1
if y:
print('YES')
else:
print('NO')
```
| 101,536 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Submitted Solution:
```
t=list(input())
if t==t[::-1]:
f=set(t)
h=set(list('BCDEFGJKLNPQRSZ'))
if f&h==set():
print('YES')
else:
print('NO')
else:
print('NO')
```
Yes
| 101,537 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Submitted Solution:
```
n=input()
i=0
k=len(n)-1
_b=True
while i<=k and _b:
if n[i]==n[k] and n[i] in ['A','H','I','M','O','T','U','V','W','X','Y']:
_b=True
i+=1
k-=1
else:
_b=False
if _b: print('YES')
else: print('NO')
```
Yes
| 101,538 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Submitted Solution:
```
s = input()
a = set([chr(i + ord('A')) for i in range(26)])
b = set(s)
c = set(['A', 'H', 'I', 'M', 'O', 'T', 'U', 'V', 'W', 'X', 'Y'])
a &= b
if a<=c and s==s[::-1]:
print('YES')
else:
print('NO')
```
Yes
| 101,539 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Submitted Solution:
```
word = list(input())
def poop(word):
correct = ['A','H','I','M','O','T','U','V','W','X','Y']
for i in word:
if i not in correct:
return "NO"
if list(reversed(word)) == word:
return "YES"
return "NO"
print(poop(word))
```
Yes
| 101,540 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Submitted Solution:
```
def rev(n):
s=''
for i in range(len(n)-1,-1,-1):
s+=n[i]
return s
l=['A','H','I','M','O','T','U','V,','W','X','Y']
n=input()
i=0
while i<len(n):
if(n[i] in l):
i+=1
else:
i=0
break
if(i==0):
print('NO')
else:
if(len(n)%2==0):
j=len(n)//2
a=n[0:j]
b=rev(n[j:])
if(a==b):
print('YES')
else:
print('NO')
else:
j=len(n)//2
a=n[0:j]
b=rev(n[j+1:])
if(a==b):
print('YES')
else:
print('NO')
```
No
| 101,541 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Submitted Solution:
```
ch=input()
b=len(ch)
if (len(ch)==1):
print("NO")
elif(b%2==0):
if(ch[:int(b/2)]==ch[int(b/2):][::-1]):
print("YES")
else :
print("NO")
elif(b%2!=0):
if(ch[:int(b/2)]==ch[int(b/2)+1:][::-1]):
print("YES")
else :
print("NO")
```
No
| 101,542 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Submitted Solution:
```
# Name : Sachdev Hitesh
# College : GLSICA
user = input()
resu = user[::-1]
c = 0
if user == resu:
for i in user:
if i == 'A' or i == 'H' or i == 'I' or i == 'O' or i == 'T' or i == 'V' or \
i == 'W' or i == 'X' or i == 'Y' :
c = c + 1
if c == 0:
print("NO")
else:
print("YES")
```
No
| 101,543 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Recently, a start up by two students of a state university of city F gained incredible popularity. Now it's time to start a new company. But what do we call it?
The market analysts came up with a very smart plan: the name of the company should be identical to its reflection in a mirror! In other words, if we write out the name of the company on a piece of paper in a line (horizontally, from left to right) with large English letters, then put this piece of paper in front of the mirror, then the reflection of the name in the mirror should perfectly match the line written on the piece of paper.
There are many suggestions for the company name, so coming up to the mirror with a piece of paper for each name wouldn't be sensible. The founders of the company decided to automatize this process. They asked you to write a program that can, given a word, determine whether the word is a 'mirror' word or not.
Input
The first line contains a non-empty name that needs to be checked. The name contains at most 105 large English letters. The name will be written with the next sans serif font:
<image>
Output
Print 'YES' (without the quotes), if the given name matches its mirror reflection. Otherwise, print 'NO' (without the quotes).
Examples
Input
AHA
Output
YES
Input
Z
Output
NO
Input
XO
Output
NO
Submitted Solution:
```
ch=input()
b=len(ch)
if (len(ch)==1):
print("NO")
if(b%2==0):
if(ch[:int(b/2)]==ch[int(b/2):]):
print("YES")
else :
print("NO")
if(b%2!=0):
if(ch[:int(b/2)]==ch[int(b/2)+1:]):
print("YES")
else :
print("NO")
```
No
| 101,544 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Tags: brute force, implementation
Correct Solution:
```
n=int(input())
j,k=1,1
for i in range(n-1):
if j<n:
print(j+1)
else:
print((j%n)+1)
k+=1
j+=k
```
| 101,545 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Tags: brute force, implementation
Correct Solution:
```
def main_function():
n = int(input())
throw_counter = 1
children_who_got_the_ball = []
ball_holder = 1
while throw_counter < n:
if ball_holder + throw_counter <= n:
ball_holder += throw_counter
else:
ball_holder = ball_holder + throw_counter - n
#if not str(ball_holder) in children_who_got_the_ball:
children_who_got_the_ball.append(str(ball_holder))
throw_counter += 1
return " ".join(children_who_got_the_ball)
print(main_function())
```
| 101,546 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Tags: brute force, implementation
Correct Solution:
```
# import sys
# sys.stdin=open('input.in','r')
# sys.stdout=open('output.out','w')
n=int(input())
k=1
p=1
for x in range(n-1):
k+=p
if k>n:
print(k-n,end=' ')
k=k-n
else:
print(k,end=' ')
p+=1
```
| 101,547 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Tags: brute force, implementation
Correct Solution:
```
import math
