message stringlengths 2 44.5k | message_type stringclasses 2 values | message_id int64 0 1 | conversation_id int64 276 109k | cluster float64 23 23 | __index_level_0__ int64 552 217k |
|---|---|---|---|---|---|
Provide tags and a correct Python 3 solution for this coding contest problem.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border). | instruction | 0 | 100,754 | 23 | 201,508 |
Tags: geometry, implementation
Correct Solution:
```
n = int(input())
stars = []
for i in range(n):
x, y = list(map(int, input().split()))
stars.append((x, y))
x1, y1 = stars[0]
ind1 = 0
x2, y2 = stars[1]
ind2 = 1
x3, y3 = 0, 0
ind3 = 0
for i in range(2, n):
x0, y0 = stars[i]
if (x1 - x0) * (y2 - y1) - (x2 - x1) * (y1 - y0) != 0:
x3, y3 = x0, y0
ind3 = i
break
for i in range(2, n):
x0, y0 = stars[i]
if i == ind1 or i == ind2 or i == ind3:
continue
d1 = (x1 - x0) * (y2 - y1) - (x2 - x1) * (y1 - y0)
d2 = (x2 - x0) * (y3 - y2) - (x3 - x2) * (y2 - y0)
d3 = (x3 - x0) * (y1 - y3) - (x1 - x3) * (y3 - y0)
if (d1 >= 0 and d2 >= 0 and d3 >= 0) or (d1 <= 0 and d2 <= 0 and d3 <= 0):
if d1 == 0 or d2 == 0:
ind2 = i
x2, y2 = x0, y0
elif d3 == 0 or (d1 > 0 and d2 > 0 and d3 > 0) or (d1 < 0 and d2 < 0 and d3 < 0):
ind1 = i
x1, y1 = x0, y0
print(ind1 + 1, ind2 + 1, ind3 + 1)
``` | output | 1 | 100,754 | 23 | 201,509 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border). | instruction | 0 | 100,755 | 23 | 201,510 |
Tags: geometry, implementation
Correct Solution:
```
n = int(input())
p = []
for i in range(n):
p += [list(map(int,input().split()))+[i+1]]
p = sorted(p)
l = [[p[0]]]
for i in range(1,n):
if l[-1][0][0] < p[i][0]:
l += [[p[i]]]
else:
l[-1] += [p[i]]
m = len(l)
for i in range(m):
if len(l[i]) > 1:
r = 1 if i == 0 else -1
print(l[i][0][2],l[i][1][2],l[i+r][0][2])
break
else:
u, v = l[0][0], l[1][0]
n = [v[0]-u[0],v[1]-u[1]]
a, b = -n[1], n[0]
c = - a * u[0] - b * u[1]
for i in range(2,m):
z = l[i][0]
if a * z[0] + b * z[1] + c != 0:
print(u[2],v[2],z[2])
break
else:
u = v
v = z
``` | output | 1 | 100,755 | 23 | 201,511 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border). | instruction | 0 | 100,756 | 23 | 201,512 |
Tags: geometry, implementation
Correct Solution:
```
#!/usr/bin/env python3
from collections import namedtuple
from itertools import islice
Point = namedtuple("Point", "x y")
try:
while True:
n = int(input())
points = [Point(*map(int, input().split())) for i in range(n)]
min_d = 1e20
i1 = i2 = 0
p0 = points[0]
p1 = p2 = None
for i, p in enumerate(islice(points, 1, None), 1):
d = (p.x - p0.x)**2 + (p.y - p0.y)**2
if d < min_d:
min_d = d
p1 = p
i1 = i
assert p1 is not None
dx1 = p1.x - p0.x
dy1 = p1.y - p0.y
min_d = 1e20
for i, p in enumerate(islice(points, 1, None), 1):
if p is p1:
continue
dx2 = p.x - p0.x
dy2 = p.y - p0.y
if dx1 == 0:
ok = dx2 != 0
elif dy1 == 0:
ok = dy2 != 0
else:
ok = dy1 * dx2 != dy2 * dx1
if ok:
d = dx2**2 + dy2**2
if d < min_d:
min_d = d
p2 = p
i2 = i
# assert p2 is not None
while p2 is None:
pass
print(1, i1 + 1, i2 + 1)
except EOFError:
pass
``` | output | 1 | 100,756 | 23 | 201,513 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border). | instruction | 0 | 100,757 | 23 | 201,514 |
Tags: geometry, implementation
Correct Solution:
```
t = [(list(map(int, input().split())) + [i + 1]) for i in range(int(input()))]
t.sort()
x, y, i = t[0]
u, v, j = t[1]
for a, b, k in t[2:]:
if (u - x) * (b - y) - (v - y) * (a - x): break
print(i, j, k)
# Made By Mostafa_Khaled
``` | output | 1 | 100,757 | 23 | 201,515 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border). | instruction | 0 | 100,758 | 23 | 201,516 |
Tags: geometry, implementation
Correct Solution:
```
import math
def on_one_line(x1, y1, x2, y2, x3, y3):
