message stringlengths 2 19.9k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 322 108k | cluster float64 15 15 | __index_level_0__ int64 644 217k |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
There are N robots numbered 1 to N placed on a number line. Robot i is placed at coordinate X_i. When activated, it will travel the distance of D_i in the positive direction, and then it will be removed from the number line. All the robots move at the same speed, and their sizes are ignorable.
Takahashi, who is a mischievous boy, can do the following operation any number of times (possibly zero) as long as there is a robot remaining on the number line.
* Choose a robot and activate it. This operation cannot be done when there is a robot moving.
While Robot i is moving, if it touches another robot j that is remaining in the range [X_i, X_i + D_i) on the number line, Robot j also gets activated and starts moving. This process is repeated recursively.
How many possible sets of robots remaining on the number line are there after Takahashi does the operation some number of times? Compute this count modulo 998244353, since it can be enormous.
Constraints
* 1 \leq N \leq 2 \times 10^5
* -10^9 \leq X_i \leq 10^9
* 1 \leq D_i \leq 10^9
* X_i \neq X_j (i \neq j)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
X_1 D_1
:
X_N D_N
Output
Print the number of possible sets of robots remaining on the number line, modulo 998244353.
Examples
Input
2
1 5
3 3
Output
3
Input
3
6 5
-1 10
3 3
Output
5
Input
4
7 10
-10 3
4 3
-4 3
Output
16
Input
20
-8 1
26 4
0 5
9 1
19 4
22 20
28 27
11 8
-3 20
-25 17
10 4
-18 27
24 28
-11 19
2 27
-2 18
-1 12
-24 29
31 29
29 7
Output
110 | instruction | 0 | 64,606 | 15 | 129,212 |
"Correct Solution:
```
def examA():
S = SI()
if S=="AAA" or S=="BBB":
print("No")
else:
print("Yes")
return
def examB():
N, A, B = LI()
loop = N//(A+B)
ans = loop*A + min(A,N%(A+B))
print(ans)
return
def examC():
A, B = LI()
ans = -1
for i in range(1,20000):
if i*8//100==A:
if i*10//100==B:
ans = i
break
print(ans)
return
def examD():
S = SI()
Q = I()
rev = 0
L = ""; R = ""
for _ in range(Q):
q = LSI()
if q[0]=="1":
rev += 1
else:
c = int(q[1])
if (c+rev)%2==1:
L += q[2]
else:
R += q[2]
ans = ""
if rev%2==0:
ans = L[::-1] + S + R
else:
ans = R[::-1] + S[::-1] + L
print(ans)
return
def examE():
N, P = LI()
S = SI()
A = [0]*(N+1)
cur = 0
if P==5:
ans = 0
for i in range(N):
if int(S[N-1-i])%5==0:
ans += N-i
print(ans)
return
elif P==2:
ans = 0
for i in range(N):
if int(S[N-1-i])%2==0:
ans += N-i
print(ans)
return
for i in range(N):
s = int(S[N-1-i])
cur += s*pow(10,i,P)
A[i+1] = cur%P
D = [0]*P
for a in A:
D[a] += 1
ans = 0
#print(A)
for d in D:
ans += d*(d-1)//2
print(ans)
return
def examF():
def dfs(n, s):
#input()
#print(n,s)
cur = 1
can = sum(X[s])
for i in range(s,n):
if X[i][0]>=can:
V[s] = cur
return cur, i
if i==n-1:
return cur,i
now, visited = dfs(n, i+1)
cur += now
V[s] = cur
return cur, n
N = I()
X = [LI()for _ in range(N)]
X.sort()
V = [[]for _ in range(N)]
neg = 0
ans = dfs(N,0)
print(V)
print(ans)
return
def examF2():
N = I()
X = [LI()for _ in range(N)]
N += 1
X.sort()
parent = [-1] * N
#print(X)
stack = [(inf,-1)]
for i,(x,d) in enumerate(X):
d += x
# x座標近いやつからチェック
# 届かないやつ排除
while(stack[-1][0]<=x):
stack.pop()
parent[i] = stack[-1][1]
stack.append((d,i))
#print(parent)
dp = [1]*N
ans = 1
for i in range(N-1)[::-1]:
p = parent[i]
if p==-1:
ans *= dp[i]+1
ans %= mod2
continue
dp[p] *= dp[i]+1
dp[p] %= mod2
print(ans)
return
import sys,copy,bisect,itertools,heapq,math,random
from heapq import heappop,heappush,heapify
from collections import Counter,defaultdict,deque
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))
def LSI(): return list(map(str,sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def SI(): return sys.stdin.readline().strip()
global mod,mod2,inf,alphabet,_ep
mod = 10**9 + 7
mod2 = 998244353
inf = 10**18
_ep = 10**(-12)
alphabet = [chr(ord('a') + i) for i in range(26)]
sys.setrecursionlimit(10**6)
if __name__ == '__main__':
examF2()
"""
"""
``` | output | 1 | 64,606 | 15 | 129,213 |
Provide a correct Python 3 solution for this coding contest problem.
There are N robots numbered 1 to N placed on a number line. Robot i is placed at coordinate X_i. When activated, it will travel the distance of D_i in the positive direction, and then it will be removed from the number line. All the robots move at the same speed, and their sizes are ignorable.
Takahashi, who is a mischievous boy, can do the following operation any number of times (possibly zero) as long as there is a robot remaining on the number line.
* Choose a robot and activate it. This operation cannot be done when there is a robot moving.
While Robot i is moving, if it touches another robot j that is remaining in the range [X_i, X_i + D_i) on the number line, Robot j also gets activated and starts moving. This process is repeated recursively.
How many possible sets of robots remaining on the number line are there after Takahashi does the operation some number of times? Compute this count modulo 998244353, since it can be enormous.
Constraints
* 1 \leq N \leq 2 \times 10^5
* -10^9 \leq X_i \leq 10^9
* 1 \leq D_i \leq 10^9
* X_i \neq X_j (i \neq j)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
X_1 D_1
:
X_N D_N
Output
Print the number of possible sets of robots remaining on the number line, modulo 998244353.
Examples
Input
2
1 5
3 3
Output
3
Input
3
6 5
-1 10
3 3
Output
5
Input
4
7 10
-10 3
4 3
-4 3
Output
16
Input
20
-8 1
26 4
0 5
9 1
19 4
22 20
28 27
11 8
-3 20
-25 17
10 4
-18 27
24 28
-11 19
2 27
-2 18
-1 12
-24 29
31 29
29 7
Output
110 | instruction | 0 | 64,607 | 15 | 129,214 |
"Correct Solution:
```
import bisect
import operator
import os
import sys
from functools import reduce
class SegmentTree:
# http://codeforces.com/blog/entry/18051
def __init__(self, values, op=operator.add):
"""
:param list values:
:param callable op: 結合律を満たす二項演算
"""
self._size = len(values)
self._op = op
tree = [None] * self._size * 2
tree[self._size:] = values[:]
for i in reversed(range(1, self._size)):
tree[i] = self._op(tree[i << 1], tree[i << 1 | 1])
self._tree = tree
def set(self, i, value):
"""
values[i] = value
:param int i:
:param value:
"""
i += self._size
self._tree[i] = value
i >>= 1
while i > 0:
self._tree[i] = self._op(self._tree[i << 1], self._tree[i << 1 | 1])
i >>= 1
def add(self, i, value):
"""
values[i] = values[i]・value
:param int i:
:param value:
"""
new_value = self._op(self._tree[self._size + i], value)
self.set(i, new_value)
def get(self, l, r=None):
"""
[l, r) に op を順番に適用した値
:param int l:
:param int|None r:
"""
if r is None:
return self._tree[self._size + l]
ret_l = []
ret_r = []
l += self._size
r += self._size
while l < r:
if l & 1:
ret_l.append(self._tree[l])
l += 1
if r & 1:
r -= 1
ret_r.append(self._tree[r])
l >>= 1
r >>= 1
return reduce(self._op, ret_l + ret_r)
def __len__(self):
return self._size
def get_values_copy(self):
return self._tree[self._size:]
if os.getenv("LOCAL"):
sys.stdin = open("_in.txt", "r")
sys.setrecursionlimit(10 ** 9)
INF = float("inf")
IINF = 10 ** 18
MOD = 998244353
N = int(sys.stdin.buffer.readline())
XD = [list(map(int, sys.stdin.buffer.readline().split())) for _ in range(N)]
XD.sort()
X = [x for x, d in XD]
D = [d for x, d in XD]
# R[i]: i 番目のロボットがどこまで行くか
st = SegmentTree(list(range(N)), op=max)
for i, (x, d) in reversed(list(enumerate(XD))):
ri = bisect.bisect_left(X, x + d) - 1
st.set(i, st.get(i, ri + 1))
R = st.get_values_copy()
# dp[i]: ロボット i からロボット N - 1 までを使うときの組み合わせの数
dp = [0] * (N + 1)
dp[-1] = 1
for i, r in reversed(list(enumerate(R))):
# 使わない場合
dp[i] += dp[i + 1]
# 使う場合
dp[i] += dp[r + 1]
dp[i] %= MOD
# print(dp)
print(dp[0])
``` | output | 1 | 64,607 | 15 | 129,215 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N robots numbered 1 to N placed on a number line. Robot i is placed at coordinate X_i. When activated, it will travel the distance of D_i in the positive direction, and then it will be removed from the number line. All the robots move at the same speed, and their sizes are ignorable.
Takahashi, who is a mischievous boy, can do the following operation any number of times (possibly zero) as long as there is a robot remaining on the number line.
* Choose a robot and activate it. This operation cannot be done when there is a robot moving.
While Robot i is moving, if it touches another robot j that is remaining in the range [X_i, X_i + D_i) on the number line, Robot j also gets activated and starts moving. This process is repeated recursively.
How many possible sets of robots remaining on the number line are there after Takahashi does the operation some number of times? Compute this count modulo 998244353, since it can be enormous.
Constraints
* 1 \leq N \leq 2 \times 10^5
* -10^9 \leq X_i \leq 10^9
* 1 \leq D_i \leq 10^9
* X_i \neq X_j (i \neq j)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
X_1 D_1
:
X_N D_N
Output
Print the number of possible sets of robots remaining on the number line, modulo 998244353.
Examples
Input
2
1 5
3 3
Output
3
Input
3
6 5
-1 10
3 3
Output
5
Input
4
7 10
-10 3
4 3
-4 3
Output
16
Input
20
-8 1
26 4
0 5
9 1
19 4
22 20
28 27
11 8
-3 20
-25 17
10 4
-18 27
24 28
-11 19
2 27
-2 18
-1 12
-24 29
31 29
29 7
Output
110
Submitted Solution:
```
import bisect
import sys
stdin = sys.stdin
ni = lambda: int(ns())
na = lambda: list(map(int, stdin.readline().split()))
ns = lambda: stdin.readline().rstrip() # ignore trailing spaces
n = ni()
co = []
for i in range(n):
co.append(na())
co[-1][1] += co[-1][0]
co.sort(key=lambda x: x[0])
class Segtreermq:
def __init__(self, n):
self.H = 1
while self.H < n:
self.H *= 2
self.M = self.H * 2
self.vals = [999999999999] * self.M
def update(self, pos, v):
self.vals[self.H+pos] = v
x = self.H+pos>>1
while x >= 1:
self.vals[x] = min(self.vals[2*x], self.vals[2*x+1])
x>>=1
def min(self, l, r):
ret = 999999999999999
if l >= r:
return ret
while l != 0:
f = l&-l
if l+f > r:
break
v = self.vals[(self.H+l)//f]
if v < ret:
ret = v
l += f
while l < r:
f = r & -r
v = self.vals[(self.H+r)//f-1]
if v < ret:
ret = v
r -= f
return ret
xs = [_[0] for _ in co]
st = Segtreermq(n)
for i in range(n-1,-1,-1):
ind = bisect.bisect_left(xs, co[i][1])
reach = max(co[i][1], -st.min(i, ind))
st.update(i, -reach)
co[i][1] = reach
mod = 998244353
stack = []
dp = [0] * n
for i in range(n-1,-1,-1):
val = 1
while len(stack) > 0 and co[stack[-1]][1] <= co[i][1]:
val = val * dp[stack[-1]] % mod
stack.pop(-1)
dp[i] = (val + 1) % mod
stack.append(i)
ans = 1
for s in stack:
ans = ans * dp[s] % mod
print(ans)
``` | instruction | 0 | 64,608 | 15 | 129,216 |
Yes | output | 1 | 64,608 | 15 | 129,217 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N robots numbered 1 to N placed on a number line. Robot i is placed at coordinate X_i. When activated, it will travel the distance of D_i in the positive direction, and then it will be removed from the number line. All the robots move at the same speed, and their sizes are ignorable.
