message stringlengths 2 16.2k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 575 109k | cluster float64 16 16 | __index_level_0__ int64 1.15k 217k |
|---|---|---|---|---|---|
Provide a correct Python 3 solution for this coding contest problem.
Snuke is playing with red and blue balls, placing them on a two-dimensional plane.
First, he performed N operations to place red balls. In the i-th of these operations, he placed RC_i red balls at coordinates (RX_i,RY_i). Then, he performed another N operations to place blue balls. In the i-th of these operations, he placed BC_i blue balls at coordinates (BX_i,BY_i). The total number of red balls placed and the total number of blue balls placed are equal, that is, \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i. Let this value be S.
Snuke will now form S pairs of red and blue balls so that every ball belongs to exactly one pair. Let us define the score of a pair of a red ball at coordinates (rx, ry) and a blue ball at coordinates (bx, by) as |rx-bx| + |ry-by|.
Snuke wants to maximize the sum of the scores of the pairs. Help him by finding the maximum possible sum of the scores of the pairs.
Constraints
* 1 \leq N \leq 1000
* 0 \leq RX_i,RY_i,BX_i,BY_i \leq 10^9
* 1 \leq RC_i,BC_i \leq 10
* \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
RX_1 RY_1 RC_1
RX_2 RY_2 RC_2
\vdots
RX_N RY_N RC_N
BX_1 BY_1 BC_1
BX_2 BY_2 BC_2
\vdots
BX_N BY_N BC_N
Output
Print the maximum possible sum of the scores of the pairs.
Examples
Input
2
0 0 1
3 2 1
2 2 1
5 0 1
Output
8
Input
3
0 0 1
2 2 1
0 0 2
1 1 1
1 1 1
3 3 2
Output
16
Input
10
582463373 690528069 8
621230322 318051944 4
356524296 974059503 6
372751381 111542460 9
392867214 581476334 6
606955458 513028121 5
882201596 791660614 9
250465517 91918758 3
618624774 406956634 6
426294747 736401096 5
974896051 888765942 5
726682138 336960821 3
715144179 82444709 6
599055841 501257806 6
390484433 962747856 4
912334580 219343832 8
570458984 648862300 6
638017635 572157978 10
435958984 585073520 7
445612658 234265014 6
Output
45152033546 | instruction | 0 | 54,596 | 16 | 109,192 |
"Correct Solution:
```
def main():
import sys
input=sys.stdin.readline
from collections import deque
inf=10**12
class MinCostFlow:
def __init__(self,n):
self.n=n
self.edges=[[] for i in range(n)]
def add_edge(self,fr,to,cap,cost):
self.edges[fr].append([to,cap,cost,len(self.edges[to])])
self.edges[to].append([fr,0,-cost,len(self.edges[fr])-1])
def MinCost(self,source,sink,flow):
n=self.n; E=self.edges
mincost=0
prev_v=[0]*n; prev_e=[0]*n
while flow:
dist=[inf]*n
dist[source]=0
q=deque([source])
Flag=[False]*n
Flag[source]=True
while q:
v=q.popleft()
if not Flag[v]:
continue
Flag[v]=False
for i,(to,cap,cost,_) in enumerate(E[v]):
if cap>0 and dist[to]>dist[v]+cost:
dist[to]=dist[v]+cost
prev_v[to],prev_e[to]=v,i
q.append(to)
Flag[to]=True
f,v=flow,sink
while v!=source:
f=min(f,E[prev_v[v]][prev_e[v]][1])
v=prev_v[v]
flow-=f
mincost+=f*dist[sink]
v=sink
while v!=source:
E[prev_v[v]][prev_e[v]][1]-=f
rev=E[prev_v[v]][prev_e[v]][3]
E[v][rev][1]+=f
v=prev_v[v]
return mincost
n=int(input())
flow=MinCostFlow(2*n+6)
s=0
for i in range(n):
rx,ry,rc=map(int,input().split())
s+=rc
flow.add_edge(0,i+1,rc,0)
flow.add_edge(i+1,n+1,inf,-rx-ry)
flow.add_edge(i+1,n+2,inf,rx-ry)
flow.add_edge(i+1,n+3,inf,-rx+ry)
flow.add_edge(i+1,n+4,inf,rx+ry)
for i in range(n):
bx,by,bc=map(int,input().split())
flow.add_edge(n+5+i,2*n+5,bc,0)
flow.add_edge(n+1,n+5+i,inf,bx+by)
flow.add_edge(n+2,n+5+i,inf,-bx+by)
flow.add_edge(n+3,n+5+i,inf,bx-by)
flow.add_edge(n+4,n+5+i,inf,-bx-by)
print(-(flow.MinCost(0,2*n+5,s)))
if __name__=='__main__':
main()
``` | output | 1 | 54,596 | 16 | 109,193 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke is playing with red and blue balls, placing them on a two-dimensional plane.
First, he performed N operations to place red balls. In the i-th of these operations, he placed RC_i red balls at coordinates (RX_i,RY_i). Then, he performed another N operations to place blue balls. In the i-th of these operations, he placed BC_i blue balls at coordinates (BX_i,BY_i). The total number of red balls placed and the total number of blue balls placed are equal, that is, \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i. Let this value be S.
Snuke will now form S pairs of red and blue balls so that every ball belongs to exactly one pair. Let us define the score of a pair of a red ball at coordinates (rx, ry) and a blue ball at coordinates (bx, by) as |rx-bx| + |ry-by|.
Snuke wants to maximize the sum of the scores of the pairs. Help him by finding the maximum possible sum of the scores of the pairs.
Constraints
* 1 \leq N \leq 1000
* 0 \leq RX_i,RY_i,BX_i,BY_i \leq 10^9
* 1 \leq RC_i,BC_i \leq 10
* \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
RX_1 RY_1 RC_1
RX_2 RY_2 RC_2
\vdots
RX_N RY_N RC_N
BX_1 BY_1 BC_1
BX_2 BY_2 BC_2
\vdots
BX_N BY_N BC_N
Output
Print the maximum possible sum of the scores of the pairs.
Examples
Input
2
0 0 1
3 2 1
2 2 1
5 0 1
Output
8
Input
3
0 0 1
2 2 1
0 0 2
1 1 1
1 1 1
3 3 2
Output
16
Input
10
582463373 690528069 8
621230322 318051944 4
356524296 974059503 6
372751381 111542460 9
392867214 581476334 6
606955458 513028121 5
882201596 791660614 9
250465517 91918758 3
618624774 406956634 6
426294747 736401096 5
974896051 888765942 5
726682138 336960821 3
715144179 82444709 6
599055841 501257806 6
390484433 962747856 4
912334580 219343832 8
570458984 648862300 6
638017635 572157978 10
435958984 585073520 7
445612658 234265014 6
Output
45152033546 | instruction | 0 | 54,597 | 16 | 109,194 |
"Correct Solution:
```
import sys
from collections import deque
def min_cost_flow(links, links_from, s, t, flow, n2):
remain = flow
result = 0
INF = 10 ** 12
predecessors = [0] * n2 # link_id
while remain:
# print(remain)
distances = [INF] * n2
updated = [False] * n2
distances[s] = 0
updated[s] = True
q = deque([s])
while q:
v = q.popleft()
vc = distances[v]
updated[v] = False
for li in links_from[v]:
_, u, cap, cost = links[li]
if cap == 0:
continue
new_cost = vc + cost
if new_cost >= distances[u]:
continue
distances[u] = new_cost
predecessors[u] = li
if not updated[u]:
updated[u] = True
q.append(u)
min_cap = remain
v = t
while v != s:
li = predecessors[v]
l = links[li]
min_cap = min(min_cap, l[2])
v = l[0]
v = t
while v != s:
li = predecessors[v]
l = links[li]
l[2] -= min_cap
links[li ^ 1][2] += min_cap
v = l[0]
remain -= min_cap
result -= min_cap * distances[t]
return result
n = int(input())
lines = sys.stdin.readlines()
n2 = 2 * n + 6
s, t = 0, 2 * n + 1
k1, k2, k3, k4 = range(n2 - 4, n2)
balls = 0
links_from = [[] for _ in range(n2)]
links = [] # [[src, tgt, capacity, unit_cost], ]
def add_link(s, t, cap, cost):
i = len(links)
links.append([s, t, cap, cost])
links.append([t, s, 0, -cost])
links_from[s].append(i)
links_from[t].append(i + 1)
for i in range(n):
ri = i + 1
rx, ry, rc = map(int, lines[i].split())
balls += rc
add_link(s, ri, rc, 0)
add_link(ri, k1, rc, rx + ry)
add_link(ri, k2, rc, -rx + ry)
add_link(ri, k3, rc, rx - ry)
add_link(ri, k4, rc, -rx - ry)
for i in range(n, 2 * n):
bi = i + 1
bx, by, bc = map(int, lines[i].split())
add_link(bi, t, bc, 0)
add_link(k1, bi, bc, -bx - by)
add_link(k2, bi, bc, bx - by)
add_link(k3, bi, bc, -bx + by)
add_link(k4, bi, bc, bx + by)
print(min_cost_flow(links, links_from, s, t, balls, n2))
``` | output | 1 | 54,597 | 16 | 109,195 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is playing with red and blue balls, placing them on a two-dimensional plane.