result = x1 * y2 - y1 * x2 + y1 * x3 - x1 * y3 + x2 * y3 - x3 * y2;
if result == 0:
return True
else:
return False
n = int(input().strip())
node = []
for i in range(n):
a, b = input().strip().split()
node.append([int(a), int(b)])
mindis1 = 0
minidx1 = 0
for i in range(1, n):
dis1 = math.sqrt(math.pow((node[i][0]-node[0][0]),2) + math.pow((node[i][1]-node[0][1]),2))
if i == 1:
mindis1 = dis1
minidx1 = i
elif dis1 < mindis1:
mindis1 = dis1
minidx1 = i
mindis2 = 10000000000000
minidx2 = 0
for i in range(1, n):
if on_one_line(node[0][0], node[0][1], node[minidx1][0], node[minidx1][1], node[i][0], node[i][1]) == False:
dis2 = math.sqrt(math.pow((node[i][0]-node[minidx1][0]),2) + math.pow((node[i][1]-node[minidx1][1]),2))
if dis2 < mindis2:
mindis2 = dis2
minidx2 = i
print("1 " + str(minidx1+1) + " " + str(minidx2+1))
``` | output | 1 | 100,758 | 23 | 201,517 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border). | instruction | 0 | 100,759 | 23 | 201,518 |
Tags: geometry, implementation
Correct Solution:
```
n = int(input())
ans = []
arr = [0] * n
for idx in range(n):
x, y = input().split()
arr[idx] = (int(x) + int(y), int(x), idx + 1, int(y))
arr.sort()
ans.append(arr[0][2])
ans.append(arr[1][2])
if arr[0][0] == arr[1][0]:
w = arr[0][0]
idx = 2
while(True):
if arr[idx][0] == w:
idx += 1
else:
ans.append(arr[idx][2])
break
else:
idx = 2
while(True):
if (arr[1][3] - arr[0][3]) * (arr[idx][1] - arr[1][1]) == (arr[idx][3] - arr[1][3]) * (arr[1][1] - arr[0][1]):
idx += 1
else:
ans.append(arr[idx][2])
break
print(' '.join(map(str, ans)))
``` | output | 1 | 100,759 | 23 | 201,519 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border). | instruction | 0 | 100,760 | 23 | 201,520 |
Tags: geometry, implementation
Correct Solution:
```
import sys
import itertools
def s(p1,p2,p3):
return (p1[0]-p3[0])*(p2[1]-p3[1])-(p2[0]-p3[0])*(p1[1]-p3[1])
e = 1e-22
def inTri(p, p1, p2, p3):
l = [p1,p2,p3]
for i in itertools.permutations(l):
if abs(t(i[0],i[1])-t(i[0],p))<=e and min(i[0][0],i[1][0])<=p[0]<=max(i[0][0],i[1][0]) and min(i[0][1],i[1][1])<=p[1]<=max(i[0][1],i[1][1]):
return True
return (s(p,p1,p2)<=0)==(s(p,p2,p3)<=0) and (s(p,p2,p3)<=0)==(s(p,p3,p1)<=0)
def t(p1, p2):
if p2[0] == p1[0]: return 2e9
return (p2[1]-p1[1])/(p2[0]-p1[0])
n = int(input())
l = []
n1 = 0
n2 = 1
n3 = -1
for i in range(n):
p = tuple(map(int,input().split()))
l.append(p)
for i in range(2,n):
if t(l[n1],l[n2]) == t(l[n1],l[i]) and (l[n1][0]-l[n2][0])**2+(l[n1][1]-l[n2][1])**2 > (l[n1][0]-l[i][0])**2+(l[n1][1]-l[i][1])**2:
n2 = i
for i in range(n):
if i==n1 or i==n2: continue
if abs(t(l[i],l[n1])-t(l[i],l[n2]))<=e:
continue
if n3<0:
n3=i
continue
if inTri(l[i], l[n1],l[n2],l[n3]):
n3 = i
continue
print(n1+1,n2+1,n3+1)
``` | output | 1 | 100,760 | 23 | 201,521 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border).
Submitted Solution:
```
def cross_pr(a_):
x1, y1, x2, y2 = a_[:]
return x1 * y2 - x2 * y1
def vector(a_):
x1, y1, x2, y2 = a_[:]
return [x1 - x2, y1 - y2]
def dist(a_):
x1, y1 = a_[:]
return (x1 * x1 + y1 * y1) ** 0.5
n = int(input())
x = [[] for i in range(n)]
for i in range(n):
x[i] = [int(i) for i in input().split()]
a = [[0] * 2 for i in range(n - 1)]
for i in range(1, n):
a[i - 1][0] = dist(vector(x[i] + x[0]))
a[i - 1][1] = i
a.sort()
ans = [0] * 3
ans[0] = 0
ans[1] = a[0][1]
now = 2 * 10 ** 21 + 1
v1 = vector(x[ans[0]] + x[ans[1]])
for i in range(n):
v2 = vector(x[i] + x[ans[1]])
if abs(cross_pr(v1 + v2)) > 0:
if abs(cross_pr(v1 + v2)) < now:
now = abs(cross_pr(v1 + v2))
ans[2] = i
for i in range(3):
ans[i] += 1
print(*ans)
``` | instruction | 0 | 100,761 | 23 | 201,522 |
Yes | output | 1 | 100,761 | 23 | 201,523 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border).
