text stringlengths 198 433k | conversation_id int64 0 109k |
|---|---|
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
And again a misfortune fell on Poor Student. He is being late for an exam.
Having rushed to a bus stop that is in point (0, 0), he got on a minibus and they drove along a straight line, parallel to axis OX, in the direction of increasing x.
Poor Student knows the following:
* during one run the minibus makes n stops, the i-th stop is in point (xi, 0)
* coordinates of all the stops are different
* the minibus drives at a constant speed, equal to vb
* it can be assumed the passengers get on and off the minibus at a bus stop momentarily
* Student can get off the minibus only at a bus stop
* Student will have to get off the minibus at a terminal stop, if he does not get off earlier
* the University, where the exam will be held, is in point (xu, yu)
* Student can run from a bus stop to the University at a constant speed vs as long as needed
* a distance between two points can be calculated according to the following formula: <image>
* Student is already on the minibus, so, he cannot get off at the first bus stop
Poor Student wants to get to the University as soon as possible. Help him to choose the bus stop, where he should get off. If such bus stops are multiple, choose the bus stop closest to the University.
Input
The first line contains three integer numbers: 2 ≤ n ≤ 100, 1 ≤ vb, vs ≤ 1000. The second line contains n non-negative integers in ascending order: coordinates xi of the bus stop with index i. It is guaranteed that x1 equals to zero, and xn ≤ 105. The third line contains the coordinates of the University, integers xu and yu, not exceeding 105 in absolute value.
Output
In the only line output the answer to the problem — index of the optimum bus stop.
Examples
Input
4 5 2
0 2 4 6
4 1
Output
3
Input
2 1 1
0 100000
100000 100000
Output
2
Note
As you know, students are a special sort of people, and minibuses usually do not hurry. That's why you should not be surprised, if Student's speed is higher than the speed of the minibus.
Submitted Solution:
```
n, m, s = map(int, input().split())
a = list(map(int, input().split()))
x, y = map(int, input().split())
t, ans = 100000000, 0
for i in range(1, n):
tt = ((a[i] - x)**2 + y**2)**0.5
if t > tt:
t = tt
ans = i + 1
print(tt)
print(ans)
```
No
| 87,300 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
And again a misfortune fell on Poor Student. He is being late for an exam.
Having rushed to a bus stop that is in point (0, 0), he got on a minibus and they drove along a straight line, parallel to axis OX, in the direction of increasing x.
Poor Student knows the following:
* during one run the minibus makes n stops, the i-th stop is in point (xi, 0)
* coordinates of all the stops are different
* the minibus drives at a constant speed, equal to vb
* it can be assumed the passengers get on and off the minibus at a bus stop momentarily
* Student can get off the minibus only at a bus stop
* Student will have to get off the minibus at a terminal stop, if he does not get off earlier
* the University, where the exam will be held, is in point (xu, yu)
* Student can run from a bus stop to the University at a constant speed vs as long as needed
* a distance between two points can be calculated according to the following formula: <image>
* Student is already on the minibus, so, he cannot get off at the first bus stop
Poor Student wants to get to the University as soon as possible. Help him to choose the bus stop, where he should get off. If such bus stops are multiple, choose the bus stop closest to the University.
Input
The first line contains three integer numbers: 2 ≤ n ≤ 100, 1 ≤ vb, vs ≤ 1000. The second line contains n non-negative integers in ascending order: coordinates xi of the bus stop with index i. It is guaranteed that x1 equals to zero, and xn ≤ 105. The third line contains the coordinates of the University, integers xu and yu, not exceeding 105 in absolute value.
Output
In the only line output the answer to the problem — index of the optimum bus stop.
Examples
Input
4 5 2
0 2 4 6
4 1
Output
3
Input
2 1 1
0 100000
100000 100000
Output
2
Note
As you know, students are a special sort of people, and minibuses usually do not hurry. That's why you should not be surprised, if Student's speed is higher than the speed of the minibus.
Submitted Solution:
```
from sys import stdin,stdout
from math import gcd, ceil, sqrt
ii1 = lambda: int(stdin.readline().strip())
is1 = lambda: stdin.readline().strip()
iia = lambda: list(map(int, stdin.readline().strip().split()))
isa = lambda: stdin.readline().strip().split()
mod = 1000000007
n, b, s = iia()
arr = iia()
x,y = iia()
if s > b:
print(2)
else:
for i in range(1, n):
if arr[i] == x:
print(i+1)
break
elif arr[i] > x:
print(max(i,2))
break
else:
print(n)
```
No
| 87,301 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
And again a misfortune fell on Poor Student. He is being late for an exam.
Having rushed to a bus stop that is in point (0, 0), he got on a minibus and they drove along a straight line, parallel to axis OX, in the direction of increasing x.
Poor Student knows the following:
* during one run the minibus makes n stops, the i-th stop is in point (xi, 0)
* coordinates of all the stops are different
* the minibus drives at a constant speed, equal to vb
* it can be assumed the passengers get on and off the minibus at a bus stop momentarily
* Student can get off the minibus only at a bus stop
* Student will have to get off the minibus at a terminal stop, if he does not get off earlier
* the University, where the exam will be held, is in point (xu, yu)
* Student can run from a bus stop to the University at a constant speed vs as long as needed
* a distance between two points can be calculated according to the following formula: <image>
* Student is already on the minibus, so, he cannot get off at the first bus stop
Poor Student wants to get to the University as soon as possible. Help him to choose the bus stop, where he should get off. If such bus stops are multiple, choose the bus stop closest to the University.
Input
The first line contains three integer numbers: 2 ≤ n ≤ 100, 1 ≤ vb, vs ≤ 1000. The second line contains n non-negative integers in ascending order: coordinates xi of the bus stop with index i. It is guaranteed that x1 equals to zero, and xn ≤ 105. The third line contains the coordinates of the University, integers xu and yu, not exceeding 105 in absolute value.
Output
In the only line output the answer to the problem — index of the optimum bus stop.
Examples
Input
4 5 2
0 2 4 6
4 1
Output
3
Input
2 1 1
0 100000
100000 100000
Output
2
Note
As you know, students are a special sort of people, and minibuses usually do not hurry. That's why you should not be surprised, if Student's speed is higher than the speed of the minibus.
Submitted Solution:
```
n,vb,vs=map(int,input().split())
stops=list(map(int,input().split()))
ux,uy=map(int,input().split())
d=lambda x: x//vb+ (((ux-x)**2+uy**2)**0.5)//vs
ans=[100000000000000000000000,-1]
index=0
for i in range(1,len(stops)):
a=d(stops[i])
#print("At station",i," Ans=",ans)
if a<ans[0]:
ans=[a,stops[i]]
index=i
if a==ans[0]:
#print("Found equal dist....")
if ((stops[i]-ux)**2+uy**2)**0.5 < ((ans[1]-ux)**2+uy**2)**0.5:
ans=[a,stops[i]]
index=i
print(index+1)
```
No
| 87,302 |
Provide a correct Python 3 solution for this coding contest problem.
Given are integer sequences A and B of length 3N. Each of these two sequences contains three copies of each of 1, 2, \dots, N. In other words, A and B are both arrangements of (1, 1, 1, 2, 2, 2, \dots, N, N, N).
Tak can perform the following operation to the sequence A arbitrarily many times:
* Pick a value from 1, 2, \dots, N and call it x. A contains exactly three copies of x. Remove the middle element of these three. After that, append x to the beginning or the end of A.
Check if he can turn A into B. If he can, print the minimum required number of operations to achieve that.
Constraints
* 1 \leq N \leq 33
* A and B are both arrangements of (1, 1, 1, 2, 2, 2, \dots, N, N, N).
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_{3N}
B_1 B_2 ... B_{3N}
Output
If Tak can turn A into B, print the minimum required number of operations to achieve that. Otherwise, print -1.