First, he performed N operations to place red balls. In the i-th of these operations, he placed RC_i red balls at coordinates (RX_i,RY_i). Then, he performed another N operations to place blue balls. In the i-th of these operations, he placed BC_i blue balls at coordinates (BX_i,BY_i). The total number of red balls placed and the total number of blue balls placed are equal, that is, \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i. Let this value be S.
Snuke will now form S pairs of red and blue balls so that every ball belongs to exactly one pair. Let us define the score of a pair of a red ball at coordinates (rx, ry) and a blue ball at coordinates (bx, by) as |rx-bx| + |ry-by|.
Snuke wants to maximize the sum of the scores of the pairs. Help him by finding the maximum possible sum of the scores of the pairs.
Constraints
* 1 \leq N \leq 1000
* 0 \leq RX_i,RY_i,BX_i,BY_i \leq 10^9
* 1 \leq RC_i,BC_i \leq 10
* \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
RX_1 RY_1 RC_1
RX_2 RY_2 RC_2
\vdots
RX_N RY_N RC_N
BX_1 BY_1 BC_1
BX_2 BY_2 BC_2
\vdots
BX_N BY_N BC_N
Output
Print the maximum possible sum of the scores of the pairs.
Examples
Input
2
0 0 1
3 2 1
2 2 1
5 0 1
Output
8
Input
3
0 0 1
2 2 1
0 0 2
1 1 1
1 1 1
3 3 2
Output
16
Input
10
582463373 690528069 8
621230322 318051944 4
356524296 974059503 6
372751381 111542460 9
392867214 581476334 6
606955458 513028121 5
882201596 791660614 9
250465517 91918758 3
618624774 406956634 6
426294747 736401096 5
974896051 888765942 5
726682138 336960821 3
715144179 82444709 6
599055841 501257806 6
390484433 962747856 4
912334580 219343832 8
570458984 648862300 6
638017635 572157978 10
435958984 585073520 7
445612658 234265014 6
Output
45152033546
Submitted Solution:
```
from heapq import heappush, heappop
N = int(input())
R = [[int(i) for i in input().split()] for _ in range(N)]
B = [[int(i) for i in input().split()] for _ in range(N)]
class MinCostFlow :
def __init__(self, N) :
self.N = N
self.G = [[] for i in range(N)]
def add_edge(self, fr, to, cap, cost) :
G = self.G
G[fr].append([to, cap, cost, len(G[to])])
G[to].append([fr, 0, -cost, len(G[fr]) - 1])
def flow(self, s, t, f) :
N, G = self.N, self.G
ret = 0
H = [0] * N
pre_v = [0] * N
pre_e = [0] * N
while f :
dist = [float('inf')] * N
dist[s] = 0
que = [(0, s)]
while que :
c, v = heappop(que)
if dist[v] < c :
continue
for i, (w, cap, cost, _) in enumerate(G[v]) :
if cap > 0 and dist[w] > dist[v] + cost + H[v] - H[w] :
dist[w] = r = dist[v] + cost + H[v] - H[w]
pre_v[w], pre_e[w] = v, i
heappush(que, (r, w))
if dist[t] == float('inf') :
return -1
for i in range(N) :
H[i] += dist[i]
d, v = f, t
while v != s :
d = min(d, G[pre_v[v]][pre_e[v]][1])
v = pre_v[v]
f -= d
ret += d * H[t]
v = t
while v != s :
e = G[pre_v[v]][pre_e[v]]
e[1] -= d
G[v][e[3]][1] += d
v = pre_v[v]
return ret
MCF = MinCostFlow(2 * N + 6)
f = 0
for i in range(N) :
Rx, Ry, Rc = R[i]
Bx, By, Bc = B[i]
MCF.add_edge(0, i + 1, Rc, 0)
MCF.add_edge(i + 1, N + 1, float('inf'), -(Rx + Ry))
MCF.add_edge(i + 1, N + 2, float('inf'), -(-Rx + Ry))
MCF.add_edge(i + 1, N + 3, float('inf'), -(Rx - Ry))
MCF.add_edge(i + 1, N + 4, float('inf'), -(-Rx - Ry))
MCF.add_edge(N + 1, i + N + 5, float('inf'), -(-Bx - By))
MCF.add_edge(N + 2, i + N + 5, float('inf'), -(Bx - By))
MCF.add_edge(N + 3, i + N + 5, float('inf'), -(-Bx + By))
MCF.add_edge(N + 4, i + N + 5, float('inf'), -(Bx + By))
MCF.add_edge(i + N + 5, 2 * N + 5, Bc, 0)
f += Rc
print(-MCF.flow(0, 2 * N + 5, f))
``` | instruction | 0 | 54,598 | 16 | 109,196 |
No | output | 1 | 54,598 | 16 | 109,197 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is playing with red and blue balls, placing them on a two-dimensional plane.
First, he performed N operations to place red balls. In the i-th of these operations, he placed RC_i red balls at coordinates (RX_i,RY_i). Then, he performed another N operations to place blue balls. In the i-th of these operations, he placed BC_i blue balls at coordinates (BX_i,BY_i). The total number of red balls placed and the total number of blue balls placed are equal, that is, \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i. Let this value be S.
Snuke will now form S pairs of red and blue balls so that every ball belongs to exactly one pair. Let us define the score of a pair of a red ball at coordinates (rx, ry) and a blue ball at coordinates (bx, by) as |rx-bx| + |ry-by|.
Snuke wants to maximize the sum of the scores of the pairs. Help him by finding the maximum possible sum of the scores of the pairs.
Constraints
* 1 \leq N \leq 1000
* 0 \leq RX_i,RY_i,BX_i,BY_i \leq 10^9
* 1 \leq RC_i,BC_i \leq 10
* \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
RX_1 RY_1 RC_1
RX_2 RY_2 RC_2
\vdots
RX_N RY_N RC_N
BX_1 BY_1 BC_1
BX_2 BY_2 BC_2
\vdots
BX_N BY_N BC_N
Output
Print the maximum possible sum of the scores of the pairs.
Examples
Input
2
0 0 1
3 2 1
2 2 1
5 0 1
Output
8
Input
3
0 0 1
2 2 1
0 0 2
1 1 1
1 1 1
3 3 2
Output
16
Input
10
582463373 690528069 8
621230322 318051944 4
356524296 974059503 6
372751381 111542460 9
392867214 581476334 6
606955458 513028121 5
882201596 791660614 9
250465517 91918758 3
618624774 406956634 6
426294747 736401096 5
974896051 888765942 5
726682138 336960821 3
715144179 82444709 6
599055841 501257806 6
390484433 962747856 4
912334580 219343832 8
570458984 648862300 6
638017635 572157978 10
435958984 585073520 7
445612658 234265014 6
Output
45152033546
Submitted Solution:
```
from heapq import heappush, heappop
def min_cost_flow_dijkstra(E, s, t, f):
NN = 2 * N + 6
LN = NN.bit_length()
G = [[] for _ in range(NN)]
for a, b, cap, c in E:
G[a].append([b, cap, c, len(G[b])])
G[b].append([a, 0, -c, len(G[a])-1])
prevv = [-1] * NN
preve = [-1] * NN
res = 0
h = [0] * NN
while f > 0:
dist = [-1] * NN
dist[s] = 0
Q = []
heappush(Q, s)
while len(Q):
x = heappop(Q)
d, v = (x>>LN), x % (1<<LN)
if 0 <= dist[v] < d: continue
for i, (w, _cap, c, r) in enumerate(G[v]):
if _cap > 0 and (dist[w] < 0 or dist[w] > dist[v] + c + h[v] - h[w]):
dist[w] = dist[v] + c + h[v] - h[w]
prevv[w] = v
preve[w] = i
heappush(Q, (dist[w] << LN) + w)
if dist[t] == -1:
return -1
for v in range(N):
h[v] += dist[v]
d = f
v = t
while v != s:
d = min(d, G[prevv[v]][preve[v]][1])
v = prevv[v]
f -= d
res += d * dist[t]
v = t
while v != s:
G[prevv[v]][preve[v]][1] -= d
G[v][G[prevv[v]][preve[v]][3]][1] += d
v = prevv[v]
return res
E = []
N = int(input())
su = 0
inf = 1 << 31
for i in range(N):
x, y, cnt = map(int, input().split())
E.append((2*N+4, i, cnt, 0))
E.append((i, 2*N, cnt, x + y + inf))
E.append((i, 2*N+1, cnt, x - y + inf))
E.append((i, 2*N+2, cnt, - x + y + inf))
E.append((i, 2*N+3, cnt, - x - y + inf))
su += cnt
for i in range(N):
x, y, cnt = map(int, input().split())
E.append((i+N, 2*N+5, cnt, 0))
E.append((2*N, i+N, cnt, - x - y + inf))
E.append((2*N+1, i+N, cnt, - x + y + inf))
E.append((2*N+2, i+N, cnt, x - y + inf))
E.append((2*N+3, i+N, cnt, x + y + inf))
print(su * inf * 2 - min_cost_flow_dijkstra(E, 2*N+4, 2*N+5, su))
``` | instruction | 0 | 54,599 | 16 | 109,198 |
No | output | 1 | 54,599 | 16 | 109,199 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is playing with red and blue balls, placing them on a two-dimensional plane.