Submitted Solution:
```
t = [(list(map(int, input().split())), i) for i in range(1, int(input()) + 1)]
t.sort()
(x, y), i = t[0]
(u, v), j = t[1]
for (a, b), k in t[2:]:
if (u - x) * (b - y) - (v - y) * (a - x): break
print(i, j, k)
``` | instruction | 0 | 100,762 | 23 | 201,524 |
Yes | output | 1 | 100,762 | 23 | 201,525 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border).
Submitted Solution:
```
n = int(input())
points = []
for i in range(n):
points.append(tuple(int(x) for x in input().split()))
p0 = points[0]
dist = lambda p, q: (p[0]-q[0])**2 + (p[1]-q[1])**2
s_points = sorted(list(enumerate(points)), key = lambda p: dist(p[1], p0))
p1 = s_points[1][1]
def incident(p, q, r):
u = (p[0] - q[0], p[1] - q[1])
v = (p[0] - r[0], p[1] - r[1])
return u[0]*v[1] - u[1]*v[0] == 0
for i in range(2, n):
if not incident(p0, p1, s_points[i][1]):
print(1, s_points[1][0]+1, s_points[i][0]+1)
break
else:
print('wtf, dude?')
``` | instruction | 0 | 100,763 | 23 | 201,526 |
Yes | output | 1 | 100,763 | 23 | 201,527 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border).
Submitted Solution:
```
t = [(list(map(int, input().split())) + [i + 1]) for i in range(int(input()))]
t.sort()
x, y, i = t[0]
u, v, j = t[1]
for a, b, k in t[2:]:
if (u - x) * (b - y) - (v - y) * (a - x): break
print(i, j, k)
``` | instruction | 0 | 100,764 | 23 | 201,528 |
Yes | output | 1 | 100,764 | 23 | 201,529 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border).
Submitted Solution:
```
def check(x1, y1, x2, y2, x, y):
a = (x1 - x) ** 2 + (y - y1) ** 2 + (x2 - x) ** 2 + (y - y2) ** 2
b = (x1 - x2) ** 2 + (y2 - y1) ** 2
b -= a
if b < 0:
return False
b /= 2
b **= 2
a = ((x1 - x) ** 2 + (y - y1) ** 2) * ((x2 - x) ** 2 + (y - y2) ** 2)
if a == b:
return True
else:
return False
def sqr(s):
answer = 0
for i in range(len(s)):
answer += s[i][0] * s[(i + 1) % len(s)][1] - s[i][1] * s[(i + 1) % len(s)][0]
answer /= 2
answer = abs(answer)
return answer
def main():
n = int(input())
s = []
for i in range(n):
a, b = map(int, input().split())
s.append([a, b, i + 1])
s.sort()
i = 0
print(s)
while s[i][0] == s[0][0]:
i += 1
if i > 2:
print(1, 2, i + 1)
else:
while check(s[i][0], s[i][1], s[0][0], s[0][1], s[1][0], s[1][1]):
i += 1
print(s[0][2], s[1][2], s[i][2])
main()
``` | instruction | 0 | 100,765 | 23 | 201,530 |
No | output | 1 | 100,765 | 23 | 201,531 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border).
Submitted Solution:
```
n=int(input())
points=[list(map(int,input().split())) for i in range(n)]
from random import randint
i=0
j=1
p1,p2 = points[i],points[j]
def dis(p1,p2):
return (p1[0]-p2[0])**2 + (p1[1]-p2[1])**2
def Area(p1,p2,p3):
return p1[0]*abs(p2[1]-p3[1])+p2[0]*abs(p3[1]-p1[1])+p3[0]*abs(p1[1]-p2[1])
for k in range(n):
if k==i or k==j:
continue
elif dis(points[i],points[j])==(dis(points[i],points[k])+dis(points[k],points[j])):
j=k
K=0
area=int(1e18)
for k in range(n):
if k==i or k==j:
continue
else:
a=Area(points[i],points[j],points[k])
if area>a>0:
area=a
K=k
print(i+1,j+1,K+1)
``` | instruction | 0 | 100,766 | 23 | 201,532 |
No | output | 1 | 100,766 | 23 | 201,533 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border).
Submitted Solution:
```
import math
n = int(input())
p = [ list(map(int, input().split())) for i in range(0,n)]
def isTriangle(p1,p2,p3):
area = p1[0] * (p2[1] - p3[1]) + p2[1] * (p3[1] - p1[1]) + p3[1] * (p1[1] - p2[1])
return area > 0
minLen = -1
ind = -1
for i in range(2, n):
if isTriangle(p[0],p[1], p[i]):
m = (p[0][1] - p[1][1] )/(p[0][0] - p[1][0])
c = p[0][1] - m * p[0][0]
curLen = (m*p[0][0] + c + p[0][1]) / math.sqrt(m*m + 1)
if minLen == -1 or curLen < minLen:
minLen = curLen
ind = i
print(1,2,ind + 1)
``` | instruction | 0 | 100,767 | 23 | 201,534 |
No | output | 1 | 100,767 | 23 | 201,535 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Cat Noku has obtained a map of the night sky. On this map, he found a constellation with n stars numbered from 1 to n. For each i, the i-th star is located at coordinates (xi, yi). No two stars are located at the same position.