n=int(input())
cur=1
for i in range(n-1):
cur=(cur+i+1)%n
if cur==0:
cur=n
if i<n-2:
print(cur,end=' ')
print(cur)
```
| 101,548 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Tags: brute force, implementation
Correct Solution:
```
# -*- coding: utf-8 -*-
"""
Created on Tue Mar 30 19:32:51 2021
@author: nehas
"""
n=int(input())
c=2
print(c,end=" ")
for i in range(2,n):
c=c+i
if(c>n):
c=c-n
print(c,end=" ")
```
| 101,549 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Tags: brute force, implementation
Correct Solution:
```
n = int(input())
c = 0
for i in range(n-1):
c=(c+i+1)%n
print(c+1, ' ')
```
| 101,550 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Tags: brute force, implementation
Correct Solution:
```
n=int(input())
m=2
print(m,end=' ')
for i in range(2,n):
m=m+i
if m>n:
m=m-n
print(m,end=' ')
```
| 101,551 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Tags: brute force, implementation
Correct Solution:
```
# https://codeforces.com/problemset/problem/46/A
n = int(input().strip())
ball_ps = 1
for i in range(1, n):
ball_ps += i
if ball_ps > n:
ball_ps = ball_ps - n
print(ball_ps, end=' ')
```
| 101,552 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Submitted Solution:
```
# import sys
# sys.stdin = open("test.in","r")
# sys.stdout = open("test.out","w")
n=int(input())
a=0
for i in range(n-1):
a=(a+i+1)%n
print(a+1,end=" ")
```
Yes
| 101,553 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Submitted Solution:
```
n, k, a = int(input()), 0, []
for d in range(1, n):
k = (k + d) % n
a.append(k + 1)
print(*a)
```
Yes
| 101,554 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Submitted Solution:
```
import os
import sys
debug = True
if debug and os.path.exists("input.in"):
input = open("input.in", "r").readline
else:
debug = False
input = sys.stdin.readline
def inp():
return (int(input()))
def inlt():
return (list(map(int, input().split())))
def insr():
s = input()
return (list(s[:len(s) - 1]))
def invr():
return (map(int, input().split()))
test_count = 1
if debug:
test_count = inp()
for t in range(test_count):
if debug:
print("Test Case #", t + 1)
# Start code here
n = inp()
start = 1
ans = list()
for i in range(1, n):
start += i
if start > n:
start = start % n
ans.append(start)
print(" ".join(map(str, ans)))
```
Yes
| 101,555 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Submitted Solution:
```
a=int(input())
v=a
g=0
i=1
while i<v:
g=g+i
b=g%a
i+=1
print(b+1," ")
```
Yes
| 101,556 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Submitted Solution:
```
# https://codeforces.com/problemset/problem/46/A
n = int(input())
a = 1
for i in range(1, n):
a += i
print(a % n, end=" ")
```
No
| 101,557 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Submitted Solution:
```
prev=int(1)
cur=int(1)
n=int(input())
for i in range(1,n):
prev+=cur
print((prev%n),end=" ")
cur+=1
```
No
| 101,558 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Submitted Solution:
```
import math,itertools,fractions,heapq,collections,bisect,sys,queue,copy
sys.setrecursionlimit(10**7)
inf=10**20
mod=10**9+7
dd=[(-1,0),(0,1),(1,0),(0,-1)]
ddn=[(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
# def LF(): return [float(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def LS(): return sys.stdin.readline().split()
def S(): return input()
def main():
n=I()
st=1
haba=0
ans=[]
for i in range(n-1):
haba+=1
st+=haba
st%=n
ans.append(st)
return ' '.join(str(x) for x in ans)
# main()
print(main())
```
No
| 101,559 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
A kindergarten teacher Natalia Pavlovna has invented a new ball game. This game not only develops the children's physique, but also teaches them how to count.
The game goes as follows. Kids stand in circle. Let's agree to think of the children as numbered with numbers from 1 to n clockwise and the child number 1 is holding the ball. First the first child throws the ball to the next one clockwise, i.e. to the child number 2. Then the child number 2 throws the ball to the next but one child, i.e. to the child number 4, then the fourth child throws the ball to the child that stands two children away from him, i.e. to the child number 7, then the ball is thrown to the child who stands 3 children away from the child number 7, then the ball is thrown to the child who stands 4 children away from the last one, and so on. It should be mentioned that when a ball is thrown it may pass the beginning of the circle. For example, if n = 5, then after the third throw the child number 2 has the ball again. Overall, n - 1 throws are made, and the game ends.
The problem is that not all the children get the ball during the game. If a child doesn't get the ball, he gets very upset and cries until Natalia Pavlovna gives him a candy. That's why Natalia Pavlovna asks you to help her to identify the numbers of the children who will get the ball after each throw.
Input
The first line contains integer n (2 ≤ n ≤ 100) which indicates the number of kids in the circle.
Output
In the single line print n - 1 numbers which are the numbers of children who will get the ball after each throw. Separate the numbers by spaces.