First, he performed N operations to place red balls. In the i-th of these operations, he placed RC_i red balls at coordinates (RX_i,RY_i). Then, he performed another N operations to place blue balls. In the i-th of these operations, he placed BC_i blue balls at coordinates (BX_i,BY_i). The total number of red balls placed and the total number of blue balls placed are equal, that is, \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i. Let this value be S.
Snuke will now form S pairs of red and blue balls so that every ball belongs to exactly one pair. Let us define the score of a pair of a red ball at coordinates (rx, ry) and a blue ball at coordinates (bx, by) as |rx-bx| + |ry-by|.
Snuke wants to maximize the sum of the scores of the pairs. Help him by finding the maximum possible sum of the scores of the pairs.
Constraints
* 1 \leq N \leq 1000
* 0 \leq RX_i,RY_i,BX_i,BY_i \leq 10^9
* 1 \leq RC_i,BC_i \leq 10
* \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
RX_1 RY_1 RC_1
RX_2 RY_2 RC_2
\vdots
RX_N RY_N RC_N
BX_1 BY_1 BC_1
BX_2 BY_2 BC_2
\vdots
BX_N BY_N BC_N
Output
Print the maximum possible sum of the scores of the pairs.
Examples
Input
2
0 0 1
3 2 1
2 2 1
5 0 1
Output
8
Input
3
0 0 1
2 2 1
0 0 2
1 1 1
1 1 1
3 3 2
Output
16
Input
10
582463373 690528069 8
621230322 318051944 4
356524296 974059503 6
372751381 111542460 9
392867214 581476334 6
606955458 513028121 5
882201596 791660614 9
250465517 91918758 3
618624774 406956634 6
426294747 736401096 5
974896051 888765942 5
726682138 336960821 3
715144179 82444709 6
599055841 501257806 6
390484433 962747856 4
912334580 219343832 8
570458984 648862300 6
638017635 572157978 10
435958984 585073520 7
445612658 234265014 6
Output
45152033546
Submitted Solution:
```
import sys
from heapq import heappush, heappop
input = sys.stdin.readline
N = int(input())
N_ = 2 * N + 6
N1, N2, N3, N4, N5 = range(N + 1, N + 6)
G = [[] for i in range(2 * N + 6)]
def add_edge(fr, to, cap, cost) :
G[fr].append([to, cap, cost, len(G[to])])
G[to].append([fr, 0, -cost, len(G[fr]) - 1])
def flow(s, t, f) :
ret = 0
pre_v = [0] * N_
pre_e = [0] * N_
while f :
dist = [float('inf')] * N_
dist[s] = 0
que = [(0, s)]
while que :
c, v = heappop(que)
if dist[v] < c :
continue
for i, (w, cap, cost, _) in enumerate(G[v]) :
if cap > 0 and dist[w] > dist[v] + cost:
dist[w] = r = dist[v] + cost
pre_v[w], pre_e[w] = v, i
heappush(que, (r, w))
d, v = f, t
while v != s :
d = min(d, G[pre_v[v]][pre_e[v]][1])
v = pre_v[v]
f -= d
ret += d * dist[t]
v = t
while v != s :
e = G[pre_v[v]][pre_e[v]]
e[1] -= d
G[v][e[3]][1] += d
v = pre_v[v]
return ret
S = 0
for i in range(N) :
Rx, Ry, Rc = map(int, input().split())
add_edge(0, i + 1, Rc, 0)
add_edge(i + 1, N1, float('inf'), -(Rx + Ry))
add_edge(i + 1, N2, float('inf'), -(-Rx + Ry))
add_edge(i + 1, N3, float('inf'), -(Rx - Ry))
add_edge(i + 1, N4, float('inf'), -(-Rx - Ry))
S += Rc
for i in range(N) :
Bx, By, Bc = map(int, input().split())
add_edge(N1, i + N5, float('inf'), -(-Bx - By))
add_edge(N2, i + N5, float('inf'), -(Bx - By))
add_edge(N3, i + N5, float('inf'), -(-Bx + By))
add_edge(N4, i + N5, float('inf'), -(Bx + By))
add_edge(i + N5, N_ - 1, Bc, 0)
print(-flow(0, N_ - 1, S))
``` | instruction | 0 | 54,600 | 16 | 109,200 |
No | output | 1 | 54,600 | 16 | 109,201 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is playing with red and blue balls, placing them on a two-dimensional plane.
First, he performed N operations to place red balls. In the i-th of these operations, he placed RC_i red balls at coordinates (RX_i,RY_i). Then, he performed another N operations to place blue balls. In the i-th of these operations, he placed BC_i blue balls at coordinates (BX_i,BY_i). The total number of red balls placed and the total number of blue balls placed are equal, that is, \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i. Let this value be S.
Snuke will now form S pairs of red and blue balls so that every ball belongs to exactly one pair. Let us define the score of a pair of a red ball at coordinates (rx, ry) and a blue ball at coordinates (bx, by) as |rx-bx| + |ry-by|.
Snuke wants to maximize the sum of the scores of the pairs. Help him by finding the maximum possible sum of the scores of the pairs.
Constraints
* 1 \leq N \leq 1000
* 0 \leq RX_i,RY_i,BX_i,BY_i \leq 10^9
* 1 \leq RC_i,BC_i \leq 10
* \sum_{i=1}^{N} RC_i = \sum_{i=1}^{N} BC_i
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
RX_1 RY_1 RC_1
RX_2 RY_2 RC_2
\vdots
RX_N RY_N RC_N
BX_1 BY_1 BC_1
BX_2 BY_2 BC_2
\vdots
BX_N BY_N BC_N
Output
Print the maximum possible sum of the scores of the pairs.