In the evening Noku is going to take a look at the night sky. He would like to find three distinct stars and form a triangle. The triangle must have positive area. In addition, all other stars must lie strictly outside of this triangle. He is having trouble finding the answer and would like your help. Your job is to find the indices of three stars that would form a triangle that satisfies all the conditions.
It is guaranteed that there is no line such that all stars lie on that line. It can be proven that if the previous condition is satisfied, there exists a solution to this problem.
Input
The first line of the input contains a single integer n (3 ≤ n ≤ 100 000).
Each of the next n lines contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109).
It is guaranteed that no two stars lie at the same point, and there does not exist a line such that all stars lie on that line.
Output
Print three distinct integers on a single line — the indices of the three points that form a triangle that satisfies the conditions stated in the problem.
If there are multiple possible answers, you may print any of them.
Examples
Input
3
0 1
1 0
1 1
Output
1 2 3
Input
5
0 0
0 2
2 0
2 2
1 1
Output
1 3 5
Note
In the first sample, we can print the three indices in any order.
In the second sample, we have the following picture.
<image>
Note that the triangle formed by starts 1, 4 and 3 doesn't satisfy the conditions stated in the problem, as point 5 is not strictly outside of this triangle (it lies on it's border).
Submitted Solution:
```
n=int(input())
points=[list(map(int,input().split())) for i in range(n)]
i,j=0,1
def dis(p1,p2):
return ((p1[0]-p2[0])**2 + (p1[1]-p2[1])**2)**0.5
def Area(p1,p2,p3):
return (p1[0]*abs(p2[1]-p3[1])+p2[0]*abs(p3[1]-p1[1])+p3[0]*abs(p1[1]-p2[1]))
for k in range(n):
if k==i or k==j:
continue
elif abs(dis(points[i],points[j])-(dis(points[i],points[k])+dis(points[k],points[j])))<=1e-10:
j=k
K=0
print(i,j)
area=int(1e20)
for k in range(n):
if k==i or k==j:
continue
else:
a=Area(points[i],points[j],points[k])
if area>a>0:
area=a
K=k
print(i+1,j+1,K+1)
``` | instruction | 0 | 100,768 | 23 | 201,536 |
No | output | 1 | 100,768 | 23 | 201,537 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone. | instruction | 0 | 100,800 | 23 | 201,600 |
Tags: data structures, hashing
Correct Solution:
```
def define_nearest_primes(n):
primes=[11,17,19,23,29,53,97,193,389,769,1543,3079,6151,12289,24593,49157,98317,1572869]
for i in range(0, len(primes)):
if primes[i]>1.5*n:
p=primes[i]
break
return p
def sort_box(box):
if box[0]>box[1]:
if box[0]>box[2]:
if box[1]>box[2]:
box=[box[2],box[1],box[0]]
else:
box=[box[1],box[2],box[0]]
else:
box=[box[1],box[0],box[2]]
else:
if box[0]<box[2]:
if box[1]<box[2]:
box=[box[0],box[1],box[2]]
else:
box=[box[0],box[2],box[1]]
else:
box=[box[2],box[0],box[1]]
return(box)
def hash_func(box,i,hash_table,biggest_merged_rectangular,p):
index=(50033*box[2]+box[1]) % p
while (len(hash_table[index])>0 and (box[1]!=hash_table[index][0][2] or box[2]!=hash_table[index][0][3])):
index=(index+1) % p
#print(box,index)
if len(hash_table[index])==2:
if box[0]>hash_table[index][0][1]:
if hash_table[index][0][1]<hash_table[index][1][1]:
hash_table[index][0]=[i,box[0],box[1],box[2]]
else:
hash_table[index][1]=[i,box[0],box[1],box[2]]
else:
if box[0]>hash_table[index][1][1]:
hash_table[index][1]=[i,box[0],box[1],box[2]]
temp_box=[hash_table[index][0][2],hash_table[index][0][3],hash_table[index][0][1]+hash_table[index][1][1]]
temp_box=sort_box(temp_box)
if biggest_merged_rectangular[2]<temp_box[0]:
biggest_merged_rectangular=[hash_table[index][0][0],hash_table[index][1][0],temp_box[0]]
else:
if len(hash_table[index])==1:
hash_table[index].append([i,box[0],box[1],box[2]])
temp_box=[hash_table[index][0][2],hash_table[index][0][3],hash_table[index][0][1]+hash_table[index][1][1]]
temp_box=sort_box(temp_box)
if biggest_merged_rectangular[2]<temp_box[0]:
biggest_merged_rectangular=[hash_table[index][0][0],hash_table[index][1][0],temp_box[0]]