Examples
Input
3
2 3 1 1 3 2 2 1 3
1 2 2 3 1 2 3 1 3
Output
4
Input
3
1 1 1 2 2 2 3 3 3
1 1 1 2 2 2 3 3 3
Output
0
Input
3
2 3 3 1 1 1 2 2 3
3 2 2 1 1 1 3 3 2
Output
-1
Input
8
3 6 7 5 4 8 4 1 1 3 8 7 3 8 2 4 7 5 2 2 6 5 6 1
7 5 8 1 3 6 7 5 4 8 1 3 3 8 2 4 2 6 5 6 1 4 7 2
Output
7
"Correct Solution:
```
import sys
readline = sys.stdin.buffer.readline
class E:
def __init__(self,to,nx):
self.to=to
self.nx=nx
class Graph:
def __init__(self,n):
self.n=n
self.head=[None]*n
def ae(self,a,b):
head=self.head
head[a]=E(b,head[a])
#head[b]=E(a,head[b])
return head[a]
def scc(g):
n=g.n
cur=g.head
last=[None]*n
order=[-1]*n
low=[-1]*n
bl=[-1]*n
idx=[]
st=[]
num=0
for i in range(n):
if order[i]!=-1:
continue
rec=[i]
while rec:
v=rec[-1]
if last[v] is None:
#first in v
order[v]=low[v]=num
num+=1
st.append(v)
else:
#process last edge
low[v]=min(low[v],low[last[v].to])
found=False
while cur[v] is not None:
#process next edge
e=cur[v]
cur[v]=e.nx
to=e.to
if order[to]==-1:
#visit another node
rec.append(to)
last[v]=e
found=True
break
elif bl[to]==-1:
low[v]=min(low[v],order[to])
if not found:
#last out v
rec.pop()
if order[v]==low[v]:
c=len(idx)
tmp=[]
while True:
a=st.pop()
bl[a]=c
tmp.append(a)
if v==a:
break
idx.append(tmp)
s=len(idx)
for i in range(n):
bl[i]=s-1-bl[i]
idx.reverse()
return (s,bl,idx)
class twosat:
def __init__(self,n):
self.n=n
self.g=Graph(2*n)
def add(self,x,y):
self.g.ae(x^1,y)
self.g.ae(y^1,x)
def solve(self):
s,bl,idx=scc(self.g)
for i in range(self.n):
if bl[i*2]==bl[i*2+1]:
return False
return True
n=int(readline())
N=n*3
a=list(map(int,readline().split()))
b=list(map(int,readline().split()))
for i in range(N):
a[i]-=1
b[i]-=1
apos=[[] for i in range(n)]
for i in range(N):
apos[a[i]].append(i)
bpos=[[] for i in range(n)]
for i in range(N):
bpos[b[i]].append(i)
def feasible(l,r):
t=[False]*N
def issubseq():
head=l
for i in range(N):
if t[i]:
while head<r and a[i]!=b[head]:
head+=1
if head==r:
return False
head+=1
return True
l2r=[]
r2l=[]
w=[]
for val in range(n):
z=[]
for x in bpos[val]:
if x<l:
z.append(0)
elif x<r:
z.append(1)
else:
z.append(2)
if z==[0,0,0]:
return False
elif z==[0,0,1]:
t[apos[val][2]]=1
elif z==[0,0,2]:
x=l-bpos[val][0]
y=bpos[val][2]-r
r2l.append((x,y))
elif z==[0,1,1]:
t[apos[val][0]]=1
t[apos[val][2]]=1
elif z==[0,1,2]:
x=l-bpos[val][0]
y=bpos[val][2]-r
w.append((apos[val][0],apos[val][2],x,y))
elif z==[0,2,2]:
x=l-bpos[val][0]
y=bpos[val][2]-r
l2r.append((x,y))
elif z==[1,1,1]:
t[apos[val][0]]=1
t[apos[val][1]]=1
t[apos[val][2]]=1
elif z==[1,1,2]:
t[apos[val][0]]=1
t[apos[val][2]]=1
elif z==[1,2,2]:
t[apos[val][0]]=1
elif z==[2,2,2]:
return False
else:
assert False
if not issubseq():
return False
def conflict(xa,xb,ya,yb):
return ya<=xa and xb<=yb
for xa,xb in l2r:
for ya,yb in r2l:
if conflict(xa,xb,ya,yb):
return False
s=len(w)
ts=twosat(s)
for i in range(s):
pa,pb,qa,qb=w[i]
#left is ok?
ok=True
t[pa]=1
if not issubseq():
ok=False
t[pa]=0;
if ok:
for xa,xb in l2r:
if conflict(xa,xb,qa,qb):
ok=False
if not ok:
ts.add(i*2+1,i*2+1)
#right is ok?
ok=True
t[pb]=1;
if not issubseq():
ok=False
t[pb]=0;
if ok:
for ya,yb in r2l:
if conflict(qa,qb,ya,yb):
ok=False
if not ok:
ts.add(i*2,i*2)
for i in range(s):
for j in range(i+1,s):
p0a,p0b,q0a,q0b=w[i]
p1a,p1b,q1a,q1b=w[j]
t0=bpos[a[p0a]][1]
t1=bpos[a[p1a]][1]
#left-left is ok?
ok=True
if (p0a<p1a)!=(t0<t1):
ok=False
if not ok:
ts.add(i*2+1,j*2+1)
#left-right is ok?
ok=True
if (p0a<p1b)!=(t0<t1):
ok=False
if conflict(q1a,q1b,q0a,q0b):
ok=False
if not ok:
ts.add(i*2+1,j*2)
#right-left is ok?
ok=True
if (p0b<p1a)!=(t0<t1):
ok=False;
if conflict(q0a,q0b,q1a,q1b):
ok=False
if not ok:
ts.add(i*2,j*2+1)
#right-right is ok?
ok=True
if (p0b<p1b)!=(t0<t1):
ok=False
if not ok:
ts.add(i*2,j*2);
return ts.solve();
ans=10**18
for i in range(N):
for j in range(i,N+1):
if feasible(i,j):
ans=min(ans,N-(j-i))
if ans==10**18:
ans=-1
print(ans)
```
| 87,303 |
Provide a correct Python 3 solution for this coding contest problem.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
"Correct Solution:
```
k = int(input())
s = input()
if k >= len(s):
print(s)
else:
print(s[:k]+'...')
```
| 87,304 |
Provide a correct Python 3 solution for this coding contest problem.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
"Correct Solution:
```
k=int(input())
w=input()
if len(w)<=k:
print(w)
else:
print(w[:k]+"...")
```
| 87,305 |
Provide a correct Python 3 solution for this coding contest problem.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
"Correct Solution:
```
k=int(input())
s=input().strip()
print(s if len(s)<=k else s[:k]+'...')
```
| 87,306 |
Provide a correct Python 3 solution for this coding contest problem.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
"Correct Solution:
```
n = int(input())
txt = input()
print(txt[:n]+"..." if bool(txt[n:]) else txt)
```
| 87,307 |
Provide a correct Python 3 solution for this coding contest problem.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
"Correct Solution:
```
k=int(input());s=input();l=len(s)
print(s[0:min(k,l)]+"."*3*(k<l))
```
| 87,308 |
Provide a correct Python 3 solution for this coding contest problem.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
"Correct Solution:
```
N=int(input())
S=input()
if len(S)<=N:
print(S)
else:
print(S[0:N]+"...")
```
| 87,309 |
Provide a correct Python 3 solution for this coding contest problem.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
"Correct Solution:
```
k=int(input())
s=input()
if k>=len(s):
print(s)
else:
print(s[:k]+"...")
```
| 87,310 |
Provide a correct Python 3 solution for this coding contest problem.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
"Correct Solution:
```
k,s=open(0);k=int(k);print(s[:k]+'...'*(k<~-len(s)))
```
| 87,311 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
Submitted Solution:
```
k = int(input())
s = input()
print(s) if len(s) <= k else print(s[:k] + '...')
```
Yes
| 87,312 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
Submitted Solution:
```
K=int(input())
S=input()
a=len(S)
if a<=K:
print(S)
else:
print(S[:K]+'...')
```
Yes
| 87,313 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
Submitted Solution:
```
k=int(input())
s=input()
x=s[:k]+'...'*(len(s)>k)
print(x)
```
Yes
| 87,314 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
Submitted Solution:
```
k = int(input())
s = input()
if(len(s) <= k):
print(s)
else:
print(s[:k]+"...")
```
Yes
| 87,315 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
Submitted Solution:
```
K = int(input())
S = input()
if len(S) < K:
print(K)
else:
print(S[:K] + "...")
```
No
| 87,316 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
Submitted Solution:
```
K = int(input())
S = str(input())
SK = S[0 : (K)]
if len(S) <= K:
answer = S
else:
print(SK + '...')
```
No
| 87,317 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
Submitted Solution:
```
K = input()
S = input()
if len(K) >= len(S):
print(S)
else:
strings = str(S[:K]) + '...'
print(strings)
```
No
| 87,318 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a string S consisting of lowercase English letters.
If the length of S is at most K, print S without change.
If the length of S exceeds K, extract the first K characters in S, append `...` to the end of them, and print the result.
Constraints
* K is an integer between 1 and 100 (inclusive).
* S is a string consisting of lowercase English letters.
* The length of S is between 1 and 100 (inclusive).
Input
Input is given from Standard Input in the following format:
K
S
Output
Print a string as stated in Problem Statement.
Examples
Input
7
nikoandsolstice
Output
nikoand...
Input
40
ferelibenterhominesidquodvoluntcredunt
Output
ferelibenterhominesidquodvoluntcredunt
Submitted Solution:
```
k=int(input())
s=str(input())
if len(s)<=k:
print(s)
else:
print(s[:k],"...")