Examples
Input
2
0 0 1
3 2 1
2 2 1
5 0 1
Output
8
Input
3
0 0 1
2 2 1
0 0 2
1 1 1
1 1 1
3 3 2
Output
16
Input
10
582463373 690528069 8
621230322 318051944 4
356524296 974059503 6
372751381 111542460 9
392867214 581476334 6
606955458 513028121 5
882201596 791660614 9
250465517 91918758 3
618624774 406956634 6
426294747 736401096 5
974896051 888765942 5
726682138 336960821 3
715144179 82444709 6
599055841 501257806 6
390484433 962747856 4
912334580 219343832 8
570458984 648862300 6
638017635 572157978 10
435958984 585073520 7
445612658 234265014 6
Output
45152033546
Submitted Solution:
```
import sys
from heapq import heappop, heappush
def min_cost_flow(links, s, t, flow, n2, INF, REV, potentials, predecessors_v, predecessors_i):
remain = flow
ans = 0
REV2 = REV * 2
while remain:
distances = [INF] * n2
distances[s] = 0
q = [(0, s)] # (cost, v, (p, v_idx_in_p))
while q:
cost, v = heappop(q)
if cost > distances[v]:
continue
if v == t:
break
for i, (u, cap, uc, j) in enumerate(links[v]):
if cap == 0:
continue
new_cost = cost + uc + potentials[v] - potentials[u]
if distances[u] <= new_cost:
continue
distances[u] = new_cost
predecessors_v[u] = v
predecessors_i[u] = i
heappush(q, (new_cost, u))
# if distances[t] == INF:
# return -1
for i in range(n + 1, n2):
potentials[i] += distances[i]
min_cap = remain
v = t
forward_links = []
backward_links = []
while v != s:
p = predecessors_v[v]
i = predecessors_i[v]
l = links[p][i]
forward_links.append(l)
if v != t:
backward_links.append(links[v][l[3]])
min_cap = min(min_cap, l[1])
v = p
for l in forward_links:
l[1] -= min_cap
for l in backward_links:
l[1] += min_cap
remain -= min_cap
ans += min_cap * (REV2 - potentials[t])
return ans
n = int(input())
lines = sys.stdin.readlines()
INF = 10 ** 18
REV = 10 ** 9
n2 = 2 * n + 6
t = 2 * n + 1
red_balls = []
links = [[] for _ in range(n2)] # [[tgt_node, capacity, unit_cost, idx_in_tgt], ]
for i in range(n):
ri = i + 1
rx, ry, rc = map(int, lines[i].split())
red_balls.append(rc)
ki = n2 - 4
kc = REV - (rx + ry)
links[ri].append([ki, INF, kc, len(links[ki])])
links[ki].append([ri, 0, -kc, len(links[ri]) - 1])
ki = n2 - 3
kc = REV - (-rx + ry)
links[ri].append([ki, INF, kc, len(links[ki])])
links[ki].append([ri, 0, -kc, len(links[ri]) - 1])
ki = n2 - 2
kc = REV - (rx - ry)
links[ri].append([ki, INF, kc, len(links[ki])])
links[ki].append([ri, 0, -kc, len(links[ri]) - 1])
ki = n2 - 1
kc = REV - (-rx - ry)
links[ri].append([ki, INF, kc, len(links[ki])])
links[ki].append([ri, 0, -kc, len(links[ri]) - 1])
for i in range(n):
bi = i + n + 1
bx, by, bc = map(int, lines[i + n].split())
links[bi].append([t, bc, 0, 0])
ki = n2 - 4
kc = REV - (-bx - by)
links[ki].append([bi, INF, kc, len(links[bi])])
links[bi].append([ki, 0, -kc, len(links[ki]) - 1])
ki = n2 - 3
kc = REV - (bx - by)
links[ki].append([bi, INF, kc, len(links[bi])])
links[bi].append([ki, 0, -kc, len(links[ki]) - 1])
ki = n2 - 2
kc = REV - (-bx + by)
links[ki].append([bi, INF, kc, len(links[bi])])
links[bi].append([ki, 0, -kc, len(links[ki]) - 1])
ki = n2 - 1
kc = REV - (bx + by)
links[ki].append([bi, INF, kc, len(links[bi])])
links[bi].append([ki, 0, -kc, len(links[ki]) - 1])
potentials = [0] * n2 # to adjust negative edge for dijkstra
predecessors_v = [0] * n2
predecessors_i = [0] * n2
ans = 0
for i, flow in enumerate(red_balls, start=1):
ans += min_cost_flow(links, i, t, flow, n2, INF, REV, potentials, predecessors_v, predecessors_i)
print(ans)
``` | instruction | 0 | 54,601 | 16 | 109,202 |
No | output | 1 | 54,601 | 16 | 109,203 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4 | instruction | 0 | 54,670 | 16 | 109,340 |
"Correct Solution:
```
n = int(input())
s = input()
t = input()
for i in range(n):
if s[i:n] == t[0:n-i]:
print(2*n - (n-i))
exit()
print(2*n)
``` | output | 1 | 54,670 | 16 | 109,341 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4 | instruction | 0 | 54,671 | 16 | 109,342 |
"Correct Solution:
```
n=int(input())
s=input()
t=input()
k=n
for i in range(n):
if(s[i:]==t[:n-i]):
k=i
break
print(n+k)
``` | output | 1 | 54,671 | 16 | 109,343 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4 | instruction | 0 | 54,672 | 16 | 109,344 |
"Correct Solution:
```
N = int(input())
s = input()
t = input()
k = 0
for i in range(N+1):
if s[-i:] == t[:i]:
k = i
print(2*N-k)
``` | output | 1 | 54,672 | 16 | 109,345 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4 | instruction | 0 | 54,673 | 16 | 109,346 |
"Correct Solution:
```
n = int(input()); s = input(); t = input()
for i in range(n):
if s[i:] == t[:n-i]: print(n+i); break
else: print(2*n)
``` | output | 1 | 54,673 | 16 | 109,347 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4 | instruction | 0 | 54,674 | 16 | 109,348 |
"Correct Solution:
```
N = int(input())
s = input()
t = input()
for i in range(N):
if s[i:] == t[:N-i]:
print(N + i)
break
else:
print(N * 2)
``` | output | 1 | 54,674 | 16 | 109,349 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4 | instruction | 0 | 54,675 | 16 | 109,350 |
"Correct Solution:
```
n=int(input())
s=input()
t=input()
connected=0
for i in range(1,n+1):
if s[n-i:]==t[:i]:
connected=i
print(n*2-connected)
``` | output | 1 | 54,675 | 16 | 109,351 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4 | instruction | 0 | 54,676 | 16 | 109,352 |
"Correct Solution:
```
N = int(input())
s = input()
t = input()
temp = 0
for i in range(N):
if s[-1*(i+1):] == t[0:i+1]:
temp = i+1
print(2*N-temp)
``` | output | 1 | 54,676 | 16 | 109,353 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4 | instruction | 0 | 54,677 | 16 | 109,354 |
"Correct Solution:
```
n=int(input())
s=input()
t=input()
for i in range(n+1):
p=s+t[n-i:]
if p[i:]==t:
break
print(n+i)
``` | output | 1 | 54,677 | 16 | 109,355 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4
Submitted Solution:
```
N=int(input())
S=input()
T=input()
ans=2*N
i=N
while i:
if S[-i:]==T[:i]:
ans-=i
break
i-=1
print(ans)
``` | instruction | 0 | 54,678 | 16 | 109,356 |
Yes | output | 1 | 54,678 | 16 | 109,357 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4
Submitted Solution:
```
N = int(input())
s = input()
t = input()
c = 0
for i in range(1,N+1):
if s[N-i:] == t[:i]:
c = i
print(2*N-c)
``` | instruction | 0 | 54,679 | 16 | 109,358 |
Yes | output | 1 | 54,679 | 16 | 109,359 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4
Submitted Solution:
```
N=int(input())
s=input()
t=input()
if s==t:
print(N)
exit()
for i in range(1,N+1):
if s[i:]==t[:-i]:
print(N+i)
exit()
``` | instruction | 0 | 54,680 | 16 | 109,360 |
Yes | output | 1 | 54,680 | 16 | 109,361 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4
Submitted Solution:
```
N = int(input())
S = input()
T = input()
for i in range(N+1):
if S[i:] == T[:N-i]:
break
print(N+i)
``` | instruction | 0 | 54,681 | 16 | 109,362 |
Yes | output | 1 | 54,681 | 16 | 109,363 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4
Submitted Solution:
```
N=int(input())
s=input()
t=input()
if int(len(s))==1 and int(len(t))==1:
print(len(s)+len(t))
elif s[N-1]==t[0]:
print(len(s)+len(t)-1)
elif s==t:
print(N)
``` | instruction | 0 | 54,682 | 16 | 109,364 |
No | output | 1 | 54,682 | 16 | 109,365 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4
Submitted Solution:
```
n = int(input())
s = list(reversed(input()))
t = list(input())
for idx, (ss, tt) in enumerate(zip(s,t)):
if ss != tt:
break
if list(reversed(s)) == t:
print(len(s))
else:
print(n + n - 2 * idx + 1)
``` | instruction | 0 | 54,683 | 16 | 109,366 |
No | output | 1 | 54,683 | 16 | 109,367 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4
Submitted Solution:
```
n = int(input())
s = input()
t = input()
if s == t: print(n)
else:
idx = False
for i in reversed(range(n)):
if s[i] == t[0]:
idx = i
for j in range(0, n - idx):
if s[idx + j] == t[j]: continue
else:
idx = False
break
if idx == False: print(len(s + t))
else: print(len(s[:idx] + t))
``` | instruction | 0 | 54,684 | 16 | 109,368 |
No | output | 1 | 54,684 | 16 | 109,369 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke is interested in strings that satisfy the following conditions:
* The length of the string is at least N.
* The first N characters equal to the string s.
* The last N characters equal to the string t.
Find the length of the shortest string that satisfies the conditions.
Constraints
* 1≤N≤100
* The lengths of s and t are both N.
* s and t consist of lowercase English letters.
Input
The input is given from Standard Input in the following format:
N
s
t
Output
Print the length of the shortest string that satisfies the conditions.