Takahashi, who is a mischievous boy, can do the following operation any number of times (possibly zero) as long as there is a robot remaining on the number line.
* Choose a robot and activate it. This operation cannot be done when there is a robot moving.
While Robot i is moving, if it touches another robot j that is remaining in the range [X_i, X_i + D_i) on the number line, Robot j also gets activated and starts moving. This process is repeated recursively.
How many possible sets of robots remaining on the number line are there after Takahashi does the operation some number of times? Compute this count modulo 998244353, since it can be enormous.
Constraints
* 1 \leq N \leq 2 \times 10^5
* -10^9 \leq X_i \leq 10^9
* 1 \leq D_i \leq 10^9
* X_i \neq X_j (i \neq j)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
X_1 D_1
:
X_N D_N
Output
Print the number of possible sets of robots remaining on the number line, modulo 998244353.
Examples
Input
2
1 5
3 3
Output
3
Input
3
6 5
-1 10
3 3
Output
5
Input
4
7 10
-10 3
4 3
-4 3
Output
16
Input
20
-8 1
26 4
0 5
9 1
19 4
22 20
28 27
11 8
-3 20
-25 17
10 4
-18 27
24 28
-11 19
2 27
-2 18
-1 12
-24 29
31 29
29 7
Output
110
Submitted Solution:
```
import sys
from bisect import bisect, bisect_left
class SquareDiv(): #区間の最大値を求める
def __init__(self, N, V):
k = 1
while k ** 2 < N: k += 1
self.array = [V] * k
self.size = k
self.indivisual = [V] * N
def update(self, i, v): #i番目をvに更新する
self.indivisual[i] = v
self.array[i // self.size] = max(self.array[i // self.size], v)
def search(self, left, right): #[left, right]の最大値を求める
lk, rk = left // self.size, right // self.size
if lk == rk:
maxN = 0
for i in range(left, right + 1): maxN = max(maxN, self.indivisual[i])
return maxN
else:
maxN = self.search(left, (lk + 1) * self.size - 1)
for k in range(lk + 1, rk): maxN = max(maxN, self.array[k])
maxN = max(maxN, self.search(rk * self.size, right))
return maxN
def solve():
input = sys.stdin.readline
N = int(input())
R = [[int(i) for i in input().split()] for _ in range(N)]
R.sort()
mod = 998244353
X = [R[i][0] for i in range(N)]
Connect = SquareDiv(N, 0)
DP = dict()
DP[N] = 1
for i in reversed(range(N)):
right = max(i, Connect.search(i, bisect_left(X, sum(R[i])) - 1))
Connect.update(i, right)
DP[i] = (DP[right + 1] + DP[i + 1]) % mod
print(DP[0])
return 0
if __name__ == "__main__":
solve()
``` | instruction | 0 | 64,609 | 15 | 129,218 |
Yes | output | 1 | 64,609 | 15 | 129,219 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N robots numbered 1 to N placed on a number line. Robot i is placed at coordinate X_i. When activated, it will travel the distance of D_i in the positive direction, and then it will be removed from the number line. All the robots move at the same speed, and their sizes are ignorable.
Takahashi, who is a mischievous boy, can do the following operation any number of times (possibly zero) as long as there is a robot remaining on the number line.
* Choose a robot and activate it. This operation cannot be done when there is a robot moving.
While Robot i is moving, if it touches another robot j that is remaining in the range [X_i, X_i + D_i) on the number line, Robot j also gets activated and starts moving. This process is repeated recursively.
How many possible sets of robots remaining on the number line are there after Takahashi does the operation some number of times? Compute this count modulo 998244353, since it can be enormous.
Constraints
* 1 \leq N \leq 2 \times 10^5
* -10^9 \leq X_i \leq 10^9
* 1 \leq D_i \leq 10^9
* X_i \neq X_j (i \neq j)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
X_1 D_1
:
X_N D_N
Output
Print the number of possible sets of robots remaining on the number line, modulo 998244353.
Examples
Input
2
1 5
3 3
Output
3
Input
3
6 5
-1 10
3 3
Output
5
Input
4
7 10
-10 3
4 3
-4 3
Output
16
Input
20
-8 1
26 4
0 5
9 1
19 4
22 20
28 27
11 8
-3 20
-25 17
10 4
-18 27
24 28
-11 19
2 27
-2 18
-1 12
-24 29
31 29
29 7
Output
110
Submitted Solution:
```
import sys
from bisect import bisect_left,bisect_right
input = sys.stdin.readline
ide = 0
def func(a,b):
return max(a,b)
class SegmentTree:
def __init__(self,ls,commutative = True):
if commutative == True:
self.n = len(ls)
self.tree = [ide for i in range(self.n)]+ls
else:
self.n = 2**((len(ls)-1).bit_length())
self.tree = [ide for i in range(self.n)]+ls+[ide for i in range(self.n-len(ls))]
for i in range(1,self.n)[::-1]:
self.tree[i] = func(self.tree[i<<1|0],self.tree[i<<1|1])
def getall(self):
return self.tree[1]
def get(self,l,r):
lret = ide
rret = ide
l += self.n
r += self.n
while l < r:
if l&1:
lret = func(lret,self.tree[l])
l += 1
if r&1:
rret = func(self.tree[r-1],rret)
l >>= 1
r >>= 1
ret = func(lret,rret)
return ret
def update(self,i,x):
i += self.n
self.tree[i] = x
while i > 1:
i >>= 1
self.tree[i] = func(self.tree[i<<1|0],self.tree[i<<1|1])
n = int(input())
xd = [list(map(int,input().split())) for i in range(n)]
mod = 998244353
xd.sort()
xls = list(zip(*xd))[0]
rls = [0]*n
st = SegmentTree(rls)
for i in range(n)[::-1]:
idx = bisect_left(xls,xd[i][0]+xd[i][1])-1
x = st.get(i,idx+1)
st.update(i,max(i,x))
dp = [0]*(n)
dp[-1] = 2
for i in range(n-1)[::-1]:
x = st.get(i,i+1)
if x == n-1:
dp[i] = dp[i+1]+1
else:
dp[i] = dp[i+1]+dp[x+1]
dp[i] %= mod
print(dp[0])
``` | instruction | 0 | 64,610 | 15 | 129,220 |
Yes | output | 1 | 64,610 | 15 | 129,221 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N robots numbered 1 to N placed on a number line. Robot i is placed at coordinate X_i. When activated, it will travel the distance of D_i in the positive direction, and then it will be removed from the number line. All the robots move at the same speed, and their sizes are ignorable.
Takahashi, who is a mischievous boy, can do the following operation any number of times (possibly zero) as long as there is a robot remaining on the number line.
* Choose a robot and activate it. This operation cannot be done when there is a robot moving.
While Robot i is moving, if it touches another robot j that is remaining in the range [X_i, X_i + D_i) on the number line, Robot j also gets activated and starts moving. This process is repeated recursively.
How many possible sets of robots remaining on the number line are there after Takahashi does the operation some number of times? Compute this count modulo 998244353, since it can be enormous.
Constraints
* 1 \leq N \leq 2 \times 10^5
* -10^9 \leq X_i \leq 10^9
* 1 \leq D_i \leq 10^9
* X_i \neq X_j (i \neq j)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
X_1 D_1
:
X_N D_N
Output
Print the number of possible sets of robots remaining on the number line, modulo 998244353.
Examples
Input
2
1 5
3 3
Output
3
Input
3
6 5
-1 10
3 3
Output
5
Input
4
7 10
-10 3
4 3
-4 3
Output
16
Input
20
-8 1
26 4
0 5
9 1
19 4
22 20
28 27
11 8
-3 20
-25 17
10 4
-18 27
24 28
-11 19
2 27
-2 18
-1 12
-24 29
31 29
29 7
Output
110
Submitted Solution:
```
class SegmentTreeMax():
def __init__(self,n,init):
self.offset=2**((n-1).bit_length())
self.tree=[init]*(2*self.offset)
self.init=init
def update(self,pos,val):
pos+=self.offset
self.tree[pos]=val
while pos>1:
pos=pos//2
self.tree[pos]=max(self.tree[2*pos],self.tree[2*pos+1])
def query(self,l,r):
l+=self.offset
r+=self.offset
ret=self.init
while l<=r:
ret=max(ret,self.tree[r])
r=(r-1)//2
ret=max(ret,self.tree[l])
l=(l+1)//2
return ret
mod=998244353
n=int(input())
arr=[list(map(int,input().split())) for _ in range(n)]
arr=sorted(arr,key=lambda x:x[0])
st=SegmentTreeMax(n,0)
ranges=[]
for i in range(n):
x=arr[i][0]+arr[i][1]
l=-1
r=n
while r-l!=1:
mid=(l+r)//2
if arr[mid][0]>=x:
r=mid
else:
l=mid
ranges.append(r-1)
st.update(i,r-1)
for i in range(n-1,-1,-1):
ranges[i]=st.query(i,ranges[i])
st.update(i,ranges[i])
dp=[0]*(n+1)
dp[-1]=1
for i in range(n-1,-1,-1):
j=ranges[i]+1
dp[i]=dp[i+1]+dp[j]
dp[i]%=mod
print(dp[0])
``` | instruction | 0 | 64,611 | 15 | 129,222 |
Yes | output | 1 | 64,611 | 15 | 129,223 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N robots numbered 1 to N placed on a number line. Robot i is placed at coordinate X_i. When activated, it will travel the distance of D_i in the positive direction, and then it will be removed from the number line. All the robots move at the same speed, and their sizes are ignorable.
Takahashi, who is a mischievous boy, can do the following operation any number of times (possibly zero) as long as there is a robot remaining on the number line.
* Choose a robot and activate it. This operation cannot be done when there is a robot moving.
While Robot i is moving, if it touches another robot j that is remaining in the range [X_i, X_i + D_i) on the number line, Robot j also gets activated and starts moving. This process is repeated recursively.
How many possible sets of robots remaining on the number line are there after Takahashi does the operation some number of times? Compute this count modulo 998244353, since it can be enormous.
Constraints
* 1 \leq N \leq 2 \times 10^5
* -10^9 \leq X_i \leq 10^9
* 1 \leq D_i \leq 10^9
* X_i \neq X_j (i \neq j)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
X_1 D_1
:
X_N D_N
Output
Print the number of possible sets of robots remaining on the number line, modulo 998244353.