```
No
| 87,319 |
Provide a correct Python 3 solution for this coding contest problem.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
"Correct Solution:
```
MOD = 10 ** 9 + 7
FACT_MAX = 10 ** 5
fact = [1] * FACT_MAX
for i in range(1, FACT_MAX):
fact[i] = fact[i - 1] * i % MOD
def comb(n, r):
return fact[n] * pow(fact[n - r], MOD - 2, MOD) * pow(fact[r], MOD - 2, MOD)
N, K = map(int, input().split())
A = sorted(map(int, input().split()))
print(sum(comb(i, K - 1) * (A[i] - A[N - i - 1]) % MOD for i in range(K - 1, N)) % MOD)
```
| 87,320 |
Provide a correct Python 3 solution for this coding contest problem.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
"Correct Solution:
```
N,K=map(int,input().split())
A=list(map(int,input().split()))
mod = 10**9+7
if K==1:print(0)
else:
factorial=[1 for i in range(N+1)]
for i in range(1,N+1):
if i==1:factorial[i]=1
else:factorial[i] = factorial[i-1]*i % mod
def comb(n,k):
return factorial[n]*pow(factorial[n-k]*factorial[k], -1, mod)
A1=sorted(A)
A2=A1[::-1]
ans=0
for i in range(N-K+1):
ans += (A2[i]-A1[i])*comb(N-i-1,K-1)
ans %= mod
print(ans)
```
| 87,321 |
Provide a correct Python 3 solution for this coding contest problem.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
"Correct Solution:
```
N,K=map(int,input().split())
A=sorted(map(int,input().split()))
r=0
MOD=10**9+7
max_n=10**5
fac=[1]*(max_n+1)
inv=[1]*(max_n+1)
ifac=[1]*(max_n+1)
for n in range(2,max_n+1):
fac[n]=(fac[n-1]*n)%MOD
inv[n]=MOD-inv[MOD%n]*(MOD//n)%MOD
ifac[n]=(ifac[n-1]*inv[n])%MOD
def comb(n,k):
if n<k:
return 0
if n<0 or k<0:
return 0
return (fac[n]*ifac[k]*ifac[n-k])%MOD
for i,a in enumerate(A):
r=(r+(comb(i,K-1)-comb(N-1-i,K-1))*a)%MOD
print(r)
```
| 87,322 |
Provide a correct Python 3 solution for this coding contest problem.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
"Correct Solution:
```
n,k=[int(i) for i in input().split()]
arr=[int(i) for i in input().split()]
ans=0
mod=10**9+7
arr.sort()
c=[0 for i in range(n)]
r=k-1
c[r]=1
def modinv(x,mod):
return pow(x,mod-2,mod)
for i in range(r+1,n):
c[i]=((c[i-1]*(i))*modinv(i-r,mod))%mod
pos=0
neg=0
for i in range(n):
pos+=(arr[-1-i]*c[-1-i])%mod
neg+=(arr[i]*c[-1-i])%mod
pos%=mod
neg%=mod
print((pos-neg)%mod)
```
| 87,323 |
Provide a correct Python 3 solution for this coding contest problem.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
"Correct Solution:
```
MOD = 10 ** 9 + 7
def comb(n, r):
return fact[n] * pow(fact[n - r], MOD - 2, MOD) * pow(fact[r], MOD - 2, MOD)
N, K = map(int, input().split())
fact = [1] * N
for i in range(1, N):
fact[i] = fact[i - 1] * i % MOD
A = sorted(map(int, input().split()))
print(sum(comb(i, K - 1) * (A[i] - A[N - i - 1]) % MOD for i in range(K - 1, N)) % MOD)
```
| 87,324 |
Provide a correct Python 3 solution for this coding contest problem.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
"Correct Solution:
```
MOD = 1000000007
N,K = map(int,input().split())
A = list(map(int,input().split()))
A.sort()
step =[1]*(N+1)
for i in range(1,N+1,1):
step[i]= (step[i-1]*i)%MOD
def nCk(n,k):
return (step[n]*pow(step[k],MOD-2,MOD)*pow(step[n-k],MOD-2,MOD))%MOD
max_sum=0
min_sum=0
for i in range(0,N,1):
if i+1 < K:
continue
max_sum += (A[i]*nCk(i,K-1) + MOD)%MOD
min_sum += (A[N-1-i]*nCk(i,K-1) + MOD)%MOD
print((max_sum-min_sum)%MOD)
```
| 87,325 |
Provide a correct Python 3 solution for this coding contest problem.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
"Correct Solution:
```
from itertools import accumulate
mod = 10 ** 9 + 7
N, K = map(int, input().split())
A = sorted([int(x) for x in input().split()])
f = [1 for _ in range(N + 1)]
inv = [1 for _ in range(N + 1)]
finv = [1 for _ in range(N + 1)]
for i in range(2, N + 1):
f[i] = f[i - 1] * i % mod
inv[i] = mod - inv[mod % i] * (mod // i) % mod
finv[i] = finv[i - 1] * inv[i] % mod
comb = [f[n] * (finv[K - 1] * finv[n - (K - 1)] % mod) % mod for n in range(K - 1, N)]
ans = 0
for i in range(N - K + 1):
ans += comb[i] * (A[i + K - 1] - A[N - i - K])
ans %= mod
print(ans)
```
| 87,326 |
Provide a correct Python 3 solution for this coding contest problem.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
"Correct Solution:
```
mod = 10**9+7
f = [1]
for i in range(10**5+7):
f.append(f[-1]*(i+1)%mod)
def comb(n, r,mod=mod):
return f[n] * pow(f[r], mod-2, mod) * pow(f[n-r], mod-2, mod) % mod
n, k = map(int, input().split())
a = sorted(list(map(int, input().split())), reverse=True)
ans = 0
for i in range(n-k+1):
ans += (a[i] - a[-1-i]) * comb(n-1-i, k-1)
ans %= mod
print(ans)
```
| 87,327 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
Submitted Solution:
```
m = 10 ** 9 + 7
f = [1]
for i in range(10 ** 5 + 5):
f.append(f[-1] * (i + 1) % m)
def nCr(n,r,mod = m):
return f[n] * pow(f[r],m - 2,m) * pow(f[n-r],m - 2,m) % m
n,k = map(int,input().split())
a = list(map(int,input().split()))
a.sort()
ans = 0
for i in range(n - k + 1):
ans += (a[-1-i] - a[i]) * nCr(n - 1 - i,k - 1)
ans %= m
print(ans)
```
Yes
| 87,328 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
Submitted Solution:
```
n_=10**5+3
mod=10**9+7
fac=[1]*(n_+1)
for i in range(1,n_+1):
fac[i]=fac[i-1]*i%mod
inv =[1]*(n_+1)
inv[n_]=pow(fac[n_],mod-2,mod)
for i in range(n_-1,0,-1):
inv[i]=inv[i+1]*(i+1)%mod
def nCr(n,r):
if n<=0 or r<0 or r>n:
return 0
return fac[n]*inv[r]%mod*inv[n-r]%mod
n,k=map(int,input().split())
A=list(map(int,input().split()))
A.sort()
ans=0
for i in range(n-k+1):
ans=(ans+(A[n-i-1]-A[i])*nCr(n-i-1,k-1))%mod
print(ans)
```
Yes
| 87,329 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
Submitted Solution:
```
MOD = 10**9 + 7
fac = [1 for k in range(200010)]
inv = [1 for k in range(200010)]
finv = [1 for k in range(200010)]
for k in range(2,200010):
fac[k] = (fac[k-1]*k)%MOD
inv[k] = (MOD - inv[MOD%k] * (MOD // k))%MOD
finv[k] = (finv[k - 1] * inv[k]) % MOD;
def nCr(n,r):
return (fac[n]*finv[r]*finv[n-r])%MOD
N, K = map(int,input().split())
A = sorted(list(map(int,input().split())))
m = 0
for k in range(N-K+1):
m += A[k]*nCr(N-k-1,K-1)
m %= MOD
A = A[::-1]
M = 0
for k in range(N-K+1):
M += A[k]*nCr(N-k-1,K-1)
M %= MOD
print(M-m if M>=m else M-m+MOD)
```
Yes
| 87,330 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
Submitted Solution:
```
N, K = map(int, input().split())
*A, = map(int, input().split())
A.sort()
mod = 10**9+7
fac = [1]*(N+1)
rev = [1]*(N+1)
for i in range(1,N+1):
fac[i] = i*fac[i-1]%mod
rev[i] = pow(fac[i], mod-2, mod)
comb = lambda a,b:(fac[a]*rev[a-b]*rev[b])%mod
maxX, minX = 0, 0
for i in range(N-K+1):
minX += A[i]*comb(N-i-1, K-1)
for j in range(K-1, N):
maxX += A[j]*comb(j, K-1)
print((maxX-minX)%mod)
```
Yes
| 87,331 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
Submitted Solution:
```
# -*- coding: utf-8 -*-
import numpy as np
iNum, iK = map(int, input().split())
iK -= 1
naA = np.array(list(map(int, input().split())), dtype = "int64")
naA = np.sort(naA)
#print(naA)
iMod = 1000000007
iRet = 1000000000000000
iRet*=0
iNmrt = 1
iDnmt = 1
for iK0 in range(iK):
iNmrt *= iNum - iK0
iDnmt *= iK0 + 1
iU0= iNmrt // iDnmt
#print(iNum, iK, iU0)
iL0=0
iU = iNum
for iL, iA in enumerate(naA):
iU -= 1
if iL > iK:
iL0 *= iL
iL0//= iL - iK
elif iL == iK:
iL0 = 1
else:
iL0 = 0
if iU >= iK:
iU0 *= iU+1-iK
iU0 //= iU+1
else:
iU0 = 0
#print("iU, iK, iU0, iA :",iU,iK,iU0, iA)
#print("iL, iK, iL0, iA :",iL,iK,iL0, iA)
iL0mU0= iL0 - iU0
iRet0 = (iL0mU0 * iA) % iMod
iRet += iRet0
#print(iRet0)
iAp = iA
print(iRet%iMod)
```
No
| 87,332 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
Submitted Solution:
```
import itertools
N,K = map(int,input().split())
A = [int(x) for x in input().split()]
def madfd(b):
return max(b)-min(b)
total = 0
mod = 10**9+7
for i in list(itertools.combinations(A,K)):
total+=madfd(i)
print(total%mod)
```
No
| 87,333 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
Submitted Solution:
```
"""
ジャガー「わからん」
先にmax,minそれぞれの和を求める
"""
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**6)
def getComb(n, k, MOD):
if n < k:
return 0
if n-k < k:
k = n-k
# n!/(n-k)!
comb = 1
for x in range(n-k+1, n+1):
comb = (comb * x) % MOD
# k!
d = 1
for x in range(1, k+1):
d = (d * x) % MOD
# n!/((n-k)!*k!)
comb *= pow(d, MOD-2, MOD)
return comb % MOD
def main():
N,K = map(int,input().split())
A = sorted([int(i) for i in input().split()])
#print(A)
mod = 10**9+7
cmb = [0] * (N-K+1)
for i in range(N-K+1):
cmb[i] = getComb(i+(K-1),K-1,mod)
#print(cmb)
sum_max = 0
for i in range(K-1,N):
sum_max = (sum_max + cmb[i-(K-1)] * A[i]) % mod
#print(sum_max)
sum_min = 0
for i in range(N-K,-1,-1):
sum_min = (sum_min + cmb[(N-K)-i] * A[i]) % mod
#print(sum_min)
answer = sum_max - sum_min
print(answer % mod)
if __name__ == "__main__":
main()
```
No
| 87,334 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq N
* |A_i| \leq 10^9
Input
Input is given from Standard Input in the following format:
N K
A_1 ... A_N
Output
Print the answer \bmod (10^9+7).
Examples
Input
4 2
1 1 3 4
Output
11
Input
6 3
10 10 10 -10 -10 -10
Output
360
Input
3 1
1 1 1
Output
0
Input
10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
Output
999998537
Submitted Solution:
```
import itertools
nk = list(map(int, input().split()))
a = list(map(int, input().split()))
S = 0
allpat = list(itertools.combinations(a, nk[1]))
for i in range(len(allpat)):
S = (S + max(allpat[i]) - min(allpat[i])) % 1000000007
print(S)
```
No
| 87,335 |
Provide a correct Python 3 solution for this coding contest problem.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
"Correct Solution:
```
"""
Writer: SPD_9X2
https://atcoder.jp/contests/agc037/tasks/agc037_b
最適な配り方とは何かを考えるべき
そうすれば自然なdpに落ちるんだろうな
RGBが出たら合体させないといけない？
→これは正しそう
RGGRBB
112212 →4+3=7
112221 →5+2=7
121212 →4+4=8
なので、RGBが出たらランダムに合わせればいいわけではない
2つでたら合体しなければいけない説
RG→合体
GR→合体
B →2通り
B →1通り
なので2通り？
それっぽいぞ
BBRGRRGRGGRBBGB
B1/B
B1/B2
R2/RB,B
G2/B
R2/RB
R2/R,RB
G2/R
R2/R2
G4/RG,R
G4/RG2
R4/RG2,R
B8/RG,R
B8/R
G8/RG
B8/
8通り…少なすぎるな
あ、5!を掛ければ答えじゃね
あってるっぽさそう？
"""
N = int(input())
S = input()
R = 0
G = 0
B = 0
RG = 0
RB = 0
GB = 0
ans = 1
mod = 998244353
for i in range(1,N+1):
ans *= i
ans %= mod
for i in range(3*N):
if S[i] == "R":
if GB > 0:
ans *= GB
GB -= 1
elif G > 0:
ans *= G
G -= 1
RG += 1
elif B > 0:
ans *= B
B -= 1
RB += 1
else:
R += 1
elif S[i] == "G":
if RB > 0:
ans *= RB
RB -= 1
elif R > 0:
ans *= R
R -= 1
RG += 1
elif B > 0:
ans *= B
B -= 1
GB += 1
else:
G += 1
else:
if RG > 0:
ans *= RG
RG -= 1
elif R > 0:
ans *= R
R -= 1
RB += 1
elif G > 0:
ans *= G
G -= 1
GB += 1
else:
B += 1
ans %= mod
print (ans)
```
| 87,336 |
Provide a correct Python 3 solution for this coding contest problem.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
"Correct Solution:
```
from bisect import*
e=enumerate
M=998244353
R,G,B=[],[],[]
n=int(input())
for i,c in e(input()):
if c=='R':R+=i,
elif c=='G':G+=i,
else:B+=i,
l,m,r=[],[],[]
for i,t in e(zip(R,G,B)):
a,b,c=sorted(t)
l+=a,
m+=b,
r+=c,
s=1
for i,b in e(m):
s=s*(bisect(l,b)-i)*(i-bisect(r,b)+1)*(i+1)%M
print(s)
```
| 87,337 |
Provide a correct Python 3 solution for this coding contest problem.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
"Correct Solution:
```
#!/usr/bin/env python3
MOD = 998244353
n = int(input())
s = input()
ans = 1
for i in range(n):
ans *= i + 1
ans %= MOD
cnt = [0] * 3
dic = {'R': 0, 'G': 1, 'B': 2}
for c in s:
p = dic[c]
m = min(cnt[p - 1], cnt[p - 2])
if m > 0:
ans *= m
cnt[p - 1] -= 1
cnt[p - 2] -= 1
else:
ans *= max(1, cnt[p - 1] + cnt[p - 2] - cnt[p])
cnt[p] += 1
ans %= MOD
print(ans)
```
| 87,338 |
Provide a correct Python 3 solution for this coding contest problem.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
"Correct Solution:
```
from functools import reduce
N = int(input())
S = input()
MOD = 998244353
class ModInt:
def __init__(self, x):
self.x = x % MOD
def __str__(self):
return str(self.x)
__repr__ = __str__
def __add__(self, other):
return (
ModInt(self.x + other.x) if isinstance(other, ModInt) else
ModInt(self.x + other)
)
def __sub__(self, other):
return (
ModInt(self.x - other.x) if isinstance(other, ModInt) else
ModInt(self.x - other)
)
def __mul__(self, other):
return (
ModInt(self.x * other.x) if isinstance(other, ModInt) else
ModInt(self.x * other)
)
def __truediv__(self, other):
return (
ModInt(
self.x * pow(other.x, MOD - 2, MOD)
) if isinstance(other, ModInt) else
ModInt(self.x * pow(other, MOD - 2, MOD))
)
def __pow__(self, other):
return (
ModInt(
pow(self.x, other.x, MOD)
) if isinstance(other, ModInt) else
ModInt(pow(self.x, other, MOD))
)
def __radd__(self, other):
return ModInt(other + self.x)
def __rsub__(self, other):
return ModInt(other - self.x)
def __rmul__(self, other):
return ModInt(other * self.x)
def __rtruediv__(self, other):
return ModInt(other * pow(self.x, MOD - 2, MOD))
def __rpow__(self, other):
return ModInt(pow(other, self.x, MOD))
# 先頭のボールから順に、割り当て可能な人のうち最もボールを持っている人に割り当てることを繰り返す
def f(s, res, z, r, g, b, rg, gb, br):
return (
(
(res * gb, z, r, g, b, rg, gb - 1, br) if gb else
(res * g, z, r, g - 1, b, rg + 1, gb, br) if g else
(res * b, z, r, g, b - 1, rg, gb, br + 1) if b else
(res * z, z - 1, r + 1, g, b, rg, gb, br)
) if s == 'R' else
(
(res * br, z, r, g, b, rg, gb, br - 1) if br else
(res * r, z, r - 1, g, b, rg + 1, gb, br) if r else
(res * b, z, r, g, b - 1, rg, gb + 1, br) if b else
(res * z, z - 1, r, g + 1, b, rg, gb, br)
) if s == 'G' else
(
(res * rg, z, r, g, b, rg - 1, gb, br) if rg else
(res * r, z, r - 1, g, b, rg, gb, br + 1) if r else
(res * g, z, r, g - 1, b, rg, gb + 1, br) if g else
(res * z, z - 1, r, g, b + 1, rg, gb, br)
)
)
ans, *_ = reduce(
lambda acc, s: f(s, *acc),
S,
(ModInt(1), N, 0, 0, 0, 0, 0, 0)
)
print(ans)
```
| 87,339 |
Provide a correct Python 3 solution for this coding contest problem.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
"Correct Solution:
```
from collections import defaultdict
mod = 998244353
N = int(input())
S = input()
colors = ['R', 'G', 'B']
invs = {'R':'GB', 'G':'BR', 'B':'RG'}
cnt = defaultdict(int)
ans = 1
for i in range(N*3):
s = S[i]
inv = invs[s]
if cnt[inv] != 0:
ans *= cnt[inv]
ans%=mod
cnt[inv]-=1
continue
flag = False
for c in colors:
if c == s:
continue
if cnt[c]:
ans*=cnt[c]
ans%=mod
cnt[c]-=1
cnt[c+s]+=1
cnt[s+c]+=1
flag = True
if not flag:
cnt[s]+=1
ans%=mod
for i in range(1, N+1):
ans*=i
ans%=mod
print(ans)
```
| 87,340 |
Provide a correct Python 3 solution for this coding contest problem.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
"Correct Solution:
```
import sys
from bisect import *
def main():
input = sys.stdin.readline
N = int(input())
S = input().strip()
M = 998244353
ri = []
gi = []
bi = []
for i, c in enumerate(S):
if c=='R':
ri.append(i)
elif c=='G':
gi.append(i)
else:
bi.append(i)
si = []
mi = []
li = []
for i, tt in enumerate(zip(ri,gi,bi)):
s, m, l = sorted(tt)
si.append(s)
mi.append(m)
li.append(l)
ans = 1
for i, mm in enumerate(mi):
st = bisect(si,mm)
lt = bisect(li,mm)