Examples
Input
10
Output
2 4 7 1 6 2 9 7 6
Input
3
Output
2 1
Submitted Solution:
```
n=int(input())
count=1
store=2
for i in range(n-1):
if store<=n:
print(store,'',end='')
else:
print(store%n,'',end='')
count+=1
store+=count
```
No
| 101,560 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Tags: binary search, implementation, math, sortings
Correct Solution:
```
nl = list(map(int, input().split()))
n = nl[0]
l = nl[1]
a = list(map(int, input().split()))
a.sort()
last = 0
max_dist = max(a[0], l - a[-1])
for elem in a:
if (elem - last) / 2 > max_dist:
max_dist = (elem - last) / 2
last = elem
print(max_dist)
```
| 101,561 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Tags: binary search, implementation, math, sortings
Correct Solution:
```
# You lost the game.
n, l = map(int, input().split())
L = list(map(int, input().split()))
L.sort()
L = [-L[0]]+L+[2*l-L[n-1]]
r = 0
for i in range(n+1):
if (L[i+1]-L[i])/2>r:
r = (L[i+1]-L[i])/2
print(r)
```
| 101,562 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Tags: binary search, implementation, math, sortings
Correct Solution:
```
n, l = map (int, input().split())
a = sorted(map(int, input().split()))
gap = 0
#print(max([a[0], l - a[n-1]] + [(a[i+1]-a[i])/2 for i in range (n-1)]))
for i in range(n-1):
if gap < (a[i+1]-a[i])/2:
gap = (a[i+1]-a[i])/2
print(max(a[0], gap, l - a[n-1]))
```
| 101,563 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Tags: binary search, implementation, math, sortings
Correct Solution:
```
n,l = map(int,input().split())
Line = [int(i) for i in input().split()]
Line.sort()
k = max(Line[0],l-Line[n-1])
for i in range(1,n):
p = Line[i]-Line[i-1]
k = max(k,p/2)
print(k)
```
| 101,564 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Tags: binary search, implementation, math, sortings
Correct Solution:
```
first = input().split(" ")
n = int(first[0])
l = int(first[1])
second = [int(s) for s in input().split(" ")]
second.sort()
d = 0
for i in range(len(second)-1):
d = max(second[i+1]-second[i], d)
if second[0] != 0 and second[-1] != l:
print(max(max(second[0], d/2), max(l-second[-1], d/2)))
elif second[0] != 0:
print(max(second[0], d/2))
elif second[-1] != l:
print(max(l-second[-1], d/2))
else:
print(d / 2)
```
| 101,565 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Tags: binary search, implementation, math, sortings
Correct Solution:
```
[n, l] = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]
a.append(0)
a.append(l)
a.sort()
a = [a[i+1] - a[i] for i in range(len(a) - 1)]
a[0] = a[0] * 2
a[len(a) - 1] = a[len(a) - 1] * 2
print(max(a)/2)
```
| 101,566 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Tags: binary search, implementation, math, sortings
Correct Solution:
```
n,m=map(int,input().split())
l=sorted(list(map(int,input().split())))
r=[min(l),m-max(l)]
for i in range(1,len(l)):
r.append((l[i]-l[i-1])/2)
print(max(r))
```
| 101,567 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Tags: binary search, implementation, math, sortings
Correct Solution:
```
n,l=map(int,input().split())
A=list(map(int,input().split()))
B=sorted(A)
C=[]
if n==1:
print(max(A[0],l-A[0]))
else:
for i in range(1,n):
b=B[i]-B[i-1]
C.append(b)
c=max(C)
d=max(c,2*B[0],2*(l-B[n-1]))
print(float(d/2))
```
| 101,568 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Submitted Solution:
```
n, l = map(int, input().split())
ls = list(map(int, input().split()))
ls.sort()
d = [ls[i+1] - ls[i] for i in range(len(ls)-1)]
d = list(map(lambda x: x/2, d)) + [ls[0], l-ls[n-1]]
print(max(d))
```
Yes
| 101,569 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Submitted Solution:
```
n, l = map(int, input().split())
list_of_lantern = list(map(int, input().split()))
sort_list = sorted(list_of_lantern)
ans = max(sort_list[0], l - sort_list[n - 1])
for i in range(n - 1):
ans = max(ans, (sort_list[i+1] - sort_list[i]) / 2)
print(ans)
```
Yes
| 101,570 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Submitted Solution:
```
entrada = list(map(int, input().split()))
linternas = list(map(int, input().split()))
final = entrada[1]
linternas.sort()
max = linternas[0]
prev = 0
for j in linternas:
distance = (j - prev)/2
if distance>max:
max = distance
prev = j
if (final-linternas[-1]) > max:
max = final-linternas[-1]
print (max)
```
Yes
| 101,571 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Submitted Solution:
```
n,l = map(int,input().split())
a=list(map(int,input().split()))
a.sort()
m=0
for i in range(n-1):
m=max(m,a[i+1]-a[i])
m=m/2
m=max(a[0]-0, m, l-a[n-1])
m=m*(1.0000000000)
print("{0:.10f}".format(m))
```
Yes
| 101,572 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Submitted Solution:
```
LT=input()
L=input()
LT=LT.split(" ")
L=L.split(" ")
Tama=L
Tama.append(0)
Tama.append(LT[1])
print(Tama)
T=[]
for i in range(0,len(Tama)):
T.append(int(Tama[i]))
Tama=T
Tama=sorted(Tama)
D=[]
print(len(Tama))
print(Tama)
for i in range(0,len(Tama)-1):
if(i==0 or i==len(Tama)):
D.append(Tama[i+1]-Tama[i])
else:
D.append((Tama[i+1]-Tama[i])/2)
D=sorted(D)
print(D[-1:])
```
No
| 101,573 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Submitted Solution:
```
n, l = map(int, input().split())
a = sorted(map(int, input().split()))
dis = [a[i+1]-a[i] for i in range(n-1)]
if a[0] == 0:
print(max(dis)/2)
else:
if max(dis)/2 < a[0]:
print(a[0])
else:
print(max(dis)/2)
```
No
| 101,574 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Submitted Solution:
```
n,l=[int(x) for x in input().split()]
m= list(map(int,input().split()))
m.sort()
maxi=0
for i in range(len(m)-1):
if m[i+1]-m[i]>maxi:
maxi=m[i+1]-m[i]
if 0 not in m:
print(m[0])
else:
print(maxi/2)
print(m)
```
No
| 101,575 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Vanya walks late at night along a straight street of length l, lit by n lanterns. Consider the coordinate system with the beginning of the street corresponding to the point 0, and its end corresponding to the point l. Then the i-th lantern is at the point ai. The lantern lights all points of the street that are at the distance of at most d from it, where d is some positive number, common for all lanterns.