Examples
Input
2
1 5
3 3
Output
3
Input
3
6 5
-1 10
3 3
Output
5
Input
4
7 10
-10 3
4 3
-4 3
Output
16
Input
20
-8 1
26 4
0 5
9 1
19 4
22 20
28 27
11 8
-3 20
-25 17
10 4
-18 27
24 28
-11 19
2 27
-2 18
-1 12
-24 29
31 29
29 7
Output
110
Submitted Solution:
```
import sys
import bisect
input = sys.stdin.readline
class SegmentTree:
def __init__(self, a):
self.padding = -float('inf')
self.n = len(a)
self.N = 2 ** (self.n-1).bit_length()
self.data = [self.padding]*(self.N-1) + a + [self.padding]*(self.N-self.n)
for i in range(2*self.N-2, 0, -2):
self.data[(i-1)//2] = max([self.data[i], self.data[i-1]])
def __len__(self):
return self.n
def update(self, i, x):
idx = self.N - 1 + i
self.data[idx] = x
while idx:
idx = (idx-1) // 2
self.data[idx] = max([self.data[2*idx+1], self.data[2*idx+2]])
def query(self, i, j):
# [i, j)
if i == j:
return self.data[self.N - 1 + i]
else:
idx1 = self.N - 1 + i
idx2 = self.N - 2 + j # 閉区間にする
result = self.padding
while idx1 + 1 < idx2:
if idx1&1 == 0: # idx1が偶数
result = max([result, self.data[idx1]])
if idx2&1 == 1: # idx2が奇数
result = max([result, self.data[idx2]])
idx2 -= 1
idx1 //= 2
idx2 = (idx2 - 1)//2
if idx1 == idx2:
result = max([result, self.data[idx1]])
else: # idx1 + 1 == idx2
result = max([result, self.data[idx1], self.data[idx2]])
return result
MOD = 998244353
N = int(input())
XD = [list(map(int, input().split())) for i in range(N)]
XD.sort()
X = [xd[0] for xd in XD]
dp = [0]*N + [1]
touch_range = [i for i in range(N)]
st = SegmentTree(touch_range)
for i in range(N-1, -1, -1):
right = X[i] + XD[i][1]
idx = bisect.bisect_left(X, right)-1
if idx > i:
idx = st.query(i, idx+1)
st.update(i, idx)
dp[i] = (dp[i+1] + dp[idx+1]) % MOD
print(dp[0])
``` | instruction | 0 | 64,612 | 15 | 129,224 |
No | output | 1 | 64,612 | 15 | 129,225 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N robots numbered 1 to N placed on a number line. Robot i is placed at coordinate X_i. When activated, it will travel the distance of D_i in the positive direction, and then it will be removed from the number line. All the robots move at the same speed, and their sizes are ignorable.
Takahashi, who is a mischievous boy, can do the following operation any number of times (possibly zero) as long as there is a robot remaining on the number line.
* Choose a robot and activate it. This operation cannot be done when there is a robot moving.
While Robot i is moving, if it touches another robot j that is remaining in the range [X_i, X_i + D_i) on the number line, Robot j also gets activated and starts moving. This process is repeated recursively.
How many possible sets of robots remaining on the number line are there after Takahashi does the operation some number of times? Compute this count modulo 998244353, since it can be enormous.
Constraints
* 1 \leq N \leq 2 \times 10^5
* -10^9 \leq X_i \leq 10^9
* 1 \leq D_i \leq 10^9
* X_i \neq X_j (i \neq j)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
X_1 D_1
:
X_N D_N
Output
Print the number of possible sets of robots remaining on the number line, modulo 998244353.
Examples
Input
2
1 5
3 3
Output
3
Input
3
6 5
-1 10
3 3
Output
5
Input
4
7 10
-10 3
4 3
-4 3
Output
16
Input
20
-8 1
26 4
0 5
9 1
19 4
22 20
28 27
11 8
-3 20
-25 17
10 4
-18 27
24 28
-11 19
2 27
-2 18
-1 12
-24 29
31 29
29 7
Output
110
Submitted Solution:
```
# -*- coding: utf-8 -*-
N = int(input())
X_D_list = []
for i in range(N):
X_D_list.append(list(map(int, input().split())))
X_D_list.sort()
ans = 2 ** N
i = 0
before_max_reach = X_D_list[0][0] + X_D_list[0][1]
for _ in range(N):
for j in range(1, N - i):
X_D = X_D_list[i + j]
if X_D[0] > before_max_reach:
i += j
ans *= (1 - (2 ** (j - 1) - 1) // (2 ** j))
break
before_max_reach = max(before_max_reach, X_D[0] + X_D[1])
else:
ans *= (1 - (2 ** j - 1) / (2 ** (j + 1)))
if i <= N - 1:
break
mod_div_num = 998244353
print(int(ans % mod_div_num))
``` | instruction | 0 | 64,613 | 15 | 129,226 |
No | output | 1 | 64,613 | 15 | 129,227 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N robots numbered 1 to N placed on a number line. Robot i is placed at coordinate X_i. When activated, it will travel the distance of D_i in the positive direction, and then it will be removed from the number line. All the robots move at the same speed, and their sizes are ignorable.
Takahashi, who is a mischievous boy, can do the following operation any number of times (possibly zero) as long as there is a robot remaining on the number line.
* Choose a robot and activate it. This operation cannot be done when there is a robot moving.
While Robot i is moving, if it touches another robot j that is remaining in the range [X_i, X_i + D_i) on the number line, Robot j also gets activated and starts moving. This process is repeated recursively.
How many possible sets of robots remaining on the number line are there after Takahashi does the operation some number of times? Compute this count modulo 998244353, since it can be enormous.
Constraints
* 1 \leq N \leq 2 \times 10^5
* -10^9 \leq X_i \leq 10^9
* 1 \leq D_i \leq 10^9
* X_i \neq X_j (i \neq j)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
X_1 D_1
:
X_N D_N
Output
Print the number of possible sets of robots remaining on the number line, modulo 998244353.
Examples
Input
2
1 5
3 3
Output
3
Input
3
6 5
-1 10
3 3
Output
5
Input
4
7 10
-10 3
4 3
-4 3
Output
16
Input
20
-8 1
26 4
0 5
9 1
19 4
22 20
28 27
11 8
-3 20
-25 17
10 4
-18 27
24 28
-11 19
2 27
-2 18
-1 12
-24 29
31 29
29 7
Output
110
Submitted Solution:
```
import heapq
def dfs(v: int) -> int:
res = 1
for u in child[v]:
res *= dfs(u)
return res + 1
n = int(input())
robot = [tuple(map(int, input().split())) for _ in range(n)]
robot.sort()
child = [[] for _ in range(n)]
root = []
for i in range(n-1, -1, -1):
x, d = robot[i]
while root:
r = heapq.heappop(root)
if r[0] < x + d:
child[i].append(r[1])
else:
heapq.heappush(root, r)
break
heapq.heappush(root, (x, i))
count = 1
for r in root:
count *= dfs(r[1])
print(count)
``` | instruction | 0 | 64,614 | 15 | 129,228 |
No | output | 1 | 64,614 | 15 | 129,229 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
There are N robots numbered 1 to N placed on a number line. Robot i is placed at coordinate X_i. When activated, it will travel the distance of D_i in the positive direction, and then it will be removed from the number line. All the robots move at the same speed, and their sizes are ignorable.
Takahashi, who is a mischievous boy, can do the following operation any number of times (possibly zero) as long as there is a robot remaining on the number line.
* Choose a robot and activate it. This operation cannot be done when there is a robot moving.
While Robot i is moving, if it touches another robot j that is remaining in the range [X_i, X_i + D_i) on the number line, Robot j also gets activated and starts moving. This process is repeated recursively.
How many possible sets of robots remaining on the number line are there after Takahashi does the operation some number of times? Compute this count modulo 998244353, since it can be enormous.
Constraints
* 1 \leq N \leq 2 \times 10^5
* -10^9 \leq X_i \leq 10^9
* 1 \leq D_i \leq 10^9
* X_i \neq X_j (i \neq j)
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
X_1 D_1
:
X_N D_N
Output
Print the number of possible sets of robots remaining on the number line, modulo 998244353.
Examples
Input
2
1 5
3 3
Output
3
Input
3
6 5
-1 10
3 3
Output
5
Input
4
7 10
-10 3
4 3
-4 3
Output
16
Input
20
-8 1
26 4
0 5
9 1
19 4
22 20
28 27
11 8
-3 20
-25 17
10 4
-18 27
24 28
-11 19
2 27
-2 18
-1 12
-24 29
31 29
29 7
Output
110
Submitted Solution:
```
def i1():
return int(input())
def i2():
return [int(i) for i in input().split()]
import bisect
import sys
sys.setrecursionlimit(10**6)
mod=998244353
n=i1()
d=[]
for i in range(n):
d.append(i2())
d=sorted(d)
dx=[]
dd=[]
for i,j in d:
dx.append(i)
dd.append(j)
r=[]
dt=[0 for i in range(n)]
dt[-1]=1
for i in range(n):
r.append(bisect.bisect_left(dx,dx[i]+dd[i]))
for i in range(n)[::-1]:
dt[i]=max([i]+dt[i+1:r[i]])
dp=[0 for i in range(n+1)]
dp[-1]=1
for i in range(n)[::-1]:
dp[i]+=dp[i+1]
dp[i]+=dp[dt[i]+1]
dp[i]%=mod
print(dp[0])
``` | instruction | 0 | 64,615 | 15 | 129,230 |
No | output | 1 | 64,615 | 15 | 129,231 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000 | instruction | 0 | 65,427 | 15 | 130,854 |
"Correct Solution:
```
h,w=map(int,input().split())
if h==1 or w==1:
ans=1
else:
ans=-int(-(h*w)//2)
print(ans)
``` | output | 1 | 65,427 | 15 | 130,855 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000 | instruction | 0 | 65,428 | 15 | 130,856 |
"Correct Solution:
```
n,m=map(int,input().split())
if n==1 or m==1:print(1);exit()
print(n*(m//2)+((n+1)//2)*(m%2))
``` | output | 1 | 65,428 | 15 | 130,857 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000 | instruction | 0 | 65,429 | 15 | 130,858 |
"Correct Solution:
```
h, w = map(int, input().split())
if h == 1 or w == 1:
print(1)
exit()
print(-(-h * w // 2))
``` | output | 1 | 65,429 | 15 | 130,859 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000 | instruction | 0 | 65,430 | 15 | 130,860 |
"Correct Solution:
```
h,w = map(int, input().split())
if h!=1 and w!=1: print(-(-h*w//2))
else:print('1')
``` | output | 1 | 65,430 | 15 | 130,861 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000 | instruction | 0 | 65,431 | 15 | 130,862 |
"Correct Solution:
```
h,w=map(int,input().split());print([0--h*w//2,1][h<2 or w<2])
``` | output | 1 | 65,431 | 15 | 130,863 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000 | instruction | 0 | 65,432 | 15 | 130,864 |
"Correct Solution:
```
a,b=map(int,input().split())
if 1 in (a,b):
print(1)
else: print((a*b+1)//2)
``` | output | 1 | 65,432 | 15 | 130,865 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000 | instruction | 0 | 65,433 | 15 | 130,866 |
"Correct Solution:
```
H, W = map(int, input().split())
if min(H, W) == 1:
print(1)
exit()
print((H * W + 1) // 2)
``` | output | 1 | 65,433 | 15 | 130,867 |
Provide a correct Python 3 solution for this coding contest problem.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000 | instruction | 0 | 65,434 | 15 | 130,868 |
"Correct Solution:
```
a,b=map(int,input().split())
if (a == 1 or b == 1):
print(1)
else:
print ((a*b+1)//2)
``` | output | 1 | 65,434 | 15 | 130,869 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000
Submitted Solution:
```
a,b=(int(x) for x in input().split())
ret = int((a*b+1)//2) if a!=1 and b!=1 else 1
print(ret)
``` | instruction | 0 | 65,435 | 15 | 130,870 |
Yes | output | 1 | 65,435 | 15 | 130,871 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000
Submitted Solution:
```
import math
h,w=map(int,input().split())
print(math.ceil(h*w/2) if h!=1 and w!=1 else 1)
``` | instruction | 0 | 65,436 | 15 | 130,872 |
Yes | output | 1 | 65,436 | 15 | 130,873 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000
Submitted Solution:
```
h,w=map(int,input().split())
print([1,sum(divmod(h*w, 2))][h>1<w])
``` | instruction | 0 | 65,437 | 15 | 130,874 |
Yes | output | 1 | 65,437 | 15 | 130,875 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000
Submitted Solution:
```
w, h = map(int, input().split())
ret = ((w * h) + 1) // 2 if w != 1 and h != 1 else 1
print(ret)
``` | instruction | 0 | 65,438 | 15 | 130,876 |
Yes | output | 1 | 65,438 | 15 | 130,877 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000
Submitted Solution:
```
# coding: utf-8
H, W = map(int, input().split())
# print(H, W)
N = H * W / 2
print(int(N))
``` | instruction | 0 | 65,439 | 15 | 130,878 |
No | output | 1 | 65,439 | 15 | 130,879 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000
Submitted Solution:
```
h, w = map(int, input().split())
if h == 1 or w == 0:
print(0)
elif h*w % 2 == 0:
print(int(h*w/2))
else:
print(int(h*w//2) + 1)
``` | instruction | 0 | 65,440 | 15 | 130,880 |
No | output | 1 | 65,440 | 15 | 130,881 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000
Submitted Solution:
```
import math
H,W=[int(s) for s in input().split(" ")]
print(math.ceil(H*W/2))
``` | instruction | 0 | 65,441 | 15 | 130,882 |
No | output | 1 | 65,441 | 15 | 130,883 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a board with H horizontal rows and W vertical columns of squares. There is a bishop at the top-left square on this board. How many squares can this bishop reach by zero or more movements?