ans = ans*(st-i)*(i+1-lt)*(i+1)
ans = ans%M
print(ans)
if __name__ == "__main__":
main()
```
| 87,341 |
Provide a correct Python 3 solution for this coding contest problem.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
"Correct Solution:
```
import math
n=int(input())
a=1;c={"R":0,"G":0,"B":0}
m=998244353
for i in input():
s=sorted(c.values())
c[i]+=1
if c[i]>s[2]:pass
elif c[i]>s[1]:a*=s[2]-s[1]
else:a*=s[1]-s[0]
a%=m
print(math.factorial(n)*a%m)
```
| 87,342 |
Provide a correct Python 3 solution for this coding contest problem.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
"Correct Solution:
```
import math
n=int(input())
a=1;c={"R":0,"G":0,"B":0}
m=998244353
for i in input():
f,s,t=sorted(c.values())
c[i]+=1
a*=(s-f,t-s,1)[(c[i]>t)+(c[i]>s)]
a%=m
print(math.factorial(n)*a%m)
```
| 87,343 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
Submitted Solution:
```
#B問題
import bisect
N = int(input())
S = list(str(input()))
mod = 998244353
N_factorial = 1
for i in range(N):
N_factorial*=(i+1)
N_factorial%=mod
r,g,b = [],[],[]
for i,s in enumerate(S):
if s == "R":
r.append(i)
if s == "G":
g.append(i)
if s == "B":
b.append(i)
A,B,C = [],[],[]
for i in range(N):
rgb = [r[i],g[i],b[i]]
rgb.sort()
A.append(rgb[0])
B.append(rgb[1])
C.append(rgb[2])
ans = N_factorial
for i,B_ind in enumerate(B):
x = bisect.bisect_left(A,B_ind)-i
y = i+1-bisect.bisect_left(C,B_ind)
ans*=(x*y)
ans%=mod
print(ans)
```
Yes
| 87,344 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
Submitted Solution:
```
import sys
sys.setrecursionlimit(10**6)
def main():
input = sys.stdin.readline
N = int(input())
S = str(input().strip())
MOD = 998244353
#state = (_, r, g, b, rg, gb, br)
def f(i, ans, state):
if i > 3*N-1:
return ans
if min(state) < 0:
return 0
no_ball, r, g, b, rg, gb, br = state
if S[i] == 'R':
if gb > 0:
ans = (ans * gb) % MOD
return f(i+1, ans, [no_ball, r, g, b, rg, gb-1, br])
elif g > 0 or b > 0:
ans = ans * (g + b) % MOD
s1 = [no_ball, r, g-1, b, rg+1, gb, br]
s2 = [no_ball, r, g, b-1, rg, gb, br+1]
return (f(i+1, ans, s1) + f(i+1, ans, s2)) % MOD
else:
ans = (ans * no_ball) % MOD
return f(i+1, ans, [no_ball-1, r+1, g, b, rg, gb, br])
elif S[i] == 'G':
if br > 0:
ans = (ans * br) % MOD
return f(i+1, ans, [no_ball, r, g, b, rg, gb, br-1])
elif r > 0 or b > 0:
ans = ans * (r + b) % MOD
s1 = [no_ball, r-1, g, b, rg+1, gb, br]
s2 = [no_ball, r, g, b-1, rg, gb+1, br]
return (f(i+1, ans, s1) + f(i+1, ans, s2)) % MOD
else:
ans = (ans * no_ball) % MOD
return f(i+1, ans, [no_ball-1, r, g+1, b, rg, gb, br])
else: #S[i] == 'B':
if rg > 0:
ans = (ans * rg) % MOD
return f(i+1, ans, [no_ball, r, g, b, rg-1, gb, br])
elif r > 0 or g > 0:
ans = ans * (r + g) % MOD
s1 = [no_ball, r-1, g, b, rg, gb, br+1]
s2 = [no_ball, r, g-1, b, rg, gb+1, br]
return (f(i+1, ans, s1) + f(i+1, ans, s2)) % MOD
else:
ans = (ans * no_ball) % MOD
return f(i+1, ans, [no_ball-1, r, g, b+1, rg, gb, br])
return f(0, 1, [N, 0, 0, 0, 0, 0, 0]) % MOD
if __name__ == '__main__':
print(main())
```
Yes
| 87,345 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
Submitted Solution:
```
mod = 998244353
n = int(input())
s = input()
ans = 1
R,G,B,RG,GB,BR = 0,0,0,0,0,0
if s[0] == 'R':
R = 1
elif s[0] == 'G':
G = 1
else:
B = 1
for i in range(1,3*n):
if s[i] == 'R':
if GB > 0:
ans = (ans * GB) % mod
GB -= 1
elif G > 0:
ans = (ans * G) % mod
G -= 1
RG += 1
elif B > 0:
ans = (ans * B) % mod
B -= 1
BR += 1
else:
R += 1
elif s[i] == 'G':
if BR > 0:
ans = (ans * BR) % mod
BR -= 1
elif R > 0:
ans = (ans * R) % mod
R -= 1
RG += 1
elif B > 0:
ans = (ans * B) % mod
B -= 1
GB += 1
else:
G += 1
else:
if RG > 0:
ans = (ans * RG) % mod
RG -= 1
elif R > 0:
ans = (ans * R) % mod
R -= 1
BR += 1
elif G > 0:
ans = (ans * G) % mod
G -= 1
GB += 1
else:
B += 1
for i in range(n):
ans = (ans * (i+1)) % mod
print(ans)
```
Yes
| 87,346 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
Submitted Solution:
```
def factorial(n):
ans = 1
for i in range(n):
ans *= i+1
ans %= mod
return ans
mod = 998244353
n = int(input())
s = input()
ans = 1
r,g,b = 0,0,0
rg,rb,gb = 0,0,0
for i in s:
if i == "R":
if gb > 0:
ans *= gb
gb -= 1
elif g > 0:
ans *= g
g -= 1
rg += 1
elif b > 0:
ans *= b
b -= 1
rb += 1
else:
r += 1
elif i == "G":
if rb > 0:
ans *= rb
rb -= 1
elif r > 0:
ans *= r
r -= 1
rg += 1
elif b > 0:
ans *= b
b -= 1
gb += 1
else:
g += 1
elif i == "B":
if rg > 0:
ans *= rg
rg -= 1
elif r > 0:
ans *= r
r -= 1
rb += 1
elif g > 0:
ans *= g
g -= 1
gb += 1
else:
b += 1
ans %= mod
print((factorial(n) * ans) % mod)
```
Yes
| 87,347 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
Submitted Solution:
```
import bisect
import collections
import math
n = int(input())
s = input()
r = []
g = []
b = []
for i in range(3 * n):
if s[i] == "R":
r.append(i)
if s[i] == "G":
g.append(i)
if s[i] == "B":
b.append(i)
def comp(a, b):
t = []
for i in range(n):
t.append(bisect.bisect_left(a,b[i]))
c = collections.Counter(t)
ans = 1
for i in list(c.values()):
ans = ans * math.factorial(i)
return ans
p = comp(r, g) * comp(g, b) * comp(b, r)
q = comp(g, r) * comp(b, g) * comp(r, b)
print(max(p, q))
```
No
| 87,348 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
Submitted Solution:
```
n=int(input())
s=input()
df={"R":0, "G":0, "B":0}
db={"R":0, "G":0, "B":0}
ans=1
for i in range(3*n):
db[s[i]]+=1
for i in range(3*n):
df[s[i]]+=1
db[s[i]]-=1
if df["R"]>0 and df["G"]>0:
ans*=df["R"]*df["G"]*db["B"]
df["R"] -=1
df["G"] -=1
df[s[i]] =0
db["B"] -=1
if df["R"]>0 and df["B"]>0:
ans*=df["R"]*df["B"]*db["G"]
df["R"] -=1
df["B"] -=1
df[s[i]] =0
db["G"] -=1
if df["B"]>0 and df["G"]>0:
ans*=df["B"]*df["G"]*db["R"]
df["B"] -=1
df["G"] -=1
df[s[i]] =0
db["R"] -=1
for i in range(1,n+1):
ans*=i
print(ans)
```
No
| 87,349 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
Submitted Solution:
```
from operator import mul
from functools import reduce
N = int(input())
S = input()
MOD = 998244353
# make A, B, C oredesr
r, g, b = 0, 0, 0
T = {'R': 0, 'G': 0, 'B': 0}
ABC = ''
for s in S:
T[s] += 1
ge = [t >= T[s] for t in T.values()].count(True)
lt = [t < T[s] for t in T.values()].count(True)
if ge == 1:
ABC += 'A'
elif lt == 0:
ABC += 'C'
else:
ABC += 'B'
la, rc = 0, 0 # selectable num of left A and right C
ans = 1
# # from left for A
# for d in ABC:
# if d == 'A':
# la += 1
# elif d == 'B':
# ans *= la
# ans %= MOD
# la -= 1
# # from right for C
# for d in ABC[::-1]:
# if d == 'C':
# rc += 1
# elif d == 'B':
# ans *= rc
# ans %= MOD
# rc -= 1
# # human permutation
# ans *= reduce(mul, range(1, N+1))
# ans %= MOD
print(ans)
```
No
| 87,350 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have 3N colored balls with IDs from 1 to 3N. A string S of length 3N represents the colors of the balls. The color of Ball i is red if S_i is `R`, green if S_i is `G`, and blue if S_i is `B`. There are N red balls, N green balls, and N blue balls.