Vanya wonders: what is the minimum light radius d should the lanterns have to light the whole street?
Input
The first line contains two integers n, l (1 ≤ n ≤ 1000, 1 ≤ l ≤ 109) — the number of lanterns and the length of the street respectively.
The next line contains n integers ai (0 ≤ ai ≤ l). Multiple lanterns can be located at the same point. The lanterns may be located at the ends of the street.
Output
Print the minimum light radius d, needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.
Examples
Input
7 15
15 5 3 7 9 14 0
Output
2.5000000000
Input
2 5
2 5
Output
2.0000000000
Note
Consider the second sample. At d = 2 the first lantern will light the segment [0, 4] of the street, and the second lantern will light segment [3, 5]. Thus, the whole street will be lit.
Submitted Solution:
```
"""
IIIIIIIIII OOOOOOOOOOO IIIIIIIIII
II OO OO II
II OO OO II
II OO OO II
II OO OO II
II OO OO II
II OO OO II
IIIIIIIIII OOOOOOOOOOO IIIIIIIIII
"""
n, l = map(int, input().split())
m = list(map(int, input().split()))
m.sort(reverse = True)
mx = -float("inf")
for i in range(n - 1):
mx = max(m[i] - m[i + 1], mx)
mx /= 2
if 0 not in m:
mx += abs(mx - abs(m[-1] - mx))
if l not in m:
mx += abs(mx - (l - m[0]))
print("%.10f" %mx)
```
No
| 101,576 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Tags: greedy, math, sortings
Correct Solution:
```
x = int(input())
y = input()
ct = {0:[0, 0, 0, 0], 1:[0, 0, 0, 0], 2:[1, 0, 0, 0], 3:[1, 1, 0, 0], 4:[3, 1, 0, 0], 5:[3, 1, 1, 0], 6:[4, 2, 1, 0], 7:[4, 2, 1, 1], 8:[7, 2, 1, 1], 9:[7, 4, 1, 1]}
real = {2:[1, 0, 0, 0], 3:[1, 1, 0, 0], 4:[3, 1, 0, 0], 5:[3, 1, 1, 0], 6:[4, 2, 1, 0], 7:[4, 2, 1, 1], 8:[7, 2, 1, 1], 9:[7, 4, 1, 1]}
ut = {2:[1, 0, 0, 0], 3:[1, 1, 0, 0], 5:[3, 1, 1, 0], 7:[4, 2, 1, 1]}
lx = [0, 0, 0, 0]
for i in y:
i = int(i)
bad = ct[i]
lx[0] += bad[0]
lx[1] += bad[1]
lx[2] += bad[2]
lx[3] += bad[3]
s = ''
if lx[-1] >= 1:
copies = lx[-1]
lx[0] -= 4*copies
lx[1] -= 2*copies
lx[2] -= copies
lx[3] -= copies
s += '7' * copies
if lx[-2] >= 1:
copies = lx[-2]
lx[0] -= 3*copies
lx[1] -= copies
lx[2] -= copies
s += '5' * copies
if lx[-3] >= 1:
copies = lx[-3]
lx[0] -= copies
lx[1] -= copies
s += '3' * copies
if lx[-4] >= 1:
copies = lx[-4]
lx[0] -= copies
s += '2' * copies
print(s)
```
| 101,577 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Tags: greedy, math, sortings
Correct Solution:
```
n = input()
s = input()
s = s.replace('9','7332')
s = s.replace('8','7222')
s = s.replace('6','53')
s = s.replace('4','322')
s = s.replace('1','')
s = s.replace('0','')
s = ''.join(sorted(s,reverse=True))
print(s)
```
| 101,578 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Tags: greedy, math, sortings
Correct Solution:
```
I=lambda:list(map(int,input().split()))
n=I()
f=['','','2','3','223','5','53','7','7222','7332']
v=''
for i in input():
v+=f[int(i)]
v=list(v)
v.sort(reverse=True)
print(''.join(v))
```
| 101,579 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Tags: greedy, math, sortings
Correct Solution:
```
n=int(input())
a=[int(x) for x in list(input())]
fac={2:0,3:0,5:0,7:0}
ans=[]
for i in range(2,10):
t=a.count(i)
if i==9:
fac[2]+=7*t
fac[3]+=4*t
fac[5]+=t
fac[7]+=t
if i==8:
fac[2]+=7*t
fac[3]+=2*t
fac[5]+=t
fac[7]+=t
if i==7:
fac[2]+=4*t
fac[3]+=2*t
fac[5]+=t
fac[7]+=t
if i==6:
fac[2]+=4*t
fac[3]+=2*t
fac[5]+=t
if i==5:
fac[2]+=3*t
fac[3]+=t
fac[5]+=t
if i==4:
fac[2]+=3*t
fac[3]+=t
if i==3:
fac[2]+=t
fac[3]+=t
if i==2:
fac[2]+=t
for i in [7,5,3,2]:
t=fac[i]
ans=ans+[i]*t
if i==7:
fac[2]-=4*t
fac[3]-=2*t
fac[5]-=t
fac[7]-=t
if i==5:
fac[2]-=3*t
fac[3]-=t
fac[5]-=t
if i==3:
fac[2]-=t
fac[3]-=t
ans.sort(reverse=True)
print(''.join([str(x) for x in ans]))
```
| 101,580 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Tags: greedy, math, sortings
Correct Solution:
```
n = int(input())
s = input()
ans = ""
for i in s:
if(i=="1" or i=="0"):
continue
elif(i=="4"):
ans+="322"
elif(i=="6"):
ans+="53"
elif(i=="8"):
ans+="7222"
elif(i=="9"):
ans+="7332"
else:
ans+=i
ans = list(ans)
ans.sort(reverse=True)
for i in ans:
print(i,end="")
```
| 101,581 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Tags: greedy, math, sortings
Correct Solution:
```
a = int(input())
b = str(input())
answer = list()
for x in b:
if x != "0" and x != "1":
if x == "4":
answer += ["3", "2", "2"]
elif x == "6":
answer += ["5", "3"]
elif x == "8":
answer += ["7", "2", "2", "2"]