Here the bishop can only move diagonally. More formally, the bishop can move from the square at the r_1-th row (from the top) and the c_1-th column (from the left) to the square at the r_2-th row and the c_2-th column if and only if exactly one of the following holds:
* r_1 + c_1 = r_2 + c_2
* r_1 - c_1 = r_2 - c_2
For example, in the following figure, the bishop can move to any of the red squares in one move:
<image>
Constraints
* 1 \leq H, W \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
H \ W
Output
Print the number of squares the bishop can reach.
Examples
Input
4 5
Output
10
Input
7 3
Output
11
Input
1000000000 1000000000
Output
500000000000000000
Submitted Solution:
```
a,b=map(int,input().split())
c=(a*b)
if c%2!=0:
ans=int((c/2))+1
else:
ans=int((c/2))
print(ans)
``` | instruction | 0 | 65,442 | 15 | 130,884 |
No | output | 1 | 65,442 | 15 | 130,885 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a garden consisting entirely of grass and weeds. Your garden is described by an n × m grid, with rows numbered 1 to n from top to bottom, and columns 1 to m from left to right. Each cell is identified by a pair (r, c) which means that the cell is located at row r and column c. Each cell may contain either grass or weeds. For example, a 4 × 5 garden may look as follows (empty cells denote grass):
<image>
You have a land-mower with you to mow all the weeds. Initially, you are standing with your lawnmower at the top-left corner of the garden. That is, at cell (1, 1). At any moment of time you are facing a certain direction — either left or right. And initially, you face right.
In one move you can do either one of these:
1) Move one cell in the direction that you are facing.
* if you are facing right: move from cell (r, c) to cell (r, c + 1)
<image>
* if you are facing left: move from cell (r, c) to cell (r, c - 1)
<image>
2) Move one cell down (that is, from cell (r, c) to cell (r + 1, c)), and change your direction to the opposite one.
* if you were facing right previously, you will face left
<image>
* if you were facing left previously, you will face right
<image>
You are not allowed to leave the garden. Weeds will be mowed if you and your lawnmower are standing at the cell containing the weeds (your direction doesn't matter). This action isn't counted as a move.
What is the minimum number of moves required to mow all the weeds?
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 150) — the number of rows and columns respectively. Then follow n lines containing m characters each — the content of the grid. "G" means that this cell contains grass. "W" means that this cell contains weeds.
It is guaranteed that the top-left corner of the grid will contain grass.
Output
Print a single number — the minimum number of moves required to mow all the weeds.
Examples
Input
4 5
GWGGW
GGWGG
GWGGG
WGGGG
Output
11
Input
3 3
GWW
WWW
WWG
Output
7
Input
1 1
G
Output
0
Note
For the first example, this is the picture of the initial state of the grid:
<image>
A possible solution is by mowing the weeds as illustrated below:
<image> | instruction | 0 | 65,676 | 15 | 131,352 |
Tags: greedy, sortings
Correct Solution:
```
from sys import maxsize, stdout, stdin,stderr
mod = int(1e9 + 7)
def I(): return int(stdin.readline())
def lint(): return [int(x) for x in stdin.readline().split()]
def S(): return input().strip()
def grid(r, c): return [lint() for i in range(r)]
from collections import defaultdict, Counter
import math
import heapq
from heapq import heappop , heappush
import bisect
from itertools import groupby
def gcd(a,b):
while b:
a %= b
tmp = a
a = b
b = tmp
return a
def lcm(a,b):
return a / gcd(a, b) * b
def check_prime(n):
for i in range(2, int(n ** (1 / 2)) + 1):
if not n % i:
return False
return True
def Bs(a, x):
i=0
j=0
left = 0
right = len(a)
flag=False
while left<right:
mi = (left+right)//2
#print(smi,a[mi],x)
if a[mi]<=x:
left = mi+1
i+=1
else:
right = mi
j+=1
#print(left,right,"----")
#print(i-1,j)
if left>0 and a[left-1]==x:
return i-1, j
else:
return -1, -1
def nCr(n, r):
return (fact(n) // (fact(r)
* fact(n - r)))
# Returns factorial of n
def fact(n):
res = 1
for i in range(2, n+1):
res = res * i
return res
def primefactors(n):
num=0
while n % 2 == 0:
num+=1
n = n / 2
for i in range(3,int(math.sqrt(n))+1,2):
while n % i== 0:
num+=1
n = n // i
if n > 2:
num+=1
return num
'''
def iter_ds(src):
store=[src]
while len(store):
tmp=store.pop()
if not vis[tmp]:
vis[tmp]=True
for j in ar[tmp]:
store.append(j)
'''
def ask(a):
print('? {}'.format(a),flush=True)
n=lint()
return n
d = defaultdict(lambda:[])
def dfs(i,p):
a,tmp=0,0
for j in d[i]:
if j!=p:
a+=1
tmp+=dfs(j,i)
if a==0:
return 0
return tmp/a + 1
n,m=lint()
s = [input() for _ in range(n)]
l=[]
new_n=0
for i in range(n):
mi,ma=None ,None
for j in range(m):
if s[i][j]=='W':
if mi==None:
mi=j
ma=j
if mi!=None:
new_n=i
l.append([mi,ma])
f=['R','L']
ans=0
j=0
for i in range(new_n+1):
if i==n-1:
if f[i%2]=='R':
t=l[i][1]
if l[i][1]==None:
t=0
tmp=max(t,j)
ans+=tmp-j
j=tmp
else:
t=l[i][0]
if l[i][0]==None:
t=m
tmp=min(t,j)
ans+=j-tmp
j=tmp
else:
if f[i%2]=='R':
t,t2=l[i+1][1],l[i][1]
if l[i+1][1]==None:
t=0
if l[i][1]==None:
t2=0
tmp=max(t,max(t2,j))
ans+=tmp-j
j=tmp
else:
t,t2=l[i+1][0],l[i][0]
if l[i+1][0]==None:
t=m
if l[i][0]==None:
t2=m
tmp=min(t,min(t2,j))
ans+=j-tmp
j=tmp
ans+=1
print(ans-1)
``` | output | 1 | 65,676 | 15 | 131,353 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a garden consisting entirely of grass and weeds. Your garden is described by an n × m grid, with rows numbered 1 to n from top to bottom, and columns 1 to m from left to right. Each cell is identified by a pair (r, c) which means that the cell is located at row r and column c. Each cell may contain either grass or weeds. For example, a 4 × 5 garden may look as follows (empty cells denote grass):
<image>
You have a land-mower with you to mow all the weeds. Initially, you are standing with your lawnmower at the top-left corner of the garden. That is, at cell (1, 1). At any moment of time you are facing a certain direction — either left or right. And initially, you face right.
In one move you can do either one of these:
1) Move one cell in the direction that you are facing.
* if you are facing right: move from cell (r, c) to cell (r, c + 1)
<image>
* if you are facing left: move from cell (r, c) to cell (r, c - 1)
<image>
2) Move one cell down (that is, from cell (r, c) to cell (r + 1, c)), and change your direction to the opposite one.
* if you were facing right previously, you will face left
<image>
* if you were facing left previously, you will face right
<image>
You are not allowed to leave the garden. Weeds will be mowed if you and your lawnmower are standing at the cell containing the weeds (your direction doesn't matter). This action isn't counted as a move.
What is the minimum number of moves required to mow all the weeds?
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 150) — the number of rows and columns respectively. Then follow n lines containing m characters each — the content of the grid. "G" means that this cell contains grass. "W" means that this cell contains weeds.
It is guaranteed that the top-left corner of the grid will contain grass.
Output
Print a single number — the minimum number of moves required to mow all the weeds.
Examples
Input
4 5
GWGGW
GGWGG
GWGGG
WGGGG
Output
11
Input
3 3
GWW
WWW
WWG
Output
7
Input
1 1
G
Output
0
Note
For the first example, this is the picture of the initial state of the grid:
<image>
A possible solution is by mowing the weeds as illustrated below:
<image> | instruction | 0 | 65,677 | 15 | 131,354 |
Tags: greedy, sortings
Correct Solution:
```
n, m = map(int, input().split())
a = [(s.find("W"), s.rfind("W")) for s in [input() for i in range(n)]]
steps = n-1
prev = 0
tr = True
while steps > 0 and a[steps][0] == -1:
steps -= 1
for i, j in a[:steps+1]:
if i != -1:
if tr == True:
steps += abs(i-prev)+j-i
prev = j
else:
steps += abs(j-prev)+j-i
prev = i
tr = not(tr)
print(steps)
"""
c = -1
for i in range(n):
if i % 2 != 0:
for j in range(m):
if "W" not in a[i] and i+1 <= n-1:
c += 1
if "W" in a[i+1][:j-1]:
for x in range(j, -1, -1):
c += 1
else:
for x in range(j, m):
c += 1
i += 1
break
c += 1
if a[i][j] == "W":
a[i][j] = "G"
else:
for j in range(m-1, -1, -1):
if "W" not in a[i] and i+1 <= n-1:
c += 1
if "W" in a[i+1][:j-1]:
for x in range(j, -1, -1):
c += 1
else:
for x in range(j, m):
c += 1
i += 1
break
c += 1
if a[i][j] == "W":
a[i][j] = "G"
print(c)
"""
``` | output | 1 | 65,677 | 15 | 131,355 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a garden consisting entirely of grass and weeds. Your garden is described by an n × m grid, with rows numbered 1 to n from top to bottom, and columns 1 to m from left to right. Each cell is identified by a pair (r, c) which means that the cell is located at row r and column c. Each cell may contain either grass or weeds. For example, a 4 × 5 garden may look as follows (empty cells denote grass):
<image>
You have a land-mower with you to mow all the weeds. Initially, you are standing with your lawnmower at the top-left corner of the garden. That is, at cell (1, 1). At any moment of time you are facing a certain direction — either left or right. And initially, you face right.
In one move you can do either one of these:
1) Move one cell in the direction that you are facing.
* if you are facing right: move from cell (r, c) to cell (r, c + 1)
<image>
* if you are facing left: move from cell (r, c) to cell (r, c - 1)
<image>
2) Move one cell down (that is, from cell (r, c) to cell (r + 1, c)), and change your direction to the opposite one.
* if you were facing right previously, you will face left
<image>
* if you were facing left previously, you will face right
<image>
You are not allowed to leave the garden. Weeds will be mowed if you and your lawnmower are standing at the cell containing the weeds (your direction doesn't matter). This action isn't counted as a move.
What is the minimum number of moves required to mow all the weeds?
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 150) — the number of rows and columns respectively. Then follow n lines containing m characters each — the content of the grid. "G" means that this cell contains grass. "W" means that this cell contains weeds.
It is guaranteed that the top-left corner of the grid will contain grass.
Output
Print a single number — the minimum number of moves required to mow all the weeds.