else:
hash_table[index].append([i,box[0],box[1],box[2]])
return hash_table, biggest_merged_rectangular
def print_result(biggest_rectangular,biggest_merged_rectangular):
if biggest_rectangular[1]>biggest_merged_rectangular[2]:
print('1'+'\n'+str(biggest_rectangular[0]))
else:
if (biggest_merged_rectangular[0]<biggest_merged_rectangular[1]):
print('2'+'\n'+str(biggest_merged_rectangular[0])+' '+str(biggest_merged_rectangular[1]))
else:
print('2'+'\n'+str(biggest_merged_rectangular[1])+' '+str(biggest_merged_rectangular[0]))
def main():
n=int(input()) #the number of boxes
p=define_nearest_primes(n)
hash_table=[[] for i in range(0,p)]
biggest_rectangular=[0,0] #we will also search in online format for largest rectangular: [index,radius]
biggest_merged_rectangular=[0,0,0] #and merged rectangular: [index1,index2,radius]
for i in range(1,n+1):
box=input().split(" ")
box=[int(box[0]),int(box[1]),int(box[2])]
#print(box)
if box[1]==box[0] and box[0]==box[2]:
if biggest_rectangular[1]<box[0]:
biggest_rectangular[0]=i
biggest_rectangular[1]=box[0]
else:
box=sort_box(box) #now sides of the box are sorted from smallest to largest
#print(sort_box(box))
if biggest_rectangular[1]<box[0]:
biggest_rectangular[0]=i
biggest_rectangular[1]=box[0]
hashing=hash_func(box,i,hash_table,biggest_merged_rectangular,p) #online hashing process
hash_table=hashing[0] #include the box into hash table
biggest_merged_rectangular=hashing[1] #update the merged rectangular
#print(biggest_merged_rectangular)
#print(biggest_rectangular)
print_result(biggest_rectangular,biggest_merged_rectangular)
#f=open("output.txt", "w")
#f.write(chosen_boxes[0]+'\n')
if __name__ == "__main__":
main()
``` | output | 1 | 100,800 | 23 | 201,601 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone. | instruction | 0 | 100,801 | 23 | 201,602 |
Tags: data structures, hashing
Correct Solution:
```
n = int(input())
lst = []
for i in range(n):
lst.append([i + 1] + sorted([int(x) for x in input().split(' ')]))
d = {}
for elem in lst:
if (elem[3], elem[2]) in d:
d[(elem[3], elem[2])].append((elem[0], elem[1]))
else:
d[(elem[3], elem[2])] = [(elem[0], elem[1])]
m = 0
ans = []
# print(d)
for pair in d:
m1, m2 = 0, 0
i1, i2 = 0, 0
for i in range(0, len(d[pair])):
if d[pair][i][1] > m2:
m1 = m2
m2 = d[pair][i][1]
i1 = i2
i2 = d[pair][i][0]
elif d[pair][i][1] > m1:
m1 = d[pair][i][1]
i1 = d[pair][i][0]
# print(pair)
# print(d[pair])
if i1 > 0:
a = min(pair[0], pair[1], m1 + m2)
if a > m:
m = a
ans = [i1, i2]
else:
a = min(pair[0], pair[1], m2)
if a > m:
m = a
ans = [i2]
# print(a, m, ans)
print(len(ans))
print(' '.join([str(x) for x in ans]))
``` | output | 1 | 100,801 | 23 | 201,603 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone. | instruction | 0 | 100,802 | 23 | 201,604 |
Tags: data structures, hashing
Correct Solution:
```
N = int(input())
maxr = 0
maxi = [-1]
sides = {}
for x in range(N):
cords = [int(x) for x in input().split()]
cords.sort()
if (cords[1], cords[2]) in sides:
sides[(cords[1], cords[2])][0].append(cords[0])
sides[(cords[1], cords[2])][1].append(x+1)
else:
sides[(cords[1], cords[2])] = [ [cords[0]], [x+1], cords[1] ]
if cords[0] > maxr:
maxr = cords[0]
maxi = [x + 1]
for key in sides:
maxA = 0
maxB = 0
Ai = 0
Bi = 0
for i,val in enumerate(sides[key][0]):
if maxA < val:
maxA = val
Ai = i
for i,val in enumerate(sides[key][0]):
if i != Ai and maxB < val:
maxB = val
Bi = i
newr2 = min(maxB+maxA, sides[key][2])
if newr2 > maxr:
maxr = newr2
maxi = [ sides[key][1][Ai], sides[key][1][Bi] ]
if len(maxi) == 1:
print(1)
print(maxi[0])
else:
print(2)
print(maxi[0], maxi[1])
``` | output | 1 | 100,802 | 23 | 201,605 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone. | instruction | 0 | 100,803 | 23 | 201,606 |
Tags: data structures, hashing
Correct Solution:
```
def add_side(side1, side2, side3, side_dict, num):
if (side1, side2) not in side_dict:
side_dict[(side1, side2)] = [(side3, num)]
else:
side_dict[(side1, side2)].append((side3, num))