Examples
Input
3
abc
cde
Output
5
Input
1
a
z
Output
2
Input
4
expr
expr
Output
4
Submitted Solution:
```
n=int(input())
s=input()
t=input()
a=0
b=-1
if s!=t:
while s[b] == t[a]:
a=a+1
b=b-1
print(2*n-a)
else:
print(n)
``` | instruction | 0 | 54,685 | 16 | 109,370 |
No | output | 1 | 54,685 | 16 | 109,371 |
Provide a correct Python 3 solution for this coding contest problem.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39 | instruction | 0 | 56,259 | 16 | 112,518 |
"Correct Solution:
```
def f(x):
return 0 if int(x)%2 else f(int(x)//2)+1
n = input()
print(sum(list(map(f,input().split()))))
``` | output | 1 | 56,259 | 16 | 112,519 |
Provide a correct Python 3 solution for this coding contest problem.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39 | instruction | 0 | 56,260 | 16 | 112,520 |
"Correct Solution:
```
n,a=int(input()),list(map(int,input().split()));ans=0
for i in a:
m=i
while m%2==0:m//=2;ans+=1
print(ans)
``` | output | 1 | 56,260 | 16 | 112,521 |
Provide a correct Python 3 solution for this coding contest problem.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39 | instruction | 0 | 56,261 | 16 | 112,522 |
"Correct Solution:
```
N = int(input())
A = list(map(int,input().split(" ")))
ans=0
for a in A:
ans += len(bin(a)) - bin(a).rfind("1") -1
print(ans)
``` | output | 1 | 56,261 | 16 | 112,523 |
Provide a correct Python 3 solution for this coding contest problem.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39 | instruction | 0 | 56,262 | 16 | 112,524 |
"Correct Solution:
```
n=int(input())
a=list(map(int,input().split()))
ans=0
for i in a:
while i%2==0:
i=i//2
ans+=1
print(ans)
``` | output | 1 | 56,262 | 16 | 112,525 |
Provide a correct Python 3 solution for this coding contest problem.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39 | instruction | 0 | 56,263 | 16 | 112,526 |
"Correct Solution:
```
N = int(input())
A = list(map(int, input().split()))
ans = 0
for a in A:
ans += bin(a)[::-1].index("1")
print(ans)
``` | output | 1 | 56,263 | 16 | 112,527 |
Provide a correct Python 3 solution for this coding contest problem.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39 | instruction | 0 | 56,264 | 16 | 112,528 |
"Correct Solution:
```
N=int(input())
A= list(map(int,input().split() ))
ans=0
for a in A:
while a%2==0:
a/=2
ans+=1
print(ans)
``` | output | 1 | 56,264 | 16 | 112,529 |
Provide a correct Python 3 solution for this coding contest problem.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39 | instruction | 0 | 56,265 | 16 | 112,530 |
"Correct Solution:
```
N = int(input())
a = list(map(int, input().split()))
res = 0
for x in a:
while x % 2 == 0:
x /= 2
res += 1
print(res)
``` | output | 1 | 56,265 | 16 | 112,531 |
Provide a correct Python 3 solution for this coding contest problem.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39 | instruction | 0 | 56,266 | 16 | 112,532 |
"Correct Solution:
```
input()
def div2(n):
i=0
while n%2==0:
i,n=i+1,n/2
return i
arr=map(div2,map(int,input().split()))
print(sum(arr))
``` | output | 1 | 56,266 | 16 | 112,533 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39
Submitted Solution:
```
N = int(input())
A = [int(i) for i in input().split()]
c = 0
for a in A:
c += bin(a)[2:][::-1].index("1")
print(c)
``` | instruction | 0 | 56,267 | 16 | 112,534 |
Yes | output | 1 | 56,267 | 16 | 112,535 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39
Submitted Solution:
```
n = int(input())
ni = list(map(int, input().split()))
cnt = 0
for i in ni:
while not i % 2:
i /= 2
cnt += 1
print(cnt)
``` | instruction | 0 | 56,268 | 16 | 112,536 |
Yes | output | 1 | 56,268 | 16 | 112,537 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39
Submitted Solution:
```
import math
N=input()
a=list(map(int,input().split()))
ans=0
for i in a:
ans+=len(bin(i))-bin(i).rfind("1")-1
print(ans)
``` | instruction | 0 | 56,269 | 16 | 112,538 |
Yes | output | 1 | 56,269 | 16 | 112,539 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39
Submitted Solution:
```
N=int(input())
A=list(map(int,input().split()))
n=0
for a in A:
while a%2==0:
n+=1
a/=2
print(n)
``` | instruction | 0 | 56,270 | 16 | 112,540 |
Yes | output | 1 | 56,270 | 16 | 112,541 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39
Submitted Solution:
```
N = int(input())
inp2 = input()
a = inp2.split()
count = 0
for i in range(int(N)):
b = int(a[i])
flag = True
while flag:
c = b/2
if c.isinstance(c,int):
count+=1
else:
flag = False
print(count)
``` | instruction | 0 | 56,271 | 16 | 112,542 |
No | output | 1 | 56,271 | 16 | 112,543 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39
Submitted Solution:
```
n = int(input())
A = list(map(int, input().split()))
A.sort(reverse=True)
ans = 0
while any(A[i] % 2 == 0 for i in range(n)):
count = 0
for i in range(n):
if A[i] % 2 == 0:
if count == 0:
A[i] = A[i] // 2
count += 1
else:
A[i] = A[i] * 3
else:
A[i] = A[i] * 3
A.sort(reverse=True)
ans += 1
print(ans)
``` | instruction | 0 | 56,272 | 16 | 112,544 |
No | output | 1 | 56,272 | 16 | 112,545 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39
Submitted Solution:
```
N = int(input())
a = np.array(input().split()).astype(int)
sum = 0
for i in range(len(a)):
sum += a[i]%2
print(sum)
``` | instruction | 0 | 56,273 | 16 | 112,546 |
No | output | 1 | 56,273 | 16 | 112,547 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
As AtCoder Beginner Contest 100 is taking place, the office of AtCoder, Inc. is decorated with a sequence of length N, a = {a_1, a_2, a_3, ..., a_N}.
Snuke, an employee, would like to play with this sequence.
Specifically, he would like to repeat the following operation as many times as possible:
For every i satisfying 1 \leq i \leq N, perform one of the following: "divide a_i by 2" and "multiply a_i by 3".
Here, choosing "multiply a_i by 3" for every i is not allowed, and the value of a_i after the operation must be an integer.
At most how many operations can be performed?
Constraints
* N is an integer between 1 and 10 \ 000 (inclusive).
* a_i is an integer between 1 and 1 \ 000 \ 000 \ 000 (inclusive).
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 a_3 ... a_N
Output
Print the maximum number of operations that Snuke can perform.
Examples
Input
3
5 2 4
Output
3
Input
4
631 577 243 199
Output
0
Input
10
2184 2126 1721 1800 1024 2528 3360 1945 1280 1776
Output
39
Submitted Solution:
```
n = int(input())
li = [int(x) for x in input().split()]
def func(li):
a = 1
for x in li:
a *= x
return a
count = 0
while True:
if func(li)%2==0:
for i in range(len(li)):
if li[i]%2==0:
li[i] = li[i]*3
else:
li[i] = li[i]/2
count += 1
else:
break
print(count)
``` | instruction | 0 | 56,274 | 16 | 112,548 |
No | output | 1 | 56,274 | 16 | 112,549 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke loves flags.
Snuke is placing N flags on a line.
The i-th flag can be placed at either coordinate x_i or coordinate y_i.
Snuke thinks that the flags look nicer when the smallest distance between two of them, d, is larger. Find the maximum possible value of d.
Constraints
* 2 ≤ N ≤ 10^{4}
* 1 ≤ x_i, y_i ≤ 10^{9}
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the answer.
Examples
Input
3
1 3
2 5
1 9
Output
4
Input
5
2 2
2 2
2 2
2 2
2 2
Output
0
Input
22
93 6440
78 6647
862 11
8306 9689
798 99
801 521
188 206
6079 971
4559 209
50 94
92 6270
5403 560
803 83
1855 99
42 504
75 484
629 11
92 122
3359 37
28 16
648 14
11 269
Output
17 | instruction | 0 | 56,307 | 16 | 112,614 |
"Correct Solution:
```
import sys
INF = 1 << 60
MOD = 10**9 + 7 # 998244353
sys.setrecursionlimit(2147483647)
input = lambda:sys.stdin.readline().rstrip()
def SCC(E):
n = len(E)
rev = [[] for _ in range(n)]
for v in range(n):
for nv in E[v]:
rev[nv].append(v)
used = [0] * n
order = []
for v in range(n):
if used[v]:
continue
stack = [~v, v]
while stack:
v = stack.pop()
if v >= 0:
if used[v]:
continue
used[v] = 1
for nv in E[v]:
if not used[nv]:
stack.append(~nv)
stack.append(nv)
else:
if used[~v] == 2:
continue
used[~v] = 2
order.append(~v)
cnt = 0
color = [-1] * n
for v in order[::-1]:
if color[v] != -1:
continue
color[v] = cnt
queue = [v]
for v in queue:
for nv in rev[v]:
if color[nv] == -1:
color[nv] = cnt
queue.append(nv)
cnt += 1
return color
from bisect import bisect_left, bisect_right
def resolve():
n = int(input())
ZI = []
for i in range(n):
x, y = map(int, input().split())
ZI.append((x, i)), ZI.append((y, i))
ZI.sort()
pair = [[] for _ in range(n)]
for i, p in enumerate(ZI):
pair[p[1]].append(i)
Z = [p[0] for p in ZI]
n *= 2
n2 = n * 2
def check(d):
N = 1 << (n2 - 1).bit_length()
E = [[] for _ in range(N * 2)]
for i in range(N - 1, 0, -1):
E[i].append(i << 1)
E[i].append(i << 1 | 1)
for u, v in pair:
E[u + N].append(v + n + N)
E[u + n + N].append(v + N)
E[v + N].append(u + n + N)
E[v + n + N].append(u + N)
for i, z in enumerate(Z):
L = bisect_right(Z, z - d)
R = bisect_left(Z, z + d)
for l, r in [(L + n, i + n), (i + 1 + n, R + n)]:
l += N
r += N
while l < r:
if l & 1:
E[i + N].append(l)
l += 1
if r & 1:
r -= 1
E[i + N].append(r)
l >>= 1
r >>= 1
res = SCC(E)
return all(res[i + N] != res[i + n + N] for i in range(n))
l = 0
r = max(Z)
while r - l > 1:
m = (l + r) // 2
if check(m):
l = m
else:
r = m
print(l)
resolve()
``` | output | 1 | 56,307 | 16 | 112,615 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves flags.