elif x == "9":
answer += ["7", "3", "3", "2"]
else:
answer += x
answer.sort()
answer.reverse()
final = ""
for x in answer:
final += x
print(final)
```
| 101,582 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Tags: greedy, math, sortings
Correct Solution:
```
a = input("")
b = input("")
outstring = ""
for value in b:
if value == "1":
continue
elif value == "2":
outstring = outstring + "2"
elif value == "3":
outstring = outstring + "3"
elif value == "4":
outstring = outstring + "3" + "2" + "2"
elif value == "5":
outstring = outstring + "5"
elif value == "6":
outstring = outstring + "5" + "3"
elif value == "7":
outstring = outstring + "7"
elif value == "8":
outstring = outstring + "7" + "2" + "2" + "2"
elif value == "9":
outstring = outstring + "7" + "3" + "3" + "2"
t = [i for i in outstring]
t.sort()
t.reverse()
print(''.join(t))
```
| 101,583 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Tags: greedy, math, sortings
Correct Solution:
```
def aus(argument):
switcher = {
0:[],
1:[],
2:[2],
3:[3],
4:[3,2,2],
5:[5],
6:[3,5],
7:[7],
8:[2,2,2,7],
9:[2,3,3,7],
}
return switcher.get(argument)
summ=[]
a= int(input())
b= input()
for i in range(a):
summ += aus(int(b[i]))
summ.sort(reverse=True)
print(int(''.join(map(str, summ))))
```
| 101,584 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Submitted Solution:
```
import string
NUMBERS=[]
def factor(x):
if x == 2 or x==5 or x== 7:
NUMBERS.append(x)
return
else:
xx = x
while x!= 1:
for i in range(2,4):
if x%i==0:
x = x/i
NUMBERS.append(i)
factor(xx-1)
return
n = int(input())
input_value = input()
num = []
j = 0
for i in range(n):
if input_value[i] != '1' and input_value[i] != '0':
num.append(int(input_value[i]))
j = j+1
for x in num:
factor (x)
kkk=NUMBERS
kkk.sort(reverse=True )
for x in NUMBERS:
if x==3:
kkk.pop()
print("".join( map(str, kkk)))
```
Yes
| 101,585 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Submitted Solution:
```
n = int(input())
num = str(input())
primes = {2: 0, 3: 0, 5: 0, 7: 0}
for i in range(n):
k = int(num[i])
if (k <= 1):
continue
primes[2] += 1
if (k >= 3):
primes[3] += 1
if (k >= 4):
primes[2] += 2
if (k >= 5):
primes[5] += 1
if (k >= 6):
primes[2] += 1
primes[3] += 1
if (k >= 7):
primes[7] += 1
if (k >= 8):
primes[2] += 3
if (k == 9):
primes[3] += 2
for i in range(primes[7]):
print(7, end='')
primes[2] -= 4
primes[3] -= 2
primes[5] -= 1
for i in range(primes[5]):
print(5, end='')
primes[2] -= 3
primes[3] -= 1
for i in range(primes[3]):
print(3, end='')
primes[2] -= 1
for i in range(primes[2]):
print(2, end='')
print("\n")
```
Yes
| 101,586 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Submitted Solution:
```
import math
import sys
n=int(input())
s=input()
v=[]
for i in range(0,n):
if s[i] == '2':
v.append(2)
if s[i] == '3':
v.append(3)
if s[i] == '4':
v.append(2)
v.append(2)
v.append(3)
if s[i] == '5':
v.append(5)
if s[i] == '6':
v.append(5)
v.append(3)
if s[i] == '7':
v.append(7)
if s[i] == '8':
v.append(7)
v.append(2)
v.append(2)
v.append(2)
if s[i] == '9':
v.append(7)
v.append(2)
v.append(3)
v.append(3)
v.sort()
m=0
t=1
for i in range(0,len(v)):
m+=v[i]*t
t*=10
print(m)
```
Yes
| 101,587 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Submitted Solution:
```
list1=["","","2","3","322","5","53","7","7222","7332"]
n=int(input())
p=input()
k=[]
for i in p:
k.append(list1[int(i)])
print("".join(sorted("".join(k),reverse=True)))
```
Yes
| 101,588 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Submitted Solution:
```
import math
import sys
n=int(input())
s=input()
v=[]
for i in range(0,n):
if s[i] == '2':
v.append(2)
if s[i] == '3':
v.append(3)
if s[i] == '4':
v.append(2)
v.append(2)
v.append(3)
if s[i] == '5':
v.append(5)
if s[i] == '6':
v.append(5)
v.append(2)
v.append(3)
if s[i] == '7':
v.append(7)
if s[i] == '8':
v.append(7)
v.append(2)
v.append(2)
v.append(2)
if s[i] == '9':
v.append(7)
v.append(2)
v.append(2)
v.append(2)
v.append(3)
v.append(3)
v.sort()
m=0
t=1
for i in range(0,len(v)):
m+=v[i]*t
t*=10
print(m)
```
No
| 101,589 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Submitted Solution:
```
input()
s=input()
a=""
t=[a,a,"2","3","223","5","53","7","7222","7333"]
for c in s:
a+=t[int(c)]
print(''.join(sorted(a)[::-1]))
```
No
| 101,590 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Submitted Solution:
```
input()
s = input()
ans = []
for i in range(len(s)):