Takahashi will distribute these 3N balls to N people so that each person gets one red ball, one blue ball, and one green ball. The people want balls with IDs close to each other, so he will additionally satisfy the following condition:
* Let a_j < b_j < c_j be the IDs of the balls received by the j-th person in ascending order.
* Then, \sum_j (c_j-a_j) should be as small as possible.
Find the number of ways in which Takahashi can distribute the balls. Since the answer can be enormous, compute it modulo 998244353. We consider two ways to distribute the balls different if and only if there is a person who receives different sets of balls.
Constraints
* 1 \leq N \leq 10^5
* |S|=3N
* S consists of `R`, `G`, and `B`, and each of these characters occurs N times in S.
Input
Input is given from Standard Input in the following format:
N
S
Output
Print the number of ways in which Takahashi can distribute the balls, modulo 998244353.
Examples
Input
3
RRRGGGBBB
Output
216
Input
5
BBRGRRGRGGRBBGB
Output
960
Submitted Solution:
```
n = int(input())
s = input()
mod = 998244353
ans = 1
z, o, t = n, 0, 0
O, T = "", ""
for i in range(3*n):
if T != "" and s[i] != O and s[i] != T:
ans *= t
ans %= mod
t -= 1
if t == 0:
T = ""
elif s[i] == O or O == "":
o += 1
ans *= z
ans %= mod
z -= 1
O = s[i]
else:
t += 1
ans *= o
ans %= mod
o -= 1
T = s[i]
if o == 0:
O = ""
print(ans)
```
No
| 87,351 |
Provide a correct Python 3 solution for this coding contest problem.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
"Correct Solution:
```
N = int(input())
A = [int(input()) for i in range(5)]
print(5 + (N-1)//min(A))
```
| 87,352 |
Provide a correct Python 3 solution for this coding contest problem.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
"Correct Solution:
```
n = int(input())
abcde = [int(input()) for _ in range(5)]
print(4-(-n//min(abcde)))
```
| 87,353 |
Provide a correct Python 3 solution for this coding contest problem.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
"Correct Solution:
```
print(abs(-int(input())//min(int(input()) for _ in range(5)))+4)
```
| 87,354 |
Provide a correct Python 3 solution for this coding contest problem.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
"Correct Solution:
```
n=int(input())
m=min([int(input()) for x in range(5)])
print((m+n-1)//m+4)
```
| 87,355 |
Provide a correct Python 3 solution for this coding contest problem.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
"Correct Solution:
```
n = int(input())
a = list(int(input()) for i in range(5))
print(-(-n//min(a))+4)
```
| 87,356 |
Provide a correct Python 3 solution for this coding contest problem.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
"Correct Solution:
```
N= int(input())
ts = [int(input()) for i in range(5)]
print(int((N-1)/min(ts)) + 5)
```
| 87,357 |
Provide a correct Python 3 solution for this coding contest problem.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
"Correct Solution:
```
n = int(input())
a = [int(input()) for _ in range(5)]
print((n-1)//min(a)+5)
```
| 87,358 |
Provide a correct Python 3 solution for this coding contest problem.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
"Correct Solution:
```
n = int(input())
a = [int(input()) for _ in range(5)]
print(4+(n-1)//min(a)+1)
```
| 87,359 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
Submitted Solution:
```
data = [int(input()) for i in range(6)]
print(-(-data[0]//min(data[1:]))+4)
```
Yes
| 87,360 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
Submitted Solution:
```
n = int(input()) - 1
lst = [int(input()) for i in range(5)]
m = min(lst)
print(n//m + 5)
```
Yes
| 87,361 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
Submitted Solution:
```
N=int(input())
H=[]
for i in range(5):
H += [int(input())]
print(-(-N//min(H))+4)
```
Yes
| 87,362 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
Submitted Solution:
```
n=int(input())
a=[int(input())for _ in range(5)]
print(4--n//min(a))
```
Yes
| 87,363 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
Submitted Solution:
```
N = int(input())
li = []
for i in range(5):
li.append(int(input()))
print(N//min(li)+5)
```
No
| 87,364 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
Submitted Solution:
```
N = int(input())
city = []
for i in range(5):
city.append(int(input()))
gate = min(city)
if N >= gate:
print(5)
else:
print(5 + N//gate)
```
No
| 87,365 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
Submitted Solution:
```
n = int(input())
A = [int(input()) for x in range(5)]
print('A',A)
B = []
cnt=0
for i in range(5):
if A[i]>=n:
B.append(1)
cnt+=1
else:
if A[i]==1:
B.append(n)
else:
B.append(int(n/A[i])+1)
print('B',B)
if cnt==5:
print(5)
else:
print(max(B)+4)
```
No
| 87,366 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City 1, 2, 3, 4, 5, 6)!
There are five means of transport in this empire:
* Train: travels from City 1 to 2 in one minute. A train can occupy at most A people.
* Bus: travels from City 2 to 3 in one minute. A bus can occupy at most B people.
* Taxi: travels from City 3 to 4 in one minute. A taxi can occupy at most C people.
* Airplane: travels from City 4 to 5 in one minute. An airplane can occupy at most D people.
* Ship: travels from City 5 to 6 in one minute. A ship can occupy at most E people.
For each of them, one vehicle leaves the city at each integer time (time 0, 1, 2, ...).
There is a group of N people at City 1, and they all want to go to City 6.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.
Constraints
* 1 \leq N, A, B, C, D, E \leq 10^{15}
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A
B
C
D
E
Output
Print the minimum time required for all of the people to reach City 6, in minutes.
Examples
Input
5
3
2
4
3
5
Output
7
Input
10
123
123
123
123
123
Output
5
Input
10000000007
2
3
5
7
11
Output
5000000008
Submitted Solution:
```
# むずかしい
```
No
| 87,367 |
Provide a correct Python 3 solution for this coding contest problem.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
"Correct Solution:
```
X, Y = map(int,input().rstrip().split())
print(X+Y//2)
```
| 87,368 |
Provide a correct Python 3 solution for this coding contest problem.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
"Correct Solution:
```
a, b = (int(i) for i in input().split())
print(b//2+a)
```
| 87,369 |
Provide a correct Python 3 solution for this coding contest problem.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
"Correct Solution:
```
#113 A
X,Y= map(int,input().split())
print(int(X+0.5*Y))
```
| 87,370 |
Provide a correct Python 3 solution for this coding contest problem.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
"Correct Solution:
```
x, y = (int(i) for i in input().split())
print(x + y//2)
```
| 87,371 |
Provide a correct Python 3 solution for this coding contest problem.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
"Correct Solution:
```
print(eval(input().replace(" ","*2+"))//2)
```
| 87,372 |
Provide a correct Python 3 solution for this coding contest problem.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
"Correct Solution:
```
a,b=map(int,input().split())
print(round(a+round(b/2)))
```
| 87,373 |
Provide a correct Python 3 solution for this coding contest problem.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
"Correct Solution:
```
X, Y = (int(i) for i in input().split())
print(X+Y//2)
```
| 87,374 |
Provide a correct Python 3 solution for this coding contest problem.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
"Correct Solution:
```
ab,bc=map(int,input().split())
print(int(ab+bc/2))
```
| 87,375 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
Submitted Solution:
```
a, b = map(int, input().split())
print(int(a+b/2))
```
Yes
| 87,376 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
Submitted Solution:
```
X,Y=map(int,input().split())
bus=Y/2
print(X+int(bus))
```
Yes
| 87,377 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
Submitted Solution:
```
N, M = map(int, input().split())
print(N+M//2)
```
Yes
| 87,378 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
Submitted Solution:
```
A,B=input().split()
A=int(A)
B=int(B)
print(int(A+B/2))
```
Yes
| 87,379 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
Submitted Solution:
```
# coding: utf-8
# In[1]:
x,y = map(int,input().split())
# In[2]:
y = y/2
# In[3]:
z = x + y
# In[4]:
print(z)
```
No
| 87,380 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
Submitted Solution:
```
X, Y = [int(i) for i in input().split()]
ans = X + Y/2
print(ans)
```
No
| 87,381 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
Submitted Solution:
```
x=int(input("X:"))
y=int(input("Y:"))
z=x+y/2
print(z)
```
No
| 87,382 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There is a train going from Station A to Station B that costs X yen (the currency of Japan).
Also, there is a bus going from Station B to Station C that costs Y yen.
Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.
How much does it cost to travel from Station A to Station C if she uses this ticket?