Examples
Input
4 5
GWGGW
GGWGG
GWGGG
WGGGG
Output
11
Input
3 3
GWW
WWW
WWG
Output
7
Input
1 1
G
Output
0
Note
For the first example, this is the picture of the initial state of the grid:
<image>
A possible solution is by mowing the weeds as illustrated below:
<image> | instruction | 0 | 65,678 | 15 | 131,356 |
Tags: greedy, sortings
Correct Solution:
```
n, m = map(int, input().split())
t = [(p.find('W'), p.rfind('W')) for p in [input() for i in range(n)]]
c, s, k = 0, n - 1, True
while s > 0 and t[s][0] == -1: s -= 1
for a, b in t[: s + 1]:
if a != -1:
if k:
s += abs(a - c) + b - a
c = b
else:
s += abs(b - c) + b - a
c = a
k = not k
print(s)
# Made By Mostafa_Khaled
``` | output | 1 | 65,678 | 15 | 131,357 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You have a garden consisting entirely of grass and weeds. Your garden is described by an n × m grid, with rows numbered 1 to n from top to bottom, and columns 1 to m from left to right. Each cell is identified by a pair (r, c) which means that the cell is located at row r and column c. Each cell may contain either grass or weeds. For example, a 4 × 5 garden may look as follows (empty cells denote grass):
<image>
You have a land-mower with you to mow all the weeds. Initially, you are standing with your lawnmower at the top-left corner of the garden. That is, at cell (1, 1). At any moment of time you are facing a certain direction — either left or right. And initially, you face right.
In one move you can do either one of these:
1) Move one cell in the direction that you are facing.
* if you are facing right: move from cell (r, c) to cell (r, c + 1)
<image>
* if you are facing left: move from cell (r, c) to cell (r, c - 1)
<image>
2) Move one cell down (that is, from cell (r, c) to cell (r + 1, c)), and change your direction to the opposite one.
* if you were facing right previously, you will face left
<image>
* if you were facing left previously, you will face right
<image>
You are not allowed to leave the garden. Weeds will be mowed if you and your lawnmower are standing at the cell containing the weeds (your direction doesn't matter). This action isn't counted as a move.
What is the minimum number of moves required to mow all the weeds?
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 150) — the number of rows and columns respectively. Then follow n lines containing m characters each — the content of the grid. "G" means that this cell contains grass. "W" means that this cell contains weeds.
It is guaranteed that the top-left corner of the grid will contain grass.
Output
Print a single number — the minimum number of moves required to mow all the weeds.
Examples
Input
4 5
GWGGW
GGWGG
GWGGG
WGGGG
Output
11
Input
3 3
GWW
WWW
WWG
Output
7
Input
1 1
G
Output
0
Note
For the first example, this is the picture of the initial state of the grid:
<image>
A possible solution is by mowing the weeds as illustrated below:
<image> | instruction | 0 | 65,679 | 15 | 131,358 |
Tags: greedy, sortings
Correct Solution:
```
n, m = map(int, input().split())
t = [(p.find('W'), p.rfind('W')) for p in [input() for i in range(n)]]
c, s, k = 0, n - 1, True
while s > 0 and t[s][0] == -1:
s -= 1
for a, b in t[: s + 1]:
if a != -1:
if k:
s += abs(a - c) + b - a
c = b
else:
s += abs(b - c) + b - a
c = a
k = not k
print(s)
``` | output | 1 | 65,679 | 15 | 131,359 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You have a garden consisting entirely of grass and weeds. Your garden is described by an n × m grid, with rows numbered 1 to n from top to bottom, and columns 1 to m from left to right. Each cell is identified by a pair (r, c) which means that the cell is located at row r and column c. Each cell may contain either grass or weeds. For example, a 4 × 5 garden may look as follows (empty cells denote grass):
<image>
You have a land-mower with you to mow all the weeds. Initially, you are standing with your lawnmower at the top-left corner of the garden. That is, at cell (1, 1). At any moment of time you are facing a certain direction — either left or right. And initially, you face right.
In one move you can do either one of these:
1) Move one cell in the direction that you are facing.
* if you are facing right: move from cell (r, c) to cell (r, c + 1)
<image>
* if you are facing left: move from cell (r, c) to cell (r, c - 1)
<image>
2) Move one cell down (that is, from cell (r, c) to cell (r + 1, c)), and change your direction to the opposite one.
* if you were facing right previously, you will face left
<image>
* if you were facing left previously, you will face right
<image>
You are not allowed to leave the garden. Weeds will be mowed if you and your lawnmower are standing at the cell containing the weeds (your direction doesn't matter). This action isn't counted as a move.
What is the minimum number of moves required to mow all the weeds?
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 150) — the number of rows and columns respectively. Then follow n lines containing m characters each — the content of the grid. "G" means that this cell contains grass. "W" means that this cell contains weeds.
It is guaranteed that the top-left corner of the grid will contain grass.
Output
Print a single number — the minimum number of moves required to mow all the weeds.
Examples
Input
4 5
GWGGW
GGWGG
GWGGG
WGGGG
Output
11
Input
3 3
GWW
WWW
WWG
Output
7
Input
1 1
G
Output
0
Note
For the first example, this is the picture of the initial state of the grid:
<image>
A possible solution is by mowing the weeds as illustrated below:
<image>
Submitted Solution:
```
from sys import maxsize, stdout, stdin,stderr
mod = int(1e9 + 7)
def I(): return int(stdin.readline())
def lint(): return [int(x) for x in stdin.readline().split()]
def S(): return input().strip()
def grid(r, c): return [lint() for i in range(r)]
from collections import defaultdict, Counter
import math
import heapq
from heapq import heappop , heappush
import bisect
from itertools import groupby
def gcd(a,b):
while b:
a %= b
tmp = a
a = b
b = tmp
return a
def lcm(a,b):
return a / gcd(a, b) * b
def check_prime(n):
for i in range(2, int(n ** (1 / 2)) + 1):
if not n % i:
return False
return True
def Bs(a, x):
i=0
j=0
left = 0
right = len(a)
flag=False
while left<right:
mi = (left+right)//2
#print(smi,a[mi],x)
if a[mi]<=x:
left = mi+1
i+=1
else:
right = mi
j+=1
#print(left,right,"----")
#print(i-1,j)
if left>0 and a[left-1]==x:
return i-1, j
else:
return -1, -1
def nCr(n, r):
return (fact(n) // (fact(r)
* fact(n - r)))
# Returns factorial of n
def fact(n):
res = 1
for i in range(2, n+1):
res = res * i
return res
def primefactors(n):
num=0
while n % 2 == 0:
num+=1
n = n / 2
for i in range(3,int(math.sqrt(n))+1,2):
while n % i== 0:
num+=1
n = n // i
if n > 2:
num+=1
return num
'''
def iter_ds(src):
store=[src]
while len(store):
tmp=store.pop()
if not vis[tmp]:
vis[tmp]=True
for j in ar[tmp]:
store.append(j)
'''
def ask(a):
print('? {}'.format(a),flush=True)
n=lint()
return n
d = defaultdict(lambda:[])
def dfs(i,p):
a,tmp=0,0
for j in d[i]:
if j!=p:
a+=1
tmp+=dfs(j,i)
if a==0:
return 0
return tmp/a + 1
n,m=lint()
s = [input() for _ in range(n)]
l=[]
for i in range(n):
mi,ma=None ,None
for j in range(m):
if s[i][j]=='W':
if mi==None:
mi=j
ma=j
l.append([mi,ma])
f=['R','L']
ans=0
j=0
for i in range(n):
if i==n-1:
if f[i%2]=='R':
t=l[i][1]
if l[i][1]==None:
t=0
tmp=max(t,j)
ans+=tmp-j
j=tmp
else:
t=l[i][0]
if l[i][0]==None:
t=m
tmp=min(t,j)
ans+=j-tmp
j=tmp
else:
if f[i%2]=='R':
t,t2=l[i+1][1],l[i][1]
if l[i+1][1]==None:
t=0
if l[i][1]==None:
t2=0
tmp=max(t,max(t2,j))
ans+=tmp-j
j=tmp
else:
t,t2=l[i+1][0],l[i][0]
if l[i+1][0]==None:
t=m
if l[i][0]==None:
t2=m
tmp=min(t,min(t2,j))
ans+=j-tmp
j=tmp
ans+=1
print(ans-1)
``` | instruction | 0 | 65,680 | 15 | 131,360 |
No | output | 1 | 65,680 | 15 | 131,361 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are at the top left cell (1, 1) of an n × m labyrinth. Your goal is to get to the bottom right cell (n, m). You can only move right or down, one cell per step. Moving right from a cell (x, y) takes you to the cell (x, y + 1), while moving down takes you to the cell (x + 1, y).
Some cells of the labyrinth contain rocks. When you move to a cell with rock, the rock is pushed to the next cell in the direction you're moving. If the next cell contains a rock, it gets pushed further, and so on.
The labyrinth is surrounded by impenetrable walls, thus any move that would put you or any rock outside of the labyrinth is illegal.
Count the number of different legal paths you can take from the start to the goal modulo 10^9 + 7. Two paths are considered different if there is at least one cell that is visited in one path, but not visited in the other.
Input
The first line contains two integers n, m — dimensions of the labyrinth (1 ≤ n, m ≤ 2000).
Next n lines describe the labyrinth. Each of these lines contains m characters. The j-th character of the i-th of these lines is equal to "R" if the cell (i, j) contains a rock, or "." if the cell (i, j) is empty.
It is guaranteed that the starting cell (1, 1) is empty.
Output
Print a single integer — the number of different legal paths from (1, 1) to (n, m) modulo 10^9 + 7.
Examples
Input
1 1
.
Output
1
Input
2 3
...
..R
Output
0
Input
4 4
...R
.RR.
.RR.
R...
Output
4
Note
In the first sample case we can't (and don't have to) move, hence the only path consists of a single cell (1, 1).
In the second sample case the goal is blocked and is unreachable.
Illustrations for the third sample case can be found here: <https://assets.codeforces.com/rounds/1225/index.html> | instruction | 0 | 65,701 | 15 | 131,402 |
Tags: binary search, dp
Correct Solution:
```
def getSum(dp, pos, s, e, type_):
if e < s:
return 0
if type_=='D':
if e==m-1:
return dp[pos][s]
return dp[pos][s]-dp[pos][e+1]
else:
if e==n-1:
return dp[s][pos]
return dp[s][pos]-dp[e+1][pos]
mod = 10**9+7
n, m = map(int, input().split())
a = [list(list(map(lambda x: 1 if x=='R' else 0, input()))) for _ in range(n)]
SD = [[0]*m for _ in range(n)]
SN = [[0]*m for _ in range(n)]
dpD = [[0]*m for _ in range(n)]
dpN = [[0]*m for _ in range(n)]
for i in range(n-1, -1, -1):
for j in range(m-1, -1, -1):
if i == n-1:
SD[i][j]=a[i][j]
else:
SD[i][j]=SD[i+1][j]+a[i][j]
if j == m-1:
SN[i][j]=a[i][j]
else:
SN[i][j]=SN[i][j+1]+a[i][j]
for j in range(m-1,-1,-1):
if a[n-1][j]==1:
break
dpD[n-1][j]=1
dpN[n-1][j]=1
for i in range(n-1,-1,-1):
if a[i][m-1]==1:
break
dpD[i][m-1]=1
dpN[i][m-1]=1
for j in range(m-2, -1, -1):
if i==n-1:
break
dpD[n-1][j]+=dpD[n-1][j+1]
for i in range(n-2,-1,-1):
if j==m-1:
break
dpN[i][m-1]+=dpN[i+1][m-1]
for i in range(n-2,-1,-1):
for j in range(m-2,-1,-1):
s, e = j, m-SN[i][j]-1
#print(i, j, s, e, 'N')
dpN[i][j] = getSum(dpD, i+1, s, e, 'D')
dpN[i][j] = (dpN[i][j] + dpN[i+1][j]) % mod
s, e = i, n-SD[i][j]-1
#print(i, j, s, e, 'D')
dpD[i][j] = getSum(dpN, j+1, s, e, 'N')
if i != 0:
for j in range(m-2,-1,-1):
dpD[i][j] = (dpD[i][j] + dpD[i][j+1]) % mod
print(dpD[0][0] % mod)
``` | output | 1 | 65,701 | 15 | 131,403 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are at the top left cell (1, 1) of an n × m labyrinth. Your goal is to get to the bottom right cell (n, m). You can only move right or down, one cell per step. Moving right from a cell (x, y) takes you to the cell (x, y + 1), while moving down takes you to the cell (x + 1, y).