Snuke is placing N flags on a line.
The i-th flag can be placed at either coordinate x_i or coordinate y_i.
Snuke thinks that the flags look nicer when the smallest distance between two of them, d, is larger. Find the maximum possible value of d.
Constraints
* 2 ≤ N ≤ 10^{4}
* 1 ≤ x_i, y_i ≤ 10^{9}
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the answer.
Examples
Input
3
1 3
2 5
1 9
Output
4
Input
5
2 2
2 2
2 2
2 2
2 2
Output
0
Input
22
93 6440
78 6647
862 11
8306 9689
798 99
801 521
188 206
6079 971
4559 209
50 94
92 6270
5403 560
803 83
1855 99
42 504
75 484
629 11
92 122
3359 37
28 16
648 14
11 269
Output
17
Submitted Solution:
```
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import os
def readln():
_res = list(map(int,str(input()).split(' ')))
return _res
def pos(p):
return p % n
def number(p,x):
if x == 1: return p + n
return p
def tuning(p,x,v,s,e):
if v[p]: return s[p] == x
v[p] = True
s[p] = x
for j in e[number(p,x)]:
if s[pos(j)] != 0:
if j == number(pos(j),s[pos(j)]):
if not tuning(pos(j),-s[pos(j)],v,s,e):
return False
return True
def add(p,x,s,e):
tmp = s[:]
s[p] = x
v = [False for i in range(0,p+1)]
if tuning(p,x,v,s,e):
return True
else:
s = tmp[:]
return False
def ok(d):
e = [[] for i in range(0,m)]
for i in range(0,m):
for j in range(0,i):
if abs(x[i]-x[j]) < d and i - j != n:
e[i].append(j)
e[j].append(i)
s = [0 for i in range(0,n)]
for i in range(0,n):
if (not add(i,1,s,e)) and (not add(i,-1,s,e)):
return False
return True
n = int(input())
m = n * 2
x = [0 for i in range(0,m)]
for i in range(0,n):
a = readln()
x[i],x[i+n] = a[0],a[1]
l = 0
r = max(x[0],x[1],x[n],x[n+1]) - min(x[0],x[1],x[n],x[n+1]) + 1
while l < r - 1:
mid = (l + r)//2
if ok(mid):
l = mid
else:
r = mid
print(l)
# 3
# 1 3
# 2 5
# 1 9
# 4
# 22
# 93 6440
# 78 6647
# 862 11
# 8306 9689
# 798 99
# 801 521
# 188 206
# 6079 971
# 4559 209
# 50 94
# 92 6270
# 5403 560
# 803 83
# 1855 99
# 42 504
# 75 484
# 629 11
# 92 122
# 3359 37
# 28 16
# 648 14
# 11 269
# 17
``` | instruction | 0 | 56,308 | 16 | 112,616 |
No | output | 1 | 56,308 | 16 | 112,617 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves flags.
Snuke is placing N flags on a line.
The i-th flag can be placed at either coordinate x_i or coordinate y_i.
Snuke thinks that the flags look nicer when the smallest distance between two of them, d, is larger. Find the maximum possible value of d.
Constraints
* 2 ≤ N ≤ 10^{4}
* 1 ≤ x_i, y_i ≤ 10^{9}
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the answer.
Examples
Input
3
1 3
2 5
1 9
Output
4
Input
5
2 2
2 2
2 2
2 2
2 2
Output
0
Input
22
93 6440
78 6647
862 11
8306 9689
798 99
801 521
188 206
6079 971
4559 209
50 94
92 6270
5403 560
803 83
1855 99
42 504
75 484
629 11
92 122
3359 37
28 16
648 14
11 269
Output
17
Submitted Solution:
```
import sys
class SCC:
'''
SCC class with non-recursive DFS.
'''
def __init__(self,N):
self.N = N
self.G1 = [[] for _ in range(N)]
self.G2 = [[] for _ in range(N)]
def add_edge(self,a,b):
self.G1[a].append(b)
self.G2[b].append(a)
def scc(self):
self.seen = [0]*self.N
self.postorder=[-1]*self.N
self.order = 0
for i in range(self.N):
if self.seen[i]:continue
self._dfs(i)
self.seen = [0]*self.N
scclist = []
for i in self._argsort(self.postorder,reverse=True):
if self.seen[i]:continue
cc = self._dfs2(i)
scclist.append(cc)
return scclist
def _argsort(self,arr,reverse=False):
shift = self.N.bit_length()+2
tmp = sorted([arr[i]<<shift | i for i in range(len(arr))],reverse=reverse)
mask = (1<<shift) - 1
return [tmp[i] & mask for i in range(len(arr))]
def _dfs(self,v0):
todo = [~v0, v0]
while todo:
v = todo.pop()
if v >= 0:
self.seen[v] = 1
for next_v in self.G1[v]:
if self.seen[next_v]: continue
todo.append(~next_v)
todo.append(next_v)
else:
if self.postorder[~v] == -1:
self.postorder[~v] = self.order
self.order += 1
return
def _dfs2(self,v):
todo = [v]
self.seen[v] = 1
cc = [v]
while todo:
v = todo.pop()
for next_v in self.G2[v]:
if self.seen[next_v]: continue
self.seen[next_v] = 1
todo.append(next_v)
cc.append(next_v)
return cc
class TwoSAT:
def __init__(self,N):
self.N = N
self.scc = SCC(2*N)
self.flag=-1
def add_clause(self,i,f,j,g):
self.scc.add_edge(f*self.N+i,(1^g)*self.N+j)
self.scc.add_edge(g*self.N+j,(1^f)*self.N+i)
def satisfiable(self):
if self.flag==-1:
self.scclist = self.scc.scc()
self.order = {j:i for i,scc in enumerate(self.scclist) for j in scc}
self.flag = True
self.ans = [0]*self.N
for i in range(self.N):
if self.order[i] > self.order[self.N+i]:
self.ans[i] = 1
continue
elif self.order[i] == self.order[i+self.N]:
self.flag = False
return self.flag
return self.flag
else: return self.flag
def answer(self):
return self.ans
def binary_search2(func, left, right):
while right-left>1:
middle = (left+right)//2
y_middle = func(middle)
if y_middle: left=middle
else: right=middle
return left
def is_possible(d):
ts=TwoSAT(N)
for i in range(N-1):
for j in range(i+1,N):
for k1,k2 in [(0,0),(0,1),(1,0),(1,1)]:
pos1,pos2 = xy[i][k1],xy[j][k2]
if abs(pos2-pos1)<d:
ts.add_clause(i,k1^1,j,k2^1)
return ts.satisfiable()
N = int(input())
xy = [tuple(map(int,input().split())) for _ in range(N)]
xymax = max([max(xy[i]) for i in range(N)])
print(binary_search2(is_possible,0,xymax))
``` | instruction | 0 | 56,309 | 16 | 112,618 |
No | output | 1 | 56,309 | 16 | 112,619 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves flags.
Snuke is placing N flags on a line.
The i-th flag can be placed at either coordinate x_i or coordinate y_i.
Snuke thinks that the flags look nicer when the smallest distance between two of them, d, is larger. Find the maximum possible value of d.
Constraints
* 2 ≤ N ≤ 10^{4}
* 1 ≤ x_i, y_i ≤ 10^{9}
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the answer.