Constraints
* 1 \leq X,Y \leq 100
* Y is an even number.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y
Output
If it costs x yen to travel from Station A to Station C, print x.
Examples
Input
81 58
Output
110
Input
4 54
Output
31
Submitted Solution:
```
X, Y = map(int, raw_input().split())
print(X + Y//2)
```
No
| 87,383 |
Provide a correct Python 3 solution for this coding contest problem.
There are N turkeys. We number them from 1 through N.
M men will visit here one by one. The i-th man to visit will take the following action:
* If both turkeys x_i and y_i are alive: selects one of them with equal probability, then eats it.
* If either turkey x_i or y_i is alive (but not both): eats the alive one.
* If neither turkey x_i nor y_i is alive: does nothing.
Find the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the following condition is held:
* The probability of both turkeys i and j being alive after all the men took actions, is greater than 0.
Constraints
* 2 ≤ N ≤ 400
* 1 ≤ M ≤ 10^5
* 1 ≤ x_i < y_i ≤ N
Input
Input is given from Standard Input in the following format:
N M
x_1 y_1
x_2 y_2
:
x_M y_M
Output
Print the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the condition is held.
Examples
Input
3 1
1 2
Output
2
Input
4 3
1 2
3 4
2 3
Output
1
Input
3 2
1 2
1 2
Output
0
Input
10 10
8 9
2 8
4 6
4 9
7 8
2 8
1 8
3 4
3 4
2 7
Output
5
"Correct Solution:
```
import sys
from itertools import combinations
def solve(n, pairs):
survivors = {v: {v} for v in range(1, n + 1)}
for x, y in reversed(pairs):
for v, srv in survivors.copy().items():
if x in srv:
if y in srv:
del survivors[v]
else:
srv.add(y)
elif y in srv:
srv.add(x)
return sum(su.isdisjoint(sv) for su, sv in combinations(survivors.values(), 2))
n, m = map(int, input().split())
pairs = [tuple(map(int, line.split())) for line in sys.stdin.readlines()]
print(solve(n, pairs))
```
| 87,384 |
Provide a correct Python 3 solution for this coding contest problem.
There are N turkeys. We number them from 1 through N.
M men will visit here one by one. The i-th man to visit will take the following action:
* If both turkeys x_i and y_i are alive: selects one of them with equal probability, then eats it.
* If either turkey x_i or y_i is alive (but not both): eats the alive one.
* If neither turkey x_i nor y_i is alive: does nothing.
Find the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the following condition is held:
* The probability of both turkeys i and j being alive after all the men took actions, is greater than 0.
Constraints
* 2 ≤ N ≤ 400
* 1 ≤ M ≤ 10^5
* 1 ≤ x_i < y_i ≤ N
Input
Input is given from Standard Input in the following format:
N M
x_1 y_1
x_2 y_2
:
x_M y_M
Output
Print the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the condition is held.
Examples
Input
3 1
1 2
Output
2
Input
4 3
1 2
3 4
2 3
Output
1
Input
3 2
1 2
1 2
Output
0
Input
10 10
8 9
2 8
4 6
4 9
7 8
2 8
1 8
3 4
3 4
2 7
Output
5
"Correct Solution:
```
n,m=map(int,input().split())
v=[[1 for i in range(n)] for i in range(n)]
for i in range(m):
x,y=map(int,input().split())
x-=1
y-=1
if v[x][y]:
v[x][y],v[y][x]=0,0
for j in range(n):
if v[x][j]==0:
v[j][y],v[y][j]=0,0
for j in range(n):
if v[y][j]==0:
v[j][x],v[x][j]=0,0
else:
for j in range(n):
v[j][x],v[x][j],v[j][y],v[y][j]=0,0,0,0
print((sum(map(sum,v))-sum([v[i][i] for i in range(n)]))//2)
```
| 87,385 |
Provide a correct Python 3 solution for this coding contest problem.
There are N turkeys. We number them from 1 through N.
M men will visit here one by one. The i-th man to visit will take the following action:
* If both turkeys x_i and y_i are alive: selects one of them with equal probability, then eats it.
* If either turkey x_i or y_i is alive (but not both): eats the alive one.
* If neither turkey x_i nor y_i is alive: does nothing.
Find the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the following condition is held:
* The probability of both turkeys i and j being alive after all the men took actions, is greater than 0.
Constraints
* 2 ≤ N ≤ 400
* 1 ≤ M ≤ 10^5
* 1 ≤ x_i < y_i ≤ N
Input
Input is given from Standard Input in the following format:
N M
x_1 y_1
x_2 y_2
:
x_M y_M
Output
Print the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the condition is held.
Examples
Input
3 1
1 2
Output
2
Input
4 3
1 2
3 4
2 3
Output
1
Input
3 2
1 2
1 2
Output
0
Input
10 10
8 9
2 8
4 6
4 9
7 8
2 8
1 8
3 4
3 4
2 7
Output
5
"Correct Solution:
```
def get_survivors(n, pairs):
survivors = {v: {v} for v in range(n)}
for x, y in reversed(pairs):
for v, srv in survivors.copy().items():
if x in srv:
if y in srv:
del survivors[v]
else:
srv.add(y)
elif y in srv:
srv.add(x)
return survivors
def solve(n, pairs):
survivors = get_survivors(n, pairs)
ans = 0
for u, su in survivors.items():
for v, sv in survivors.items():
if u >= v:
continue
if su.isdisjoint(sv):
ans += 1
return ans
n, m = map(int, input().split())
pairs = []
for _ in range(m):
x, y = map(int, input().split())
x -= 1
y -= 1
pairs.append((x, y))
print(solve(n, pairs))
```
| 87,386 |
Provide a correct Python 3 solution for this coding contest problem.
There are N turkeys. We number them from 1 through N.
M men will visit here one by one. The i-th man to visit will take the following action:
* If both turkeys x_i and y_i are alive: selects one of them with equal probability, then eats it.
* If either turkey x_i or y_i is alive (but not both): eats the alive one.
* If neither turkey x_i nor y_i is alive: does nothing.
Find the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the following condition is held:
* The probability of both turkeys i and j being alive after all the men took actions, is greater than 0.
Constraints
* 2 ≤ N ≤ 400
* 1 ≤ M ≤ 10^5
* 1 ≤ x_i < y_i ≤ N
Input
Input is given from Standard Input in the following format:
N M
x_1 y_1
x_2 y_2
:
x_M y_M
Output
Print the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the condition is held.
Examples
Input
3 1
1 2
Output
2
Input
4 3
1 2
3 4
2 3
Output
1
Input
3 2
1 2
1 2
Output
0
Input
10 10
8 9
2 8
4 6
4 9
7 8
2 8
1 8
3 4
3 4
2 7
Output
5
"Correct Solution:
```
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
eat=[]
for i in range(M):
x,y=map(int,input().split())
eat.append((x,y))
eat=eat[::-1]
turkey=[]
for i in range(1,N+1):
tempval=set([i])
tempid=set([])
for j in range(M):
x,y=eat[j]
if x in tempval and y in tempval:
break
elif x in tempval:
tempval.add(y)
tempid.add(j)
elif y in tempval:
tempval.add(x)
tempid.add(j)
else:
turkey.append([tempval,tempid])
ans=0
n=len(turkey)
#print(turkey)
for i in range(1,n):
for j in range(i):
aval,aid=turkey[i]
bval,bid=turkey[j]
checkval=True
checkid=True
for val in bval:
checkval=checkval&(val not in aval)
for id in bid:
checkid=checkid&(id not in aid)
if checkid and checkval:
ans+=1
#print(i,j)
print(ans)
```
| 87,387 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N turkeys. We number them from 1 through N.
M men will visit here one by one. The i-th man to visit will take the following action:
* If both turkeys x_i and y_i are alive: selects one of them with equal probability, then eats it.
* If either turkey x_i or y_i is alive (but not both): eats the alive one.
* If neither turkey x_i nor y_i is alive: does nothing.
Find the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the following condition is held:
* The probability of both turkeys i and j being alive after all the men took actions, is greater than 0.
Constraints
* 2 ≤ N ≤ 400
* 1 ≤ M ≤ 10^5
* 1 ≤ x_i < y_i ≤ N
Input
Input is given from Standard Input in the following format:
N M
x_1 y_1
x_2 y_2
:
x_M y_M
Output
Print the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the condition is held.
Examples
Input
3 1
1 2
Output
2
Input
4 3
1 2
3 4
2 3
Output
1
Input
3 2
1 2
1 2
Output
0
Input
10 10
8 9
2 8
4 6
4 9
7 8
2 8
1 8
3 4
3 4
2 7
Output
5
Submitted Solution:
```
import sys
from itertools import combinations
n, m = map(int, input().split())
survivors = {v: {v + 1} for v in range(n)}
for x, y in reversed(map(int, line.split()) for line in sys.stdin.readlines()):
for v, srv in survivors.copy().items():
if x in srv:
if y in srv:
del survivors[v]
else:
srv.add(y)
elif y in srv:
srv.add(x)
print(sum(su.isdisjoint(sv) for su, sv in combinations(survivors.values(), 2)))
```
No
| 87,388 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N turkeys. We number them from 1 through N.
M men will visit here one by one. The i-th man to visit will take the following action:
* If both turkeys x_i and y_i are alive: selects one of them with equal probability, then eats it.