Some cells of the labyrinth contain rocks. When you move to a cell with rock, the rock is pushed to the next cell in the direction you're moving. If the next cell contains a rock, it gets pushed further, and so on.
The labyrinth is surrounded by impenetrable walls, thus any move that would put you or any rock outside of the labyrinth is illegal.
Count the number of different legal paths you can take from the start to the goal modulo 10^9 + 7. Two paths are considered different if there is at least one cell that is visited in one path, but not visited in the other.
Input
The first line contains two integers n, m — dimensions of the labyrinth (1 ≤ n, m ≤ 2000).
Next n lines describe the labyrinth. Each of these lines contains m characters. The j-th character of the i-th of these lines is equal to "R" if the cell (i, j) contains a rock, or "." if the cell (i, j) is empty.
It is guaranteed that the starting cell (1, 1) is empty.
Output
Print a single integer — the number of different legal paths from (1, 1) to (n, m) modulo 10^9 + 7.
Examples
Input
1 1
.
Output
1
Input
2 3
...
..R
Output
0
Input
4 4
...R
.RR.
.RR.
R...
Output
4
Note
In the first sample case we can't (and don't have to) move, hence the only path consists of a single cell (1, 1).
In the second sample case the goal is blocked and is unreachable.
Illustrations for the third sample case can be found here: <https://assets.codeforces.com/rounds/1225/index.html>
Submitted Solution:
```
import sys
input = sys.stdin.readline
n,m = map(int,input().split())
a = [input().rstrip() for i in range(n)]
if min(n,m) == 1:
for i in a:
if "R" in i:
print(0)
break
else:
print(1)
exit()
mod = 10**9+7
acc = [[0 for i in range(m+1)] for j in range(n+1)]
for i in range(n):
for j in range(m):
if a[i][j] == "R":
acc[i+1][j+1] += acc[i][j+1]//10000*10000+10000
acc[i+1][j+1] += acc[i+1][j]%10000+1
else:
acc[i+1][j+1] += acc[i][j+1]//10000*10000+acc[i+1][j]%10000
dp = [[0 for i in range(m)] for j in range(2*n-1)]
dp[0][0] = 1
dp[1][0] = 1
for i in range(2*n-1):
if i%2 == 0:
for j in range(m-1):
if j and (acc[i//2+1][m]-acc[i//2+1][j])%10000 <= m-2-j:
dp[i][j] += dp[i][j-1]
if i and (acc[i//2+1][m]-acc[i//2+1][j+1])%10000 <= m-2-j:
dp[i][j] += dp[i-1][j]
dp[i][j] %= mod
else:
for j in range(m):
if j and (acc[n][j+1]-acc[i//2+1][j+1])//10000 <= n-i//2-2:
dp[i][j] += dp[i-1][j-1]
if i > 1 and (acc[n][j+1]-acc[i//2][j])//10000 <= n-i//2-2:
dp[i][j] += dp[i-2][j]
dp[i][j] %= mod
print(dp[-1][-2]+dp[-2][-1])
``` | instruction | 0 | 65,702 | 15 | 131,404 |
No | output | 1 | 65,702 | 15 | 131,405 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are at the top left cell (1, 1) of an n × m labyrinth. Your goal is to get to the bottom right cell (n, m). You can only move right or down, one cell per step. Moving right from a cell (x, y) takes you to the cell (x, y + 1), while moving down takes you to the cell (x + 1, y).
Some cells of the labyrinth contain rocks. When you move to a cell with rock, the rock is pushed to the next cell in the direction you're moving. If the next cell contains a rock, it gets pushed further, and so on.
The labyrinth is surrounded by impenetrable walls, thus any move that would put you or any rock outside of the labyrinth is illegal.
Count the number of different legal paths you can take from the start to the goal modulo 10^9 + 7. Two paths are considered different if there is at least one cell that is visited in one path, but not visited in the other.
Input
The first line contains two integers n, m — dimensions of the labyrinth (1 ≤ n, m ≤ 2000).
Next n lines describe the labyrinth. Each of these lines contains m characters. The j-th character of the i-th of these lines is equal to "R" if the cell (i, j) contains a rock, or "." if the cell (i, j) is empty.
It is guaranteed that the starting cell (1, 1) is empty.
Output
Print a single integer — the number of different legal paths from (1, 1) to (n, m) modulo 10^9 + 7.
Examples
Input
1 1
.
Output
1
Input
2 3
...
..R
Output
0
Input
4 4
...R
.RR.
.RR.
R...
Output
4
Note
In the first sample case we can't (and don't have to) move, hence the only path consists of a single cell (1, 1).
In the second sample case the goal is blocked and is unreachable.
Illustrations for the third sample case can be found here: <https://assets.codeforces.com/rounds/1225/index.html>
Submitted Solution:
```
def getSum(dp, pos, s, e, type_):
if e < s:
return 0
if type_=='D':
if e==m-1:
return dp[pos][s]
return dp[pos][s]-dp[pos][e+1]
else:
if e==n-1:
return dp[s][pos]
return dp[s][pos]-dp[e+1][pos]
mod = 10**9+7
n, m = map(int, input().split())
a = [list(list(map(lambda x: 1 if x=='R' else 0, input()))) for _ in range(n)]
SD = [[0]*m for _ in range(n)]
SN = [[0]*m for _ in range(n)]
dpD = [[0]*m for _ in range(n)]
dpN = [[0]*m for _ in range(n)]
for i in range(n-1, -1, -1):
for j in range(m-1, -1, -1):
if i == n-1:
SD[i][j]=a[i][j]
else:
SD[i][j]=SD[i+1][j]+a[i][j]
if j == m-1:
SN[i][j]=a[i][j]
else:
SN[i][j]=SN[i][j+1]+a[i][j]
for j in range(m-1,-1,-1):
if a[n-1][j]==1:
break
dpD[n-1][j]=1
dpN[n-1][j]=1
for i in range(n-1,-1,-1):
if a[i][m-1]==1:
break
dpD[i][m-1]=1
dpN[i][m-1]=1
for j in range(m-2, -1, -1):
#if a[n-1][j]==1:
# break
dpD[n-1][j]+=dpD[n-1][j+1]
for i in range(n-2,-1,-1):
#if a[i][m-1]==1:
# break
dpN[i][m-1]+=dpN[i+1][m-1]
for i in range(n-2,-1,-1):
for j in range(m-2,-1,-1):
s, e = j, m-SN[i][j]-1
#print(i, j, s, e, 'N')
dpN[i][j] = getSum(dpD, i+1, s, e, 'D')
dpN[i][j] = (dpN[i][j] + dpN[i+1][j]) % mod
s, e = i, n-SD[i][j]-1
#print(i, j, s, e, 'D')
dpD[i][j] = getSum(dpN, j+1, s, e, 'N')
if i != 0:
for j in range(m-2,-1,-1):
dpD[i][j] = (dpD[i][j] + dpD[i][j+1]) % mod
print(min(dpD[0][0], dpN[0][0]) % mod)
``` | instruction | 0 | 65,703 | 15 | 131,406 |
No | output | 1 | 65,703 | 15 | 131,407 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are at the top left cell (1, 1) of an n × m labyrinth. Your goal is to get to the bottom right cell (n, m). You can only move right or down, one cell per step. Moving right from a cell (x, y) takes you to the cell (x, y + 1), while moving down takes you to the cell (x + 1, y).
Some cells of the labyrinth contain rocks. When you move to a cell with rock, the rock is pushed to the next cell in the direction you're moving. If the next cell contains a rock, it gets pushed further, and so on.
The labyrinth is surrounded by impenetrable walls, thus any move that would put you or any rock outside of the labyrinth is illegal.
Count the number of different legal paths you can take from the start to the goal modulo 10^9 + 7. Two paths are considered different if there is at least one cell that is visited in one path, but not visited in the other.
Input
The first line contains two integers n, m — dimensions of the labyrinth (1 ≤ n, m ≤ 2000).
Next n lines describe the labyrinth. Each of these lines contains m characters. The j-th character of the i-th of these lines is equal to "R" if the cell (i, j) contains a rock, or "." if the cell (i, j) is empty.
It is guaranteed that the starting cell (1, 1) is empty.
Output
Print a single integer — the number of different legal paths from (1, 1) to (n, m) modulo 10^9 + 7.
Examples
Input
1 1
.
Output
1
Input
2 3
...
..R
Output
0
Input
4 4
...R
.RR.
.RR.
R...
Output
4
Note
In the first sample case we can't (and don't have to) move, hence the only path consists of a single cell (1, 1).
In the second sample case the goal is blocked and is unreachable.
Illustrations for the third sample case can be found here: <https://assets.codeforces.com/rounds/1225/index.html>
Submitted Solution:
```
n, m = map(int, input().split())
a = [input() for _ in range(n)]
dp = [[-1] * m for _ in range(n)]
dp[0][0] = 1
for i in range(n):
for j in range(m):
if dp[i][j] == -1:
dp[i][j] = 0
if 0 <= i - 1 and not (a[i][j] == 'R' and i + 2 == m):
dp[i][j] += dp[i - 1][j]
if 0 <= j - 1 and not (a[i][j] == 'R' and j + 2 == n):
dp[i][j] += dp[i][j - 1]
if a[-1][-1] != 'R':
print(dp[-1][-1] % int(1e9 + 7))
else:
print(0)
``` | instruction | 0 | 65,704 | 15 | 131,408 |
No | output | 1 | 65,704 | 15 | 131,409 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
You are at the top left cell (1, 1) of an n × m labyrinth. Your goal is to get to the bottom right cell (n, m). You can only move right or down, one cell per step. Moving right from a cell (x, y) takes you to the cell (x, y + 1), while moving down takes you to the cell (x + 1, y).
Some cells of the labyrinth contain rocks. When you move to a cell with rock, the rock is pushed to the next cell in the direction you're moving. If the next cell contains a rock, it gets pushed further, and so on.
The labyrinth is surrounded by impenetrable walls, thus any move that would put you or any rock outside of the labyrinth is illegal.
Count the number of different legal paths you can take from the start to the goal modulo 10^9 + 7. Two paths are considered different if there is at least one cell that is visited in one path, but not visited in the other.
Input
The first line contains two integers n, m — dimensions of the labyrinth (1 ≤ n, m ≤ 2000).
Next n lines describe the labyrinth. Each of these lines contains m characters. The j-th character of the i-th of these lines is equal to "R" if the cell (i, j) contains a rock, or "." if the cell (i, j) is empty.
It is guaranteed that the starting cell (1, 1) is empty.
Output
Print a single integer — the number of different legal paths from (1, 1) to (n, m) modulo 10^9 + 7.
Examples
Input
1 1
.
Output
1
Input
2 3
...
..R
Output
0
Input
4 4
...R
.RR.
.RR.
R...
Output
4
Note
In the first sample case we can't (and don't have to) move, hence the only path consists of a single cell (1, 1).
In the second sample case the goal is blocked and is unreachable.