if s[i] >= '2':
ans.append(2)
if s[i] >= '3':
ans += [3]
if s[i] >= '4':
ans += [3,2,2]
if s[i] >= '5':
ans += [5]
if s[i] >= '6':
ans += [5,3]
if s[i] >= '7':
ans += [7]
if s[i] >= '8':
ans += [7,2,2,2]
if s[i] >= '9':
ans += [7,3,3,2]
ans = reversed(sorted(ans))
print(*ans, sep='')
```
No
| 101,591 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Drazil is playing a math game with Varda.
Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.
First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:
1. x doesn't contain neither digit 0 nor digit 1.
2. <image> = <image>.
Help friends find such number.
Input
The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.
The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.
Output
Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.
Examples
Input
4
1234
Output
33222
Input
3
555
Output
555
Note
In the first case, <image>
Submitted Solution:
```
from math import factorial, log2
from operator import mul
from functools import reduce
def drazil():
input()
n = input()
count = [0 for _ in range(10)]
for c in n:
c = int(c)
if c == 9:
c -= 1
count[3] += 2
while True:
if c in [2,3,5,7]:
count[c] += 1
break
elif c in [4,8]:
count[2] += int(log2(c))
elif c in [0,1]:
break
elif c == 6:
count[2] += 1
count[3] += 1
elif c == 9:
count[3] += 2
else:
print('Shit', c)
input()
c -= 1
s = ''
for i, n in enumerate(count):
s = str(i)*n + s
print(s)
if __name__ == '__main__':
drazil()
```
No
| 101,592 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers working on a large project have just received a task to write exactly m lines of code. There are n programmers working on a project, the i-th of them makes exactly ai bugs in every line of code that he writes.
Let's call a sequence of non-negative integers v1, v2, ..., vn a plan, if v1 + v2 + ... + vn = m. The programmers follow the plan like that: in the beginning the first programmer writes the first v1 lines of the given task, then the second programmer writes v2 more lines of the given task, and so on. In the end, the last programmer writes the remaining lines of the code. Let's call a plan good, if all the written lines of the task contain at most b bugs in total.
Your task is to determine how many distinct good plans are there. As the number of plans can be large, print the remainder of this number modulo given positive integer mod.
Input
The first line contains four integers n, m, b, mod (1 ≤ n, m ≤ 500, 0 ≤ b ≤ 500; 1 ≤ mod ≤ 109 + 7) — the number of programmers, the number of lines of code in the task, the maximum total number of bugs respectively and the modulo you should use when printing the answer.
The next line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 500) — the number of bugs per line for each programmer.
Output
Print a single integer — the answer to the problem modulo mod.
Examples
Input
3 3 3 100
1 1 1
Output
10
Input
3 6 5 1000000007
1 2 3
Output
0
Input
3 5 6 11
1 2 1
Output
0
Tags: dp
Correct Solution:
```
a = list(map(int, input().split()))
n = a[0]
m = a[1]
b = a[2]
mod = a[3]
ac = list(map(int,input().split()))
ac = [0] + ac
dp = [[[0 for k in range(b+1)] for _ in range(m+1)] for z in range(2)]
for i in range(n+1) :
for x in range(b+1) :
dp[i%2][0][x] = 1
for i in range(1,n+1) :
for j in range(1,m+1) :
for x in range(b+1) :
if ac[i] <= x :
dp[i%2][j][x] = (dp[(i-1)%2][j][x] + dp[i%2][j-1][x-ac[i]] ) % mod
else :
dp[i%2][j][x] = dp[(i-1)%2][j][x] % mod
print(dp[n%2][m][b])
```
| 101,593 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers working on a large project have just received a task to write exactly m lines of code. There are n programmers working on a project, the i-th of them makes exactly ai bugs in every line of code that he writes.
Let's call a sequence of non-negative integers v1, v2, ..., vn a plan, if v1 + v2 + ... + vn = m. The programmers follow the plan like that: in the beginning the first programmer writes the first v1 lines of the given task, then the second programmer writes v2 more lines of the given task, and so on. In the end, the last programmer writes the remaining lines of the code. Let's call a plan good, if all the written lines of the task contain at most b bugs in total.
Your task is to determine how many distinct good plans are there. As the number of plans can be large, print the remainder of this number modulo given positive integer mod.