* If either turkey x_i or y_i is alive (but not both): eats the alive one.
* If neither turkey x_i nor y_i is alive: does nothing.
Find the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the following condition is held:
* The probability of both turkeys i and j being alive after all the men took actions, is greater than 0.
Constraints
* 2 ≤ N ≤ 400
* 1 ≤ M ≤ 10^5
* 1 ≤ x_i < y_i ≤ N
Input
Input is given from Standard Input in the following format:
N M
x_1 y_1
x_2 y_2
:
x_M y_M
Output
Print the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the condition is held.
Examples
Input
3 1
1 2
Output
2
Input
4 3
1 2
3 4
2 3
Output
1
Input
3 2
1 2
1 2
Output
0
Input
10 10
8 9
2 8
4 6
4 9
7 8
2 8
1 8
3 4
3 4
2 7
Output
5
Submitted Solution:
```
import sys
from itertools import combinations
def solve(n, pairs):
have_to_survive = [{v} for v in range(1, n + 1)]
survivors = [True] * n
for x, y in reversed(pairs):
for i, srv in enumerate(survivors):
if not srv:
continue
hts = have_to_survive[i]
if x in hts:
if y in hts:
survivors[i] = False
else:
hts.add(y)
elif y in hts:
hts.add(x)
finalists = [hts for srv, hts in zip(survivors, have_to_survive) if srv]
return sum(su.isdisjoint(sv) for su, sv in combinations(finalists, 2))
n, m = map(int, input().split())
pairs = [tuple(map(int, line.split())) for line in sys.stdin.readlines()]
print(solve(n, pairs))
```
No
| 87,389 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N turkeys. We number them from 1 through N.
M men will visit here one by one. The i-th man to visit will take the following action:
* If both turkeys x_i and y_i are alive: selects one of them with equal probability, then eats it.
* If either turkey x_i or y_i is alive (but not both): eats the alive one.
* If neither turkey x_i nor y_i is alive: does nothing.
Find the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the following condition is held:
* The probability of both turkeys i and j being alive after all the men took actions, is greater than 0.
Constraints
* 2 ≤ N ≤ 400
* 1 ≤ M ≤ 10^5
* 1 ≤ x_i < y_i ≤ N
Input
Input is given from Standard Input in the following format:
N M
x_1 y_1
x_2 y_2
:
x_M y_M
Output
Print the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the condition is held.
Examples
Input
3 1
1 2
Output
2
Input
4 3
1 2
3 4
2 3
Output
1
Input
3 2
1 2
1 2
Output
0
Input
10 10
8 9
2 8
4 6
4 9
7 8
2 8
1 8
3 4
3 4
2 7
Output
5
Submitted Solution:
```
import sys
from itertools import combinations
n, m = map(int, input().split())
survivors = {v: {v + 1} for v in range(n)}
for x, y in reversed(list(map(int, line.split()) for line in sys.stdin.readlines())):
for v, srv in survivors.copy().items():
if x in srv:
if y in srv:
del survivors[v]
else:
srv.add(y)
elif y in srv:
srv.add(x)
print(sum(su.isdisjoint(sv) for su, sv in combinations(survivors.values(), 2)))
```
No
| 87,390 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N turkeys. We number them from 1 through N.
M men will visit here one by one. The i-th man to visit will take the following action:
* If both turkeys x_i and y_i are alive: selects one of them with equal probability, then eats it.
* If either turkey x_i or y_i is alive (but not both): eats the alive one.
* If neither turkey x_i nor y_i is alive: does nothing.
Find the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the following condition is held:
* The probability of both turkeys i and j being alive after all the men took actions, is greater than 0.
Constraints
* 2 ≤ N ≤ 400
* 1 ≤ M ≤ 10^5
* 1 ≤ x_i < y_i ≤ N
Input
Input is given from Standard Input in the following format:
N M
x_1 y_1
x_2 y_2
:
x_M y_M
Output
Print the number of pairs (i,\ j) (1 ≤ i < j ≤ N) such that the condition is held.
Examples
Input
3 1
1 2
Output
2
Input
4 3
1 2
3 4
2 3
Output
1
Input
3 2
1 2
1 2
Output
0
Input
10 10
8 9
2 8
4 6
4 9
7 8
2 8
1 8
3 4
3 4
2 7
Output
5
Submitted Solution:
```
def get_survivors(n, pairs):
survivors = {v: {v} for v in range(n)}
for x, y in reversed(pairs):
for v, srv in survivors.copy().items():
if x in srv:
if y in srv:
del survivors[v]
else:
srv.add(y)
elif y in srv:
srv.add(x)
return list(survivors.values())
def solve(n, pairs):
survivors = get_survivors(n, pairs)
ans = 0
for i, su in enumerate(survivors):
for sv in survivors[i + 1:]:
if su.isdisjoint(sv):
ans += 1
return ans
n, m = map(int, input().split())
pairs = []
for _ in range(m):
x, y = map(int, input().split())
x -= 1
y -= 1
pairs.append((x, y))
print(solve(n, pairs))
```
No
| 87,391 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino wants to evaluate the formula "A op B". Here, A and B are integers, and the binary operator op is either `+` or `-`. Your task is to evaluate the formula instead of her.
Constraints
* 1≦A,B≦10^9
* op is either `+` or `-`.
Input
The input is given from Standard Input in the following format:
A op B
Output
Evaluate the formula and print the result.
Examples
Input
1 + 2
Output
3
Input
5 - 7
Output
-2
"Correct Solution:
```
l = input()
print(eval(l))
```
| 87,392 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino wants to evaluate the formula "A op B". Here, A and B are integers, and the binary operator op is either `+` or `-`. Your task is to evaluate the formula instead of her.
Constraints
* 1≦A,B≦10^9
* op is either `+` or `-`.
Input
The input is given from Standard Input in the following format:
A op B
Output
Evaluate the formula and print the result.
Examples
Input
1 + 2
Output
3
Input
5 - 7
Output
-2
"Correct Solution:
```
# -*- coding: utf-8 -*-
# problem A
print(eval(input()))
```
| 87,393 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino wants to evaluate the formula "A op B". Here, A and B are integers, and the binary operator op is either `+` or `-`. Your task is to evaluate the formula instead of her.
Constraints
* 1≦A,B≦10^9
* op is either `+` or `-`.
Input
The input is given from Standard Input in the following format:
A op B
Output
Evaluate the formula and print the result.
Examples
Input
1 + 2
Output
3
Input
5 - 7
Output
-2
"Correct Solution:
```
a, b, c = input().split()
x = int(a)
y = int(c)
print(x + y if b=='+' else x - y)
```
| 87,394 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino wants to evaluate the formula "A op B". Here, A and B are integers, and the binary operator op is either `+` or `-`. Your task is to evaluate the formula instead of her.
Constraints
* 1≦A,B≦10^9
* op is either `+` or `-`.
Input
The input is given from Standard Input in the following format:
A op B
Output
Evaluate the formula and print the result.
Examples
Input
1 + 2
Output
3
Input
5 - 7
Output
-2
"Correct Solution:
```
a,b,c = input().split()
print(int(a)+int(c) if b == "+" else int(a) - int(c))
```
| 87,395 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino wants to evaluate the formula "A op B". Here, A and B are integers, and the binary operator op is either `+` or `-`. Your task is to evaluate the formula instead of her.
Constraints
* 1≦A,B≦10^9
* op is either `+` or `-`.
Input
The input is given from Standard Input in the following format:
A op B
Output
Evaluate the formula and print the result.
Examples
Input
1 + 2
Output
3
Input
5 - 7
Output
-2
"Correct Solution:
```
str=input()
print(eval(str))
```
| 87,396 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino wants to evaluate the formula "A op B". Here, A and B are integers, and the binary operator op is either `+` or `-`. Your task is to evaluate the formula instead of her.
Constraints
* 1≦A,B≦10^9
* op is either `+` or `-`.
Input
The input is given from Standard Input in the following format:
A op B
Output
Evaluate the formula and print the result.
Examples
Input
1 + 2
Output
3
Input
5 - 7
Output
-2
"Correct Solution:
```
print(eval(input().replace(' ','')))
```
| 87,397 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino wants to evaluate the formula "A op B". Here, A and B are integers, and the binary operator op is either `+` or `-`. Your task is to evaluate the formula instead of her.
Constraints
* 1≦A,B≦10^9
* op is either `+` or `-`.
Input
The input is given from Standard Input in the following format:
A op B
Output
Evaluate the formula and print the result.
Examples
Input
1 + 2
Output
3
Input
5 - 7
Output
-2
"Correct Solution:
```
A, op, B = map(str, input().split())
C = A + op + B
print(eval(C))
```
| 87,398 |
Provide a correct Python 3 solution for this coding contest problem.
Joisino wants to evaluate the formula "A op B". Here, A and B are integers, and the binary operator op is either `+` or `-`. Your task is to evaluate the formula instead of her.
Constraints
* 1≦A,B≦10^9
* op is either `+` or `-`.
Input
The input is given from Standard Input in the following format:
A op B
Output
Evaluate the formula and print the result.
Examples
Input
1 + 2
Output
3
Input
5 - 7
Output
-2
"Correct Solution:
```
print(eval(input().strip()))
```
| 87,399 |
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