if len(side_dict[(side1, side2)]) > 2:
side_dict[(side1, side2)] = sorted(side_dict[(side1, side2)])[1:3]
n = int(input())
ans_k = 1
k1 = -1
ans = 0
side_dict = dict()
cubes = list()
for i in range(n):
sides = sorted([int(x) for x in input().split()])
cubes.append(sides)
if sides[0] / 2 > ans:
k1 = i + 1
ans = sides[0] / 2
add_side(sides[0], sides[1], sides[2], side_dict, i)
if sides[0] == sides[1] and sides[1] == sides[2]:
pass
else:
if sides[0] == sides[1]:
add_side(sides[0], sides[2], sides[1], side_dict, i)
elif sides[1] == sides[2]:
add_side(sides[1], sides[2], sides[0], side_dict, i)
else:
add_side(sides[0], sides[2], sides[1], side_dict, i)
add_side(sides[1], sides[2], sides[0], side_dict, i)
for pair in side_dict:
if len(side_dict[pair]) > 1:
sides = sorted([pair[0], pair[1], side_dict[pair][0][0] + side_dict[pair][1][0]])
if sides[0] / 2 > ans:
ans = sides[0] / 2
ans_k = 2
k1 = side_dict[pair][0][1] + 1
k2 = side_dict[pair][1][1] + 1
print(ans_k)
if ans_k == 1:
print(k1)
else:
print(k1, k2)
``` | output | 1 | 100,803 | 23 | 201,607 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone. | instruction | 0 | 100,804 | 23 | 201,608 |
Tags: data structures, hashing
Correct Solution:
```
def main():
d, m = {}, 0
for i in range(1, int(input()) + 1):
a, b, c = sorted(map(int, input().split()))
if (b, c) in d:
x, y, z, t = d[b, c]
if a > z:
d[b, c] = (a, i, x, y) if a > x else (x, y, a, i)
else:
d[b, c] = (a, i, 0, 0)
for (a, b), (x, y, z, t) in d.items():
if a > m < x + z:
m, res = x + z if a > x + z else a, (y, t)
print(("2\n%d %d" % res) if res[1] else ("1\n%d" % res[0]))
if __name__ == '__main__':
main()
``` | output | 1 | 100,804 | 23 | 201,609 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone. | instruction | 0 | 100,805 | 23 | 201,610 |
Tags: data structures, hashing
Correct Solution:
```
n = int(input())
ar = []
for i in range(n):
kek = list(map(int, input().split()))
kek.sort()
ar.append(kek + [i + 1])
ans = 0
kek = [0, 0]
for i in range(n):
if min(ar[i][0], ar[i][1], ar[i][2]) > ans:
ans = min(ar[i][0], ar[i][1], ar[i][2])
kek[0] = ar[i][3]
ar.sort(key=lambda x: [x[0], x[1], x[2]])
for i in range(1, n):
if ar[i][0] == ar[i - 1][0] and ar[i][1] == ar[i - 1][1]:
if min((ar[i][2] + ar[i - 1][2]), ar[i][0], ar[i][1]) > ans:
ans = min((ar[i][2] + ar[i - 1][2]), ar[i][0], ar[i][1])
kek = [ar[i][3], ar[i - 1][3]]
ar.sort(key=lambda x: [x[1], x[2], x[0]])
for i in range(1, n):
if ar[i][2] == ar[i - 1][2] and ar[i][1] == ar[i - 1][1]:
if min((ar[i][0] + ar[i - 1][0]), ar[i][2], ar[i][1]) > ans:
ans = min((ar[i][0] + ar[i - 1][0]), ar[i][2], ar[i][1])
kek = [ar[i][3], ar[i - 1][3]]
ar.sort(key=lambda x: [x[2], x[0], x[1]])
for i in range(1, n):
if ar[i][2] == ar[i - 1][2] and ar[i][0] == ar[i - 1][0]:
if min((ar[i][1] + ar[i - 1][1]), ar[i][0], ar[i][2]) > ans:
min((ar[i][1] + ar[i - 1][1]), ar[i][0], ar[i][2])
kek = [ar[i][3], ar[i - 1][3]]
ar.sort(key=lambda x:x[3])
if kek[1] == 0:
print(1)
print(kek[0])
else:
print(2)
print(*kek)
``` | output | 1 | 100,805 | 23 | 201,611 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone. | instruction | 0 | 100,806 | 23 | 201,612 |
Tags: data structures, hashing
Correct Solution:
```
import random
def get_size(N):
sizes = [23, 71, 151, 571, 1021, 1571, 5795, 11311, 15451, 50821, 96557, 160001, 262419]
size = 11
idx = 0
while size < 2*N:
size = sizes[idx]
idx += 1
return size
class Hash(object):
def __init__(self, size):
self.size = size
self.items = [[] for i in range(size)]
self.p1 = random.randint(1, size - 1)
self.p2 = random.randint(1, size - 1)
def count_index(self, b, c):
return (b*self.p1 + c*self.p2) % self.size
def get_pair(self, item):
a, b, c, num = item
idx = self.count_index(b, c)
arr = self.items[idx]
cur = None
for i, cur in enumerate(arr):
if cur[1] == b and cur[2] == c:
break
cur = None
if cur:
if cur[0] >= a:
return cur[-1], item[-1], cur[0] + a
else:
self.items[idx][i] = item
return item[-1], cur[-1], cur[0] + a
else:
self.items[idx].append(item)