Examples
Input
3
1 3
2 5
1 9
Output
4
Input
5
2 2
2 2
2 2
2 2
2 2
Output
0
Input
22
93 6440
78 6647
862 11
8306 9689
798 99
801 521
188 206
6079 971
4559 209
50 94
92 6270
5403 560
803 83
1855 99
42 504
75 484
629 11
92 122
3359 37
28 16
648 14
11 269
Output
17
Submitted Solution:
```
mycode = r'''
# distutils: language=c++
# cython: language_level=3, boundscheck=False, wraparound=False, cdivision=True
from cython.view cimport array
cdef class two_sat:
cdef:
int _n,
list _answer
scc_graph scc
def __init__(s, int n):
s._n = n
s._answer = [False] * n
s.scc = scc_graph(2 * n)
# クローズを足す
cdef add_clause(s, int i, int f, int j, int g):
s.scc.add_edge(2 * i + (not f), 2 * j + (g))
s.scc.add_edge(2 * j + (not g), 2 * i + (f))
# 判定
# O(n + m)
cdef satisfiable(s):
cdef list id = s.scc.scc_ids()[1]
cdef int i
for i in range(s._n):
if id[2 * i] == id[2 * i + 1]: return False
s._answer[i] = id[2 * i] < id[2 * i + 1]
return True
# クローズを満たす割当を返す
# satisfiableがTrueとなった後に呼ばないと意味ない
# O(1）
cdef answer(s): return s._answer
import sys
sys.setrecursionlimit(1000000)
cdef class scc_graph:
cdef int _n
cdef dict g
# n 頂点数
def __init__(s, int n):
s._n = n
s.g = {}
cdef num_vertices(s): return s._n
# 辺を追加 frm 矢元 to 矢先
# O(1)
cdef add_edge(s, int frm, int to):
if frm in s.g: s.g[frm].append(to)
else: s.g[frm] = [to]
# 再帰関数
cdef dfs(s, int v, int now_ord, int group_num, list low, list ord, list visited, list ids):
low[v] = ord[v] = now_ord
now_ord += 1
visited.append(v)
if v in s.g:
for to in s.g[v]:
if ord[to] == -1:
now_ord, group_num = s.dfs(to, now_ord, group_num, low, ord, visited, ids)
low[v] = min(low[v], low[to])
else:
low[v] = min(low[v], ord[to])
if low[v] == ord[v]:
while True:
u = visited.pop()
ord[u] = s._n
ids[u] = group_num
if u == v: break
group_num += 1
return now_ord, group_num
# グループの個数と各頂点のグループidを返す
cdef scc_ids(s):
cdef:
int now_ord = 0
int group_num = 0
list visited = []
list low = [0] * s._n
list ord = [-1] * s._n
list ids = [0] * s._n
for i in range(s._n):
if ord[i] == -1: now_ord, group_num = s.dfs(i, now_ord, group_num, low, ord, visited, ids)
for i in range(s._n):
ids[i] = group_num - 1 - ids[i]
return group_num, ids
# 強連結成分となっている頂点のリストのリスト トポロジカルソート済み
# O(n + m)
cdef scc(s):
cdef:
int group_num
list ids
group_num, ids = s.scc_ids()
cdef:
list counts = [0] * group_num
for x in ids: counts[x] += 1
cdef:
list groups = [[] for _ in range(group_num)]
for i in range(s._n):
groups[ids[i]].append(i)
return groups
def trueList(x):
x += SIZE
for i in range(1, LOG + 1): yield x >> i
def falseList(x, D):
ld = XY[x] - D
rd = XY[x] + D
ok, ng = x, -1
while abs(ok - ng) > 1:
mid = (ok + ng) // 2
if XY[mid] > ld:
ok = mid
else:
ng = mid
L = prod(ok, x)
ok, ng = x, M
while abs(ok - ng) > 1:
mid = (ok + ng) // 2
if XY[mid] < rd:
ok = mid
else:
ng = mid
L += prod(x + 1, ok + 1)
return L
def prod(l, r):
l += SIZE
r += SIZE
L = []
while l < r:
if l & 1:
L.append(l)
l += 1
if r & 1:
r -= 1
L.append(r)
l >>= 1
r >>= 1
return L
def ceil_pow2(n):
x = 0
while (1 << x) < n: x += 1
return x
def nasu(long D):
cdef two_sat ts = two_sat(2 * SIZE)
cnt = 0
for i in range(N):
x, y = L[i]
ts.add_clause(x + SIZE, True, y + SIZE, True)
ts.add_clause(x + SIZE, False, y + SIZE, False)
for i in range(M):
x = i + SIZE
for y in trueList(i):
ts.add_clause(x, False, y, True)
for y in falseList(i, D):
ts.add_clause(x, False, y, False)
return ts.satisfiable()
N = int(input())
XY = [list(map(int, input().split())) for _ in range(N)]
for i in range(N):
x, y = XY[i]
if x > y:
x, y = y, x
XY[i] = [x, y]
ng = 10 ** 9 + 1
XY.sort()
for i in range(1, N):
x1, y1 = XY[i - 1]
x2, y2 = XY[i]
ng = min(ng, max(abs(x1 - y2), abs(x2 - y1)))
XY.sort(key = lambda x: x[1])
for i in range(1, N):
x1, y1 = XY[i - 1]
x2, y2 = XY[i]
ng = min(ng, max(abs(x1 - y2), abs(x2 - y1)))
D = [[0, 0, 0] for _ in range(N * 2)]
for i in range(N):
x, y = XY[i]
D[i * 2] = [x, i, 0]
D[i * 2 + 1] = [y, i, 0]
D.sort()
XY = [0] * (N * 2)
for i in range(N * 2):
D[i][2] = i
XY[i] = D[i][0]
D.sort(key = lambda x: x[1])
L = []
for i in range(N):
L.append([D[i * 2][2], D[i * 2 + 1][2]])
M = len(XY)
LOG = ceil_pow2(M)
SIZE = 1 << LOG
ok = 0
ng += 1
while abs(ok - ng) > 1:
mid = (ok + ng) // 2
if nasu(mid):
ok = mid
else:
ng = mid
print(ok)
'''
import sys
import os
if sys.argv[-1] == 'ONLINE_JUDGE': # コンパイル時
with open('mycode.pyx', 'w') as f:
f.write(mycode)
os.system('cythonize -i -3 -b mycode.pyx')
import mycode
``` | instruction | 0 | 56,310 | 16 | 112,620 |
No | output | 1 | 56,310 | 16 | 112,621 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Snuke loves flags.
Snuke is placing N flags on a line.
The i-th flag can be placed at either coordinate x_i or coordinate y_i.
Snuke thinks that the flags look nicer when the smallest distance between two of them, d, is larger. Find the maximum possible value of d.
Constraints
* 2 ≤ N ≤ 10^{4}
* 1 ≤ x_i, y_i ≤ 10^{9}
* x_i and y_i are integers.
Input
The input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the answer.