Illustrations for the third sample case can be found here: <https://assets.codeforces.com/rounds/1225/index.html>
Submitted Solution:
```
import sys
input = sys.stdin.readline
n,m = map(int,input().split())
a = [input().rstrip() for i in range(n)]
if min(n,m) == 1:
for i in a:
if "R" in i:
print(0)
break
else:
print(1)
exit()
mod = 10**9+7
acc = [[0 for i in range(m+1)] for j in range(n+1)]
for i in range(n):
for j in range(m):
if a[i][j] == "R":
acc[i+1][j+1] += acc[i][j+1]//10000*10000+10000
acc[i+1][j+1] += acc[i+1][j]%10000+1
else:
acc[i+1][j+1] += acc[i][j+1]//10000*10000+acc[i+1][j]%10000
dp = [[0 for i in range(m)] for j in range(2*n-1)]
if (acc[1][m]-acc[1][1])%10000 <= m-2:
dp[0][0] = 1
if (acc[n][1]-acc[1][1])//10000 <= n-2:
dp[1][0] = 1
for i in range(2*n-1):
if i%2 == 0:
for j in range(m-1):
if j and (acc[i//2+1][m]-acc[i//2+1][j])%10000 <= m-2-j:
dp[i][j] += dp[i][j-1]
if i and (acc[i//2+1][m]-acc[i//2+1][j+1])%10000 <= m-2-j:
dp[i][j] += dp[i-1][j]
dp[i][j] %= mod
else:
for j in range(m):
if j and (acc[n][j+1]-acc[i//2+1][j+1])//10000 <= n-i//2-2:
dp[i][j] += dp[i-1][j-1]
if i > 1 and (acc[n][j+1]-acc[i//2][j+1])//10000 <= n-i//2-2:
dp[i][j] += dp[i-2][j]
dp[i][j] %= mod
"""
for i in range(2*n-1):
if i%2:
print(*dp[i])
else:
print("",*dp[i][:m-1])
"""
print(dp[-1][-2]+dp[-2][-1])
``` | instruction | 0 | 65,705 | 15 | 131,410 |
No | output | 1 | 65,705 | 15 | 131,411 |
Provide tags and a correct Python 3 solution for this coding contest problem.
A map of some object is a rectangular field consisting of n rows and n columns. Each cell is initially occupied by the sea but you can cover some some cells of the map with sand so that exactly k islands appear on the map. We will call a set of sand cells to be island if it is possible to get from each of them to each of them by moving only through sand cells and by moving from a cell only to a side-adjacent cell. The cells are called to be side-adjacent if they share a vertical or horizontal side. It is easy to see that islands do not share cells (otherwise they together form a bigger island).
Find a way to cover some cells with sand so that exactly k islands appear on the n × n map, or determine that no such way exists.
Input
The single line contains two positive integers n, k (1 ≤ n ≤ 100, 0 ≤ k ≤ n2) — the size of the map and the number of islands you should form.
Output
If the answer doesn't exist, print "NO" (without the quotes) in a single line.
Otherwise, print "YES" in the first line. In the next n lines print the description of the map. Each of the lines of the description must consist only of characters 'S' and 'L', where 'S' is a cell that is occupied by the sea and 'L' is the cell covered with sand. The length of each line of the description must equal n.
If there are multiple answers, you may print any of them.
You should not maximize the sizes of islands.
Examples
Input
5 2
Output
YES
SSSSS
LLLLL
SSSSS
LLLLL
SSSSS
Input
5 25
Output
NO | instruction | 0 | 66,013 | 15 | 132,026 |
Tags: constructive algorithms, implementation
Correct Solution:
```
n,k=map(int,input().split())
lm=(n*n+1)//2
if lm<k:
print('NO')
else:
print('YES')
for i in range(n):
for j in range(n):
if k>0 and (i+j)%2==0:
print('L',end='')
k-=1
else:
print('S',end='')
print()
``` | output | 1 | 66,013 | 15 | 132,027 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ari the monster always wakes up very early with the first ray of the sun and the first thing she does is feeding her squirrel.
Ari draws a regular convex polygon on the floor and numbers it's vertices 1, 2, ..., n in clockwise order. Then starting from the vertex 1 she draws a ray in the direction of each other vertex. The ray stops when it reaches a vertex or intersects with another ray drawn before. Ari repeats this process for vertex 2, 3, ..., n (in this particular order). And then she puts a walnut in each region inside the polygon.
<image>
Ada the squirrel wants to collect all the walnuts, but she is not allowed to step on the lines drawn by Ari. That means Ada have to perform a small jump if she wants to go from one region to another. Ada can jump from one region P to another region Q if and only if P and Q share a side or a corner.
Assuming that Ada starts from outside of the picture, what is the minimum number of jumps she has to perform in order to collect all the walnuts?
Input
The first and only line of the input contains a single integer n (3 ≤ n ≤ 54321) - the number of vertices of the regular polygon drawn by Ari.
Output
Print the minimum number of jumps Ada should make to collect all the walnuts. Note, that she doesn't need to leave the polygon after.
Examples
Input
5
Output
9
Input
3
Output
1
Note
One of the possible solutions for the first sample is shown on the picture above. | instruction | 0 | 66,031 | 15 | 132,062 |
Tags: math
Correct Solution:
```
n=int(input())
if (n==3):
print(1)
else:
print((n-2)**(2))
``` | output | 1 | 66,031 | 15 | 132,063 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ari the monster always wakes up very early with the first ray of the sun and the first thing she does is feeding her squirrel.
Ari draws a regular convex polygon on the floor and numbers it's vertices 1, 2, ..., n in clockwise order. Then starting from the vertex 1 she draws a ray in the direction of each other vertex. The ray stops when it reaches a vertex or intersects with another ray drawn before. Ari repeats this process for vertex 2, 3, ..., n (in this particular order). And then she puts a walnut in each region inside the polygon.
<image>
Ada the squirrel wants to collect all the walnuts, but she is not allowed to step on the lines drawn by Ari. That means Ada have to perform a small jump if she wants to go from one region to another. Ada can jump from one region P to another region Q if and only if P and Q share a side or a corner.
Assuming that Ada starts from outside of the picture, what is the minimum number of jumps she has to perform in order to collect all the walnuts?
Input
The first and only line of the input contains a single integer n (3 ≤ n ≤ 54321) - the number of vertices of the regular polygon drawn by Ari.
Output
Print the minimum number of jumps Ada should make to collect all the walnuts. Note, that she doesn't need to leave the polygon after.
Examples
Input
5
Output
9
Input
3
Output
1
Note
One of the possible solutions for the first sample is shown on the picture above. | instruction | 0 | 66,033 | 15 | 132,066 |
Tags: math
Correct Solution:
```
import sys
def main():
N = int(sys.stdin.read())
result = (N-3)*3 + (N-4)*(N-3) + 1
print(result)
main()
``` | output | 1 | 66,033 | 15 | 132,067 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ari the monster always wakes up very early with the first ray of the sun and the first thing she does is feeding her squirrel.
Ari draws a regular convex polygon on the floor and numbers it's vertices 1, 2, ..., n in clockwise order. Then starting from the vertex 1 she draws a ray in the direction of each other vertex. The ray stops when it reaches a vertex or intersects with another ray drawn before. Ari repeats this process for vertex 2, 3, ..., n (in this particular order). And then she puts a walnut in each region inside the polygon.
<image>
Ada the squirrel wants to collect all the walnuts, but she is not allowed to step on the lines drawn by Ari. That means Ada have to perform a small jump if she wants to go from one region to another. Ada can jump from one region P to another region Q if and only if P and Q share a side or a corner.
Assuming that Ada starts from outside of the picture, what is the minimum number of jumps she has to perform in order to collect all the walnuts?
Input
The first and only line of the input contains a single integer n (3 ≤ n ≤ 54321) - the number of vertices of the regular polygon drawn by Ari.
Output
Print the minimum number of jumps Ada should make to collect all the walnuts. Note, that she doesn't need to leave the polygon after.
Examples
Input
5
Output
9
Input
3
Output
1
Note
One of the possible solutions for the first sample is shown on the picture above. | instruction | 0 | 66,035 | 15 | 132,070 |
Tags: math
Correct Solution:
```
n = int(input())
if n > 3:
print((n-2)**2)
else:
print(1)
``` | output | 1 | 66,035 | 15 | 132,071 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Ari the monster always wakes up very early with the first ray of the sun and the first thing she does is feeding her squirrel.
Ari draws a regular convex polygon on the floor and numbers it's vertices 1, 2, ..., n in clockwise order. Then starting from the vertex 1 she draws a ray in the direction of each other vertex. The ray stops when it reaches a vertex or intersects with another ray drawn before. Ari repeats this process for vertex 2, 3, ..., n (in this particular order). And then she puts a walnut in each region inside the polygon.
<image>
Ada the squirrel wants to collect all the walnuts, but she is not allowed to step on the lines drawn by Ari. That means Ada have to perform a small jump if she wants to go from one region to another. Ada can jump from one region P to another region Q if and only if P and Q share a side or a corner.
Assuming that Ada starts from outside of the picture, what is the minimum number of jumps she has to perform in order to collect all the walnuts?
Input
The first and only line of the input contains a single integer n (3 ≤ n ≤ 54321) - the number of vertices of the regular polygon drawn by Ari.
Output
Print the minimum number of jumps Ada should make to collect all the walnuts. Note, that she doesn't need to leave the polygon after.
Examples
Input
5
Output
9
Input
3
Output
1
Note
One of the possible solutions for the first sample is shown on the picture above. | instruction | 0 | 66,036 | 15 | 132,072 |
Tags: math
Correct Solution:
```
x=int(input())
add=1
ans=0
for i in range(0,x-2):
ans = ans + add
add = add + 2
print(ans)
``` | output | 1 | 66,036 | 15 | 132,073 |
Provide a correct Python 3 solution for this coding contest problem.
We have a grid of H rows and W columns. Initially, there is a stone in the top left cell. Shik is trying to move the stone to the bottom right cell. In each step, he can move the stone one cell to its left, up, right, or down (if such cell exists). It is possible that the stone visits a cell multiple times (including the bottom right and the top left cell).
You are given a matrix of characters a_{ij} (1 \leq i \leq H, 1 \leq j \leq W). After Shik completes all moving actions, a_{ij} is `#` if the stone had ever located at the i-th row and the j-th column during the process of moving. Otherwise, a_{ij} is `.`. Please determine whether it is possible that Shik only uses right and down moves in all steps.
Constraints
* 2 \leq H, W \leq 8
* a_{i,j} is either `#` or `.`.
* There exists a valid sequence of moves for Shik to generate the map a.
Input
The input is given from Standard Input in the following format:
H W
a_{11}a_{12}...a_{1W}
:
a_{H1}a_{H2}...a_{HW}
Output
If it is possible that Shik only uses right and down moves, print `Possible`. Otherwise, print `Impossible`.
Examples
Input
4 5
##...
.##..
..##.
...##
Output
Possible
Input
4 5
...
.##..
..##.
...##
Output
Possible
Input
5 3
..#
..
Output
Impossible
Input
4 5
...
.###.
.###.
...##
Output
Impossible | instruction | 0 | 66,354 | 15 | 132,708 |
"Correct Solution:
```
h, w = [ int(v) for v in input().split() ]
v = 0
for i in range(h):
v += input().count("#")
if v == h + w - 1:
print("Possible")
else:
print("Impossible")
``` | output | 1 | 66,354 | 15 | 132,709 |
Provide a correct Python 3 solution for this coding contest problem.
We have a grid of H rows and W columns. Initially, there is a stone in the top left cell. Shik is trying to move the stone to the bottom right cell. In each step, he can move the stone one cell to its left, up, right, or down (if such cell exists). It is possible that the stone visits a cell multiple times (including the bottom right and the top left cell).
You are given a matrix of characters a_{ij} (1 \leq i \leq H, 1 \leq j \leq W). After Shik completes all moving actions, a_{ij} is `#` if the stone had ever located at the i-th row and the j-th column during the process of moving. Otherwise, a_{ij} is `.`. Please determine whether it is possible that Shik only uses right and down moves in all steps.
Constraints
* 2 \leq H, W \leq 8
* a_{i,j} is either `#` or `.`.
* There exists a valid sequence of moves for Shik to generate the map a.
Input
The input is given from Standard Input in the following format:
H W
a_{11}a_{12}...a_{1W}
:
a_{H1}a_{H2}...a_{HW}
Output
If it is possible that Shik only uses right and down moves, print `Possible`. Otherwise, print `Impossible`.
Examples
Input
4 5
##...
.##..
..##.
...##
Output
Possible
Input
4 5
...
.##..
..##.
...##
Output
Possible
Input
5 3
..#
..
Output
Impossible
Input
4 5
...
.###.
.###.