return None
N = int(input())
R_max = 0
best_one = None
best_pair = None
if_one = True
size = get_size(N)
hash = Hash(size)
for i in range(N):
box = input().split()
box = sorted([int(side) for side in box]) + [i + 1]
if box[0] > R_max:
best_one = i + 1
R_max = box[0]
if_one = True
cur_pair = hash.get_pair(box)
if cur_pair:
R_paired = min(box[1:-1] + [cur_pair[-1]])
if R_paired > R_max:
R_max = R_paired
best_pair = cur_pair[:-1]
if_one = False
#file = open('output.txt', 'w')
if if_one:
#file.write(str(1) + '\n' + str(best_one) + '\n' + str(R_max))
print(1)
print(best_one)
else:
#file.write(str(2) + '\n' + str(best_pair[0]) + ' ' + str(best_pair[1]) + '\n' + str(R_max))
print(2)
print(str(best_pair[0]) + ' ' + str(best_pair[1]))
``` | output | 1 | 100,806 | 23 | 201,613 |
Provide tags and a correct Python 3 solution for this coding contest problem.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone. | instruction | 0 | 100,807 | 23 | 201,614 |
Tags: data structures, hashing
Correct Solution:
```
n = int(input())
sidesInfo = {}
lengthsToIndex = {}
for i in range(n):
sides = [int(side) for side in input().split()]
sides.sort()
if sides[2] not in sidesInfo:
sidesInfo[sides[2]] = {}
if sides[1] not in sidesInfo[sides[2]]:
sidesInfo[sides[2]][sides[1]] = []
#record stone info;
sidesInfo[sides[2]][sides[1]].append(sides[0])
if f"{sides[0]}_{sides[1]}_{sides[2]}" not in lengthsToIndex:
lengthsToIndex[f"{sides[0]}_{sides[1]}_{sides[2]}"] = []
lengthsToIndex[f"{sides[0]}_{sides[1]}_{sides[2]}"].append(i + 1)
max_amount = 1
max_combination = ""
max_radius = 0
for sideLen in sidesInfo:
for sideWid in sidesInfo[sideLen]:
heightChosen = []
if len(sidesInfo[sideLen][sideWid]) >= 2:
sidesInfo[sideLen][sideWid].sort()
heightChosen.append(sidesInfo[sideLen][sideWid][-2])
heightChosen.append(sidesInfo[sideLen][sideWid][-1])
else:
heightChosen.append(sidesInfo[sideLen][sideWid][0])
radiusMax = min(sideLen, sideWid, sum(heightChosen))
if radiusMax > max_radius:
max_radius = radiusMax
max_amount = len(heightChosen)
if max_amount == 2:
pair = []
pair.append(lengthsToIndex[f"{heightChosen[0]}_{sideWid}_{sideLen}"][0])
if heightChosen[0] == heightChosen[1]:
pair.append(lengthsToIndex[f"{heightChosen[1]}_{sideWid}_{sideLen}"][1])
else:
pair.append(lengthsToIndex[f"{heightChosen[1]}_{sideWid}_{sideLen}"][0])
pair.sort()
max_combination = ' '.join(str(i) for i in pair)
else:
max_combination = lengthsToIndex[f"{heightChosen[0]}_{sideWid}_{sideLen}"][0]
print(max_amount)
print(max_combination)
``` | output | 1 | 100,807 | 23 | 201,615 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone.
Submitted Solution:
```
import math,sys,bisect,heapq
from collections import defaultdict,Counter,deque
from itertools import groupby,accumulate
#sys.setrecursionlimit(200000000)
input = iter(sys.stdin.buffer.read().decode().splitlines()).__next__
ilele = lambda: map(int,input().split())
alele = lambda: list(map(int, input().split()))
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
#MOD = 1000000000 + 7
def Y(c): print(["NO","YES"][c])
def y(c): print(["no","yes"][c])
def Yy(c): print(["No","Yes"][c])
N = int(input())
G= defaultdict(list)
for i in range(N):
a,b,c = ilele()
C = sorted([a,b,c])
a,b,c = C
l = i+1
if a==b == c:
G[(a,b)].append((c,l))
elif a==b:
G[(a,b)].append((c,l))
G[(b,c)].append((a,l))
elif b == c:
G[(b,c)].append((a,l))
G[(a,b)].append((c,l))
else:
G[(a,b)].append((c,l))
G[(b,c)].append((a,l))
G[(a,c)].append((b,l))
#print(G)
maxi= 0
choose1 = None;choose2 = None
for i,j in G.items():
if len(j) == 1:
m = min(i[0],i[1],j[0][0])
if m> maxi:
maxi = m
choose1 = j[0][1]
choose2 = None
else:
r = heapq.nlargest(2,j)
m = min(r[0][0] + r[1][0],i[0],i[1])
if m>maxi:
maxi = m
choose1 = r[0][1]
choose2 = r[1][1]
if choose2 == None:
print(1)
print(choose1)
else:
print(2)
print(choose1,choose2)
``` | instruction | 0 | 100,808 | 23 | 201,616 |
Yes | output | 1 | 100,808 | 23 | 201,617 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone.