Examples
Input
3
1 3
2 5
1 9
Output
4
Input
5
2 2
2 2
2 2
2 2
2 2
Output
0
Input
22
93 6440
78 6647
862 11
8306 9689
798 99
801 521
188 206
6079 971
4559 209
50 94
92 6270
5403 560
803 83
1855 99
42 504
75 484
629 11
92 122
3359 37
28 16
648 14
11 269
Output
17
Submitted Solution:
```
#-------最強ライブラリ2-SAT(Python)------
#最強ライブラリSCC(Python)が必要
class two_sat:
def __init__(s):
s._n = 0
s.scc = scc_graph(0)
def __init__(s, n):
s._n = n
s._answer = [False] * n
s.scc = scc_graph(2 * n)
# クローズを足す
# クローズってなに
def add_clause(s, i, f, j, g):
s.scc.add_edge(2 * i + (not f), 2 * j + (g))
s.scc.add_edge(2 * j + (not g), 2 * i + (f))
# 判定
# O(n + m)
def satisfiable(s):
id = s.scc.scc_ids()[1]
for i in range(s._n):
if id[2 * i] == id[2 * i + 1]: return False
s._answer[i] = id[2 * i] < id[2 * i + 1]
return True
# クローズを満たす割当を返す
# satisfiableがTrueとなった後に呼ばないと意味ない
# O(1だよね？）
def answer(s): return s._answer
#-------最強ライブラリここまで------
#-------最強ライブラリSCC(Python)ver25252------
import copy
import sys
sys.setrecursionlimit(1000000)
class csr:
# start 頂点iまでの頂点が、矢元として現れた回数
# elist 矢先のリストを矢元の昇順にしたもの
def __init__(s, n, edges):
s.start = [0] * (n + 1)
s.elist = [[] for _ in range(len(edges))]
for e in edges:
s.start[e[0] + 1] += 1
for i in range(1, n + 1):
s.start[i] += s.start[i - 1]
counter = copy.deepcopy(s.start)
for e in edges:
s.elist[counter[e[0]]] = e[1]
counter[e[0]] += 1
class scc_graph:
# n 頂点数
def __init__(s, n):
s._n = n
s.edges = []
def num_vertices(s): return s._n
# 辺を追加 frm 矢元 to 矢先
# O(1)
def add_edge(s, frm, to): s.edges.append([frm, [to]])
# グループの個数と各頂点のグループidを返す
def scc_ids(s):
g = csr(s._n, s.edges)
now_ord = group_num = 0
visited = []
low = [0] * s._n
ord = [-1] * s._n
ids = [0] * s._n
# 再帰関数
def dfs(self, v, now_ord, group_num):
low[v] = ord[v] = now_ord
now_ord += 1
visited.append(v)
for i in range(g.start[v], g.start[v + 1]):
to = g.elist[i][0]
if ord[to] == -1:
now_ord, group_num = self(self, to, now_ord, group_num)
low[v] = min(low[v], low[to])
else:
low[v] = min(low[v], ord[to])
if low[v] == ord[v]:
while True:
u = visited.pop()
ord[u] = s._n
ids[u] = group_num
if u == v: break
group_num += 1
return now_ord, group_num
for i in range(s._n):
if ord[i] == -1: now_ord, group_num = dfs(dfs, i, now_ord, group_num)
for i in range(s._n):
ids[i] = group_num - 1 - ids[i]
return [group_num, ids]
# 強連結成分となっている頂点のリストのリスト トポロジカルソート済み
# O(n + m)
def scc(s):
ids = s.scc_ids()
group_num = ids[0]
counts = [0] * group_num
for x in ids[1]: counts[x] += 1
groups = [[] for _ in range(group_num)]
for i in range(s._n):
groups[ids[1][i]].append(i)
return groups
def nasu(D, XY):
ts = two_sat(N)
for i in range(N):
for j in range(i + 1, N):
xi, yi = XY[i]
xj, yj = XY[j]
# 距離がD未満の組み合わせに関して、
# 少なくとも一つは使用しない
# → 少なくとも一つは別の座標を使用する
# というルールを追加する
if (abs(xi - xj) < D):
ts.add_clause(i, False, j, False)
if (abs(xi - yj) < D):
ts.add_clause(i, False, j, True)
if (abs(yi - xj) < D):
ts.add_clause(i, True, j, False)
if (abs(yi - yj) < D):
ts.add_clause(i, True, j, True)
if ts.satisfiable():
return True
return False
N = int(input())
XY = [list(map(int, input().split())) for _ in range(N)]
ok = 0
ng = 10 ** 9 + 1
while abs(ok - ng) > 1:
mid = (ok + ng) // 2
if nasu(mid, XY):
ok = mid
else:
ng = mid
print(ok)
``` | instruction | 0 | 56,311 | 16 | 112,622 |
No | output | 1 | 56,311 | 16 | 112,623 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke prepared 6 problems for a upcoming programming contest. For each of those problems, Rng judged whether it can be used in the contest or not.
You are given a string S of length 6. If the i-th character of s is `1`, it means that the i-th problem prepared by Snuke is accepted to be used; `0` means that the problem is not accepted.
How many problems prepared by Snuke are accepted to be used in the contest?
Constraints
* The length of S is 6.
* S consists of `0` and `1`.
Inputs
Input is given from Standard Input in the following format:
S
Outputs
Print the number of problems prepared by Snuke that are accepted to be used in the contest.
Examples
Input
111100
Output
4
Input
001001
Output
2
Input
000000
Output
0 | instruction | 0 | 57,021 | 16 | 114,042 |
"Correct Solution:
```
print(sum(1 for i in input() if i=="1"))
``` | output | 1 | 57,021 | 16 | 114,043 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke prepared 6 problems for a upcoming programming contest. For each of those problems, Rng judged whether it can be used in the contest or not.
You are given a string S of length 6. If the i-th character of s is `1`, it means that the i-th problem prepared by Snuke is accepted to be used; `0` means that the problem is not accepted.
How many problems prepared by Snuke are accepted to be used in the contest?
Constraints
* The length of S is 6.
* S consists of `0` and `1`.
Inputs
Input is given from Standard Input in the following format:
S
Outputs
Print the number of problems prepared by Snuke that are accepted to be used in the contest.
Examples
Input
111100
Output
4
Input
001001
Output
2
Input
000000
Output
0 | instruction | 0 | 57,022 | 16 | 114,044 |
"Correct Solution:
```
#!/usr/bin/env python3
s = input()
print(s.count('1'))
``` | output | 1 | 57,022 | 16 | 114,045 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke prepared 6 problems for a upcoming programming contest. For each of those problems, Rng judged whether it can be used in the contest or not.
You are given a string S of length 6. If the i-th character of s is `1`, it means that the i-th problem prepared by Snuke is accepted to be used; `0` means that the problem is not accepted.
How many problems prepared by Snuke are accepted to be used in the contest?
Constraints
* The length of S is 6.
* S consists of `0` and `1`.
Inputs
Input is given from Standard Input in the following format:
S
Outputs
Print the number of problems prepared by Snuke that are accepted to be used in the contest.
Examples
Input
111100
Output
4
Input
001001
Output
2
Input
000000
Output
0 | instruction | 0 | 57,023 | 16 | 114,046 |
"Correct Solution:
```
S = input()
T = S.count("1")
print(T)
``` | output | 1 | 57,023 | 16 | 114,047 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke prepared 6 problems for a upcoming programming contest. For each of those problems, Rng judged whether it can be used in the contest or not.
You are given a string S of length 6. If the i-th character of s is `1`, it means that the i-th problem prepared by Snuke is accepted to be used; `0` means that the problem is not accepted.
How many problems prepared by Snuke are accepted to be used in the contest?
Constraints
* The length of S is 6.
* S consists of `0` and `1`.
Inputs
Input is given from Standard Input in the following format:
S
Outputs
Print the number of problems prepared by Snuke that are accepted to be used in the contest.
Examples
Input
111100
Output
4
Input
001001
Output
2
Input
000000
Output
0 | instruction | 0 | 57,024 | 16 | 114,048 |
"Correct Solution:
```
S=list(str(input()))
ans=S.count('1')
print(ans)
``` | output | 1 | 57,024 | 16 | 114,049 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke prepared 6 problems for a upcoming programming contest. For each of those problems, Rng judged whether it can be used in the contest or not.
You are given a string S of length 6. If the i-th character of s is `1`, it means that the i-th problem prepared by Snuke is accepted to be used; `0` means that the problem is not accepted.
How many problems prepared by Snuke are accepted to be used in the contest?
Constraints
* The length of S is 6.
* S consists of `0` and `1`.
Inputs
Input is given from Standard Input in the following format:
S
Outputs
Print the number of problems prepared by Snuke that are accepted to be used in the contest.
Examples
Input
111100
Output
4
Input
001001
Output
2
Input
000000
Output
0 | instruction | 0 | 57,025 | 16 | 114,050 |
"Correct Solution:
```
c = 0
for i in input():
if i=='1':
c += 1
print(c)
``` | output | 1 | 57,025 | 16 | 114,051 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke prepared 6 problems for a upcoming programming contest. For each of those problems, Rng judged whether it can be used in the contest or not.
You are given a string S of length 6. If the i-th character of s is `1`, it means that the i-th problem prepared by Snuke is accepted to be used; `0` means that the problem is not accepted.
How many problems prepared by Snuke are accepted to be used in the contest?
Constraints
* The length of S is 6.
* S consists of `0` and `1`.
Inputs
Input is given from Standard Input in the following format:
S
Outputs
Print the number of problems prepared by Snuke that are accepted to be used in the contest.
Examples
Input
111100
Output
4
Input
001001
Output
2
Input
000000
Output
0 | instruction | 0 | 57,026 | 16 | 114,052 |
"Correct Solution:
```
a = list(input())
print(a.count('1'))
``` | output | 1 | 57,026 | 16 | 114,053 |
Provide a correct Python 3 solution for this coding contest problem.
Snuke prepared 6 problems for a upcoming programming contest. For each of those problems, Rng judged whether it can be used in the contest or not.
You are given a string S of length 6. If the i-th character of s is `1`, it means that the i-th problem prepared by Snuke is accepted to be used; `0` means that the problem is not accepted.
How many problems prepared by Snuke are accepted to be used in the contest?
Constraints
* The length of S is 6.
* S consists of `0` and `1`.
Inputs
Input is given from Standard Input in the following format:
S
Outputs
Print the number of problems prepared by Snuke that are accepted to be used in the contest.
Examples
Input
111100
Output
4
Input
001001
Output
2
Input
000000
Output
0 | instruction | 0 | 57,027 | 16 | 114,054 |
"Correct Solution:
```
s=input()
count=0
for i in range(6):
if s[i]=="1":
count+=1
print(count)
``` | output | 1 | 57,027 | 16 | 114,055 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.