...##
Output
Impossible | instruction | 0 | 66,355 | 15 | 132,710 |
"Correct Solution:
```
h,w = map(int,input().split())
point = 0
for _ in range(h):
s = input()
point += s.count("#")
if point == (h+w-1):
print("Possible")
else:
print("Impossible")
``` | output | 1 | 66,355 | 15 | 132,711 |
Provide a correct Python 3 solution for this coding contest problem.
We have a grid of H rows and W columns. Initially, there is a stone in the top left cell. Shik is trying to move the stone to the bottom right cell. In each step, he can move the stone one cell to its left, up, right, or down (if such cell exists). It is possible that the stone visits a cell multiple times (including the bottom right and the top left cell).
You are given a matrix of characters a_{ij} (1 \leq i \leq H, 1 \leq j \leq W). After Shik completes all moving actions, a_{ij} is `#` if the stone had ever located at the i-th row and the j-th column during the process of moving. Otherwise, a_{ij} is `.`. Please determine whether it is possible that Shik only uses right and down moves in all steps.
Constraints
* 2 \leq H, W \leq 8
* a_{i,j} is either `#` or `.`.
* There exists a valid sequence of moves for Shik to generate the map a.
Input
The input is given from Standard Input in the following format:
H W
a_{11}a_{12}...a_{1W}
:
a_{H1}a_{H2}...a_{HW}
Output
If it is possible that Shik only uses right and down moves, print `Possible`. Otherwise, print `Impossible`.
Examples
Input
4 5
##...
.##..
..##.
...##
Output
Possible
Input
4 5
...
.##..
..##.
...##
Output
Possible
Input
5 3
..#
..
Output
Impossible
Input
4 5
...
.###.
.###.
...##
Output
Impossible | instruction | 0 | 66,356 | 15 | 132,712 |
"Correct Solution:
```
h,w=map(int,input().split())
a=str()
for i in range(h):
a+=input()
print('Possible' if a.count('#')==int(h)+int(w)-1 else 'Impossible')
``` | output | 1 | 66,356 | 15 | 132,713 |
Provide a correct Python 3 solution for this coding contest problem.
We have a grid of H rows and W columns. Initially, there is a stone in the top left cell. Shik is trying to move the stone to the bottom right cell. In each step, he can move the stone one cell to its left, up, right, or down (if such cell exists). It is possible that the stone visits a cell multiple times (including the bottom right and the top left cell).
You are given a matrix of characters a_{ij} (1 \leq i \leq H, 1 \leq j \leq W). After Shik completes all moving actions, a_{ij} is `#` if the stone had ever located at the i-th row and the j-th column during the process of moving. Otherwise, a_{ij} is `.`. Please determine whether it is possible that Shik only uses right and down moves in all steps.
Constraints
* 2 \leq H, W \leq 8
* a_{i,j} is either `#` or `.`.
* There exists a valid sequence of moves for Shik to generate the map a.
Input
The input is given from Standard Input in the following format:
H W
a_{11}a_{12}...a_{1W}
:
a_{H1}a_{H2}...a_{HW}
Output
If it is possible that Shik only uses right and down moves, print `Possible`. Otherwise, print `Impossible`.
Examples
Input
4 5
##...
.##..
..##.
...##
Output
Possible
Input
4 5
...
.##..
..##.
...##
Output
Possible
Input
5 3
..#
..
Output
Impossible
Input
4 5
...
.###.
.###.
...##
Output
Impossible | instruction | 0 | 66,357 | 15 | 132,714 |
"Correct Solution:
```
h,w=map(int,input().split())
r=0
for _ in range(h):r+=input().count('#')
print('Possible'if r==h+w-1else'Impossible')
``` | output | 1 | 66,357 | 15 | 132,715 |
Provide a correct Python 3 solution for this coding contest problem.
We have a grid of H rows and W columns. Initially, there is a stone in the top left cell. Shik is trying to move the stone to the bottom right cell. In each step, he can move the stone one cell to its left, up, right, or down (if such cell exists). It is possible that the stone visits a cell multiple times (including the bottom right and the top left cell).
You are given a matrix of characters a_{ij} (1 \leq i \leq H, 1 \leq j \leq W). After Shik completes all moving actions, a_{ij} is `#` if the stone had ever located at the i-th row and the j-th column during the process of moving. Otherwise, a_{ij} is `.`. Please determine whether it is possible that Shik only uses right and down moves in all steps.
Constraints
* 2 \leq H, W \leq 8
* a_{i,j} is either `#` or `.`.
* There exists a valid sequence of moves for Shik to generate the map a.
Input
The input is given from Standard Input in the following format:
H W
a_{11}a_{12}...a_{1W}
:
a_{H1}a_{H2}...a_{HW}
Output
If it is possible that Shik only uses right and down moves, print `Possible`. Otherwise, print `Impossible`.
Examples
Input
4 5
##...
.##..
..##.
...##
Output
Possible
Input
4 5
...
.##..
..##.
...##
Output
Possible
Input
5 3
..#
..
Output
Impossible
Input
4 5
...
.###.
.###.
...##
Output
Impossible | instruction | 0 | 66,358 | 15 | 132,716 |
"Correct Solution:
```
h,w = map(int,input().split())
a=[]
for _ in range(h):
a.append(input())
cnt = 0
for i in range(h):
cnt += a[i].count("#")
if cnt == h+w-1:
print("Possible")
else:
print("Impossible")
``` | output | 1 | 66,358 | 15 | 132,717 |
Provide a correct Python 3 solution for this coding contest problem.
We have a grid of H rows and W columns. Initially, there is a stone in the top left cell. Shik is trying to move the stone to the bottom right cell. In each step, he can move the stone one cell to its left, up, right, or down (if such cell exists). It is possible that the stone visits a cell multiple times (including the bottom right and the top left cell).
You are given a matrix of characters a_{ij} (1 \leq i \leq H, 1 \leq j \leq W). After Shik completes all moving actions, a_{ij} is `#` if the stone had ever located at the i-th row and the j-th column during the process of moving. Otherwise, a_{ij} is `.`. Please determine whether it is possible that Shik only uses right and down moves in all steps.
Constraints
* 2 \leq H, W \leq 8
* a_{i,j} is either `#` or `.`.
* There exists a valid sequence of moves for Shik to generate the map a.
Input
The input is given from Standard Input in the following format:
H W
a_{11}a_{12}...a_{1W}
:
a_{H1}a_{H2}...a_{HW}
Output
If it is possible that Shik only uses right and down moves, print `Possible`. Otherwise, print `Impossible`.
Examples
Input
4 5
##...
.##..
..##.
...##
Output
Possible
Input
4 5
...
.##..
..##.
...##
Output
Possible
Input
5 3
..#
..
Output
Impossible
Input
4 5
...
.###.
.###.
...##
Output
Impossible | instruction | 0 | 66,359 | 15 | 132,718 |
"Correct Solution:
```
h, w = map(int, input().split())
a = [list(input()) for _ in range(h)]
cnt = 0
for i in range(h):
cnt += a[i].count('#')
if cnt == h + w - 1:
print('Possible')
else:
print('Impossible')
``` | output | 1 | 66,359 | 15 | 132,719 |
Provide a correct Python 3 solution for this coding contest problem.
We have a grid of H rows and W columns. Initially, there is a stone in the top left cell. Shik is trying to move the stone to the bottom right cell. In each step, he can move the stone one cell to its left, up, right, or down (if such cell exists). It is possible that the stone visits a cell multiple times (including the bottom right and the top left cell).
You are given a matrix of characters a_{ij} (1 \leq i \leq H, 1 \leq j \leq W). After Shik completes all moving actions, a_{ij} is `#` if the stone had ever located at the i-th row and the j-th column during the process of moving. Otherwise, a_{ij} is `.`. Please determine whether it is possible that Shik only uses right and down moves in all steps.
Constraints
* 2 \leq H, W \leq 8
* a_{i,j} is either `#` or `.`.
* There exists a valid sequence of moves for Shik to generate the map a.
Input
The input is given from Standard Input in the following format:
H W
a_{11}a_{12}...a_{1W}
:
a_{H1}a_{H2}...a_{HW}
Output
If it is possible that Shik only uses right and down moves, print `Possible`. Otherwise, print `Impossible`.
Examples
Input
4 5
##...
.##..
..##.
...##
Output
Possible
Input
4 5
...
.##..
..##.
...##
Output
Possible
Input
5 3
..#
..
Output
Impossible
Input
4 5
...
.###.
.###.
...##
Output
Impossible | instruction | 0 | 66,360 | 15 | 132,720 |
"Correct Solution:
```
N,M=map(int,input().split(' '))
maze = [list(input()) for i in range(N)]
tmp = 0
for i in range(N):
tmp += maze[i].count('#')
if tmp == N+M-1:
print('Possible')
else:
print('Impossible')
``` | output | 1 | 66,360 | 15 | 132,721 |
Provide a correct Python 3 solution for this coding contest problem.
We have a grid of H rows and W columns. Initially, there is a stone in the top left cell. Shik is trying to move the stone to the bottom right cell. In each step, he can move the stone one cell to its left, up, right, or down (if such cell exists). It is possible that the stone visits a cell multiple times (including the bottom right and the top left cell).
You are given a matrix of characters a_{ij} (1 \leq i \leq H, 1 \leq j \leq W). After Shik completes all moving actions, a_{ij} is `#` if the stone had ever located at the i-th row and the j-th column during the process of moving. Otherwise, a_{ij} is `.`. Please determine whether it is possible that Shik only uses right and down moves in all steps.
Constraints
* 2 \leq H, W \leq 8
* a_{i,j} is either `#` or `.`.
* There exists a valid sequence of moves for Shik to generate the map a.
Input
The input is given from Standard Input in the following format:
H W
a_{11}a_{12}...a_{1W}
:
a_{H1}a_{H2}...a_{HW}
Output
If it is possible that Shik only uses right and down moves, print `Possible`. Otherwise, print `Impossible`.
Examples
Input
4 5
##...
.##..
..##.
...##
Output
Possible
Input
4 5
...
.##..
..##.
...##
Output
Possible
Input
5 3
..#
..
Output
Impossible
Input
4 5
...
.###.
.###.
...##
Output
Impossible | instruction | 0 | 66,361 | 15 | 132,722 |
"Correct Solution:
```
h,w=map(int,input().split())
num=0
s=[str(input()) for i in range(h)]
for i in range(h):
num+=s[i].count("#")
if num>h+w-1:
print("Impossible")
exit()
print("Possible")
``` | output | 1 | 66,361 | 15 | 132,723 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
We have a grid of H rows and W columns. Initially, there is a stone in the top left cell. Shik is trying to move the stone to the bottom right cell. In each step, he can move the stone one cell to its left, up, right, or down (if such cell exists). It is possible that the stone visits a cell multiple times (including the bottom right and the top left cell).
You are given a matrix of characters a_{ij} (1 \leq i \leq H, 1 \leq j \leq W). After Shik completes all moving actions, a_{ij} is `#` if the stone had ever located at the i-th row and the j-th column during the process of moving. Otherwise, a_{ij} is `.`. Please determine whether it is possible that Shik only uses right and down moves in all steps.
Constraints
* 2 \leq H, W \leq 8
* a_{i,j} is either `#` or `.`.
* There exists a valid sequence of moves for Shik to generate the map a.
Input
The input is given from Standard Input in the following format:
H W
a_{11}a_{12}...a_{1W}
:
a_{H1}a_{H2}...a_{HW}
Output
If it is possible that Shik only uses right and down moves, print `Possible`. Otherwise, print `Impossible`.
Examples
Input
4 5
##...
.##..
..##.
...##
Output
Possible
Input
4 5
...
.##..
..##.
...##
Output
Possible
Input
5 3
..#
..
Output
Impossible
Input
4 5
...
.###.
.###.
...##
Output
Impossible
Submitted Solution:
```
h,w=map(int,input().split());print("Possible"if sum([input().count("#")for i in range(h)])==h+w-1 else "Impossible")
``` | instruction | 0 | 66,362 | 15 | 132,724 |
Yes | output | 1 | 66,362 | 15 | 132,725 |
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