Input
The first line contains four integers n, m, b, mod (1 ≤ n, m ≤ 500, 0 ≤ b ≤ 500; 1 ≤ mod ≤ 109 + 7) — the number of programmers, the number of lines of code in the task, the maximum total number of bugs respectively and the modulo you should use when printing the answer.
The next line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 500) — the number of bugs per line for each programmer.
Output
Print a single integer — the answer to the problem modulo mod.
Examples
Input
3 3 3 100
1 1 1
Output
10
Input
3 6 5 1000000007
1 2 3
Output
0
Input
3 5 6 11
1 2 1
Output
0
Tags: dp
Correct Solution:
```
n, m, b, mod = map(int, input().split())
a = list(map(int, input().split()))
dp = [[0 for i in range(b + 1)] for j in range(m + 1)]
dp[0][0] = 1
for i in range(n):
for ld in range(m):
for bugs in range(b + 1):
if bugs + a[i] <= b:
dp[ld + 1][bugs + a[i]] = (dp[ld + 1][bugs + a[i]] + dp[ld][bugs]) % mod
ans = 0
for i in range(0, b + 1):
ans = (ans + dp[m][i]) % mod
print(ans)
```
| 101,594 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers working on a large project have just received a task to write exactly m lines of code. There are n programmers working on a project, the i-th of them makes exactly ai bugs in every line of code that he writes.
Let's call a sequence of non-negative integers v1, v2, ..., vn a plan, if v1 + v2 + ... + vn = m. The programmers follow the plan like that: in the beginning the first programmer writes the first v1 lines of the given task, then the second programmer writes v2 more lines of the given task, and so on. In the end, the last programmer writes the remaining lines of the code. Let's call a plan good, if all the written lines of the task contain at most b bugs in total.
Your task is to determine how many distinct good plans are there. As the number of plans can be large, print the remainder of this number modulo given positive integer mod.
Input
The first line contains four integers n, m, b, mod (1 ≤ n, m ≤ 500, 0 ≤ b ≤ 500; 1 ≤ mod ≤ 109 + 7) — the number of programmers, the number of lines of code in the task, the maximum total number of bugs respectively and the modulo you should use when printing the answer.
The next line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 500) — the number of bugs per line for each programmer.
Output
Print a single integer — the answer to the problem modulo mod.
Examples
Input
3 3 3 100
1 1 1
Output
10
Input
3 6 5 1000000007
1 2 3
Output
0
Input
3 5 6 11
1 2 1
Output
0
Tags: dp
Correct Solution:
```
# Author : nitish420 --------------------------------------------------------------------
import os
import sys
from io import BytesIO, IOBase
def main():
n,m,b,mod=map(int,input().split())
arr=list(map(int,input().split()))
dp=[[0 for _ in range(b+1)] for _ in range(m+1)]
dp[0]=[1]*(b+1)
for item in arr:
for x in range(1,m+1):
for y in range(item,b+1):
dp[x][y]=(dp[x][y]+dp[x-1][y-item])%mod
print(dp[m][b])
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = 'x' in file.mode or 'r' not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b'\n') + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode('ascii'))
self.read = lambda: self.buffer.read().decode('ascii')
self.readline = lambda: self.buffer.readline().decode('ascii')
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip('\r\n')
# endregion
if __name__ == '__main__':
main()
```
| 101,595 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers working on a large project have just received a task to write exactly m lines of code. There are n programmers working on a project, the i-th of them makes exactly ai bugs in every line of code that he writes.
Let's call a sequence of non-negative integers v1, v2, ..., vn a plan, if v1 + v2 + ... + vn = m. The programmers follow the plan like that: in the beginning the first programmer writes the first v1 lines of the given task, then the second programmer writes v2 more lines of the given task, and so on. In the end, the last programmer writes the remaining lines of the code. Let's call a plan good, if all the written lines of the task contain at most b bugs in total.
Your task is to determine how many distinct good plans are there. As the number of plans can be large, print the remainder of this number modulo given positive integer mod.
Input
The first line contains four integers n, m, b, mod (1 ≤ n, m ≤ 500, 0 ≤ b ≤ 500; 1 ≤ mod ≤ 109 + 7) — the number of programmers, the number of lines of code in the task, the maximum total number of bugs respectively and the modulo you should use when printing the answer.
The next line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 500) — the number of bugs per line for each programmer.
Output
Print a single integer — the answer to the problem modulo mod.
Examples
Input
3 3 3 100
1 1 1
Output
10
Input
3 6 5 1000000007
1 2 3
Output
0
Input
3 5 6 11
1 2 1
Output
0
Tags: dp
Correct Solution:
```
n, m, b, mod = map(int, input().split())
a = list(map(int, input().split()))
dp = [[0 for col in range(b + 1)]for row in range(m + 1)]
dp[0][0] = 1
for i in range(n):
for j in range(1, m + 1):
for k in range(a[i], b + 1):
dp[j][k] = (dp[j][k] + dp[j - 1][k - a[i]]) % mod
ans = 0
for i in range(b + 1):
ans = (ans + dp[m][i]) % mod
print(ans)
```
| 101,596 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers working on a large project have just received a task to write exactly m lines of code. There are n programmers working on a project, the i-th of them makes exactly ai bugs in every line of code that he writes.
Let's call a sequence of non-negative integers v1, v2, ..., vn a plan, if v1 + v2 + ... + vn = m. The programmers follow the plan like that: in the beginning the first programmer writes the first v1 lines of the given task, then the second programmer writes v2 more lines of the given task, and so on. In the end, the last programmer writes the remaining lines of the code. Let's call a plan good, if all the written lines of the task contain at most b bugs in total.
Your task is to determine how many distinct good plans are there. As the number of plans can be large, print the remainder of this number modulo given positive integer mod.
Input
The first line contains four integers n, m, b, mod (1 ≤ n, m ≤ 500, 0 ≤ b ≤ 500; 1 ≤ mod ≤ 109 + 7) — the number of programmers, the number of lines of code in the task, the maximum total number of bugs respectively and the modulo you should use when printing the answer.
The next line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 500) — the number of bugs per line for each programmer.
Output
Print a single integer — the answer to the problem modulo mod.
Examples
Input
3 3 3 100
1 1 1
Output
10
Input
3 6 5 1000000007
1 2 3
Output
0
Input
3 5 6 11
1 2 1
Output
0
Tags: dp
Correct Solution:
```
n, m, b, mod = list(map(int, input().split()))
a = list(map(int, input().split()))
A = [[0 for i in range(m + 1)] for j in range(b + 1)]
A[0][0] = 1
for i in range(n):
for j in range(a[i], b + 1):
for k in range(m):
A[j][k + 1] = (A[j][k + 1] + A[j - a[i]][k]) % mod
ans = 0
for i in range(b + 1):
ans = (ans + A[i][m]) % mod
print(ans)
```
| 101,597 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers working on a large project have just received a task to write exactly m lines of code. There are n programmers working on a project, the i-th of them makes exactly ai bugs in every line of code that he writes.
Let's call a sequence of non-negative integers v1, v2, ..., vn a plan, if v1 + v2 + ... + vn = m. The programmers follow the plan like that: in the beginning the first programmer writes the first v1 lines of the given task, then the second programmer writes v2 more lines of the given task, and so on. In the end, the last programmer writes the remaining lines of the code. Let's call a plan good, if all the written lines of the task contain at most b bugs in total.
Your task is to determine how many distinct good plans are there. As the number of plans can be large, print the remainder of this number modulo given positive integer mod.
Input
The first line contains four integers n, m, b, mod (1 ≤ n, m ≤ 500, 0 ≤ b ≤ 500; 1 ≤ mod ≤ 109 + 7) — the number of programmers, the number of lines of code in the task, the maximum total number of bugs respectively and the modulo you should use when printing the answer.
The next line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 500) — the number of bugs per line for each programmer.
Output
Print a single integer — the answer to the problem modulo mod.
Examples
Input
3 3 3 100
1 1 1
Output
10
Input
3 6 5 1000000007
1 2 3
Output
0
Input
3 5 6 11
1 2 1
Output
0
Tags: dp
Correct Solution:
```
# Legends Always Come Up with Solution
# Author: Manvir Singh
import os
import sys
from io import BytesIO, IOBase
def main():
n,m,b,mod=map(int,input().split())
a=list(map(int,input().split()))
dp=[[0 for _ in range(b+1)] for _ in range(m+1)]
dp[0][0]=1
for i in a:
for j in range(1,m+1):
for k in range(i,b+1):
dp[j][k]+=dp[j-1][k-i]
dp[j][k]%=mod
su=0
for i in dp[m]:
su+=i
su%=mod
print(su)
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
if __name__ == "__main__":
main()
```
| 101,598 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Programmers working on a large project have just received a task to write exactly m lines of code. There are n programmers working on a project, the i-th of them makes exactly ai bugs in every line of code that he writes.
Let's call a sequence of non-negative integers v1, v2, ..., vn a plan, if v1 + v2 + ... + vn = m. The programmers follow the plan like that: in the beginning the first programmer writes the first v1 lines of the given task, then the second programmer writes v2 more lines of the given task, and so on. In the end, the last programmer writes the remaining lines of the code. Let's call a plan good, if all the written lines of the task contain at most b bugs in total.
Your task is to determine how many distinct good plans are there. As the number of plans can be large, print the remainder of this number modulo given positive integer mod.
Input
The first line contains four integers n, m, b, mod (1 ≤ n, m ≤ 500, 0 ≤ b ≤ 500; 1 ≤ mod ≤ 109 + 7) — the number of programmers, the number of lines of code in the task, the maximum total number of bugs respectively and the modulo you should use when printing the answer.
The next line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 500) — the number of bugs per line for each programmer.
Output
Print a single integer — the answer to the problem modulo mod.
Examples
Input
3 3 3 100
1 1 1
Output
10
Input
3 6 5 1000000007
1 2 3
Output
0
Input
3 5 6 11
1 2 1
Output
0
Tags: dp
Correct Solution:
```
# Author : nitish420 --------------------------------------------------------------------
import os
import sys
from io import BytesIO, IOBase
def main():
n,m,b,mod=map(int,input().split())
arr=list(map(int,input().split()))
dp=[[0]*(b+1) for _ in range(m+1)]
dp[0]=[1]*(b+1)
for item in arr:
for r in range(1,m+1):
for c in range(item,b+1):
dp[r][c]=(dp[r][c]+dp[r-1][c-item])%mod
print(dp[m][b])
#----------------------------------------------------------------------------------------
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = 'x' in file.mode or 'r' not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b'\n') + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode('ascii'))
self.read = lambda: self.buffer.read().decode('ascii')
self.readline = lambda: self.buffer.readline().decode('ascii')
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip('\r\n')
# endregion
if __name__ == '__main__':
main()
```
| 101,599 |
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