Submitted Solution:
```
from collections import defaultdict
n = int(input())
ab, bc, ca = defaultdict(list), defaultdict(list), defaultdict(list)
single, double = 0, 0
sidx, didx = None, None
for i in range(1, n + 1):
a, b, c = sorted(map(int, input().split()))
ab[(a, b)].append((c, i))
bc[(b, c)].append((a, i))
ca[(c, a)].append((b, i))
m = min(a, b, c)
if m > single:
single = m
sidx = i
for d in [ab, bc, ca]:
for (p, q), v in d.items():
if len(v) <= 1:
continue
*_, (x, xi), (y, yi) = sorted(v)
m = min(p, q, x + y)
if m > double:
double = m
didx = (xi, yi)
if single >= double:
print("1\n%d" % sidx)
else:
print("2\n%d %d" % didx)
``` | instruction | 0 | 100,809 | 23 | 201,618 |
Yes | output | 1 | 100,809 | 23 | 201,619 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone.
Submitted Solution:
```
n = int(input())
a = []
ans,u,v = 0,-1,-1
for i in range(n):
t = [int(x) for x in input().split()]
t.sort()
if ans < t[0]:
ans = t[0]
u = v = i
t.append(i)
a.append(t)
from operator import itemgetter
a.sort(key=itemgetter(1,2,0),reverse=True)
i = 0
while i+1 < n:
if a[i][1:3]==a[i+1][1:3]:
t = min(a[i][0]+a[i+1][0],a[i][1])
if ans < t:
ans = t
u = a[i][3]
v = a[i+1][3]
i += 1
while (i==0 or a[i][1:3]==a[i-1][1:3]) and i+1<len(a):
i += 1
if u == v:
print(1)
print(u+1)
else:
print(2)
print(u+1,v+1)
``` | instruction | 0 | 100,810 | 23 | 201,620 |
Yes | output | 1 | 100,810 | 23 | 201,621 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone.
Submitted Solution:
```
def define_nearest_primes(n):
primes = [11, 17, 19, 23, 29, 53, 97, 193, 389, 769, 1543, 3079, 6151, 12289, 24593, 49157, 98317, 1572869]
for i in range(0, len(primes)):
if primes[i] > 1.5 * n:
return primes[i]
return primes[-1]
def hash_func(box, i, hash_table, biggest_merged_rectangular, p):
index = (50033 * box[2] + box[1]) % p
while len(hash_table[index]) > 0 and (box[1] != hash_table[index][0][2] or box[2] != hash_table[index][0][3]):
index = (index + 1) % p
# print(index)
if len(hash_table[index]) == 2:
if box[0] > hash_table[index][0][1]:
if hash_table[index][0][1] < hash_table[index][1][1]:
hash_table[index][0] = [i, box[0], box[1], box[2]]
else:
hash_table[index][1] = [i, box[0], box[1], box[2]]
elif box[0] > hash_table[index][1][1]:
hash_table[index][1] = [i, box[0], box[1], box[2]]
temp_box = [hash_table[index][0][2], hash_table[index][0][3], hash_table[index][0][1] + hash_table[index][1][1]]
temp_box = sorted(temp_box)
if biggest_merged_rectangular[2] < temp_box[0]:
biggest_merged_rectangular = [hash_table[index][0][0], hash_table[index][1][0], temp_box[0]]
else:
if len(hash_table[index]) == 1:
hash_table[index].append([i, box[0], box[1], box[2]])
temp_box = [hash_table[index][0][2], hash_table[index][0][3],
hash_table[index][0][1] + hash_table[index][1][1]]
temp_box = sorted(temp_box)
if biggest_merged_rectangular[2] < temp_box[0]:
biggest_merged_rectangular = [hash_table[index][0][0], hash_table[index][1][0], temp_box[0]]
else:
if biggest_merged_rectangular[2] < box[0]:
biggest_merged_rectangular = [i, None, box[0]]
hash_table[index].append([i, box[0], box[1], box[2]])
return hash_table, biggest_merged_rectangular
if __name__ == "__main__":
n = int(input()) # the number of boxes
p = define_nearest_primes(n)
hash_table = [[] for _ in range(0, p)]
biggest_merged_rectangular = [0, 0, 0] # [index1,index2,radius]
for i in range(1, n + 1):
box = list(map(int, input().split()))
box = sorted(box)
# print(box)
hashing = hash_func(box, i, hash_table, biggest_merged_rectangular, p) # online hashing process
hash_table, biggest_merged_rectangular = hashing
if biggest_merged_rectangular[1] is None:
print('1\n{}'.format(biggest_merged_rectangular[0]))
else:
inds = sorted(biggest_merged_rectangular[:2])
print('2\n{} {}'.format(inds[0], inds[1]))
``` | instruction | 0 | 100,811 | 23 | 201,622 |
Yes | output | 1 | 100,811 | 23 | 201,623 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone.
Submitted Solution:
```
hash_table = {}
n = int(input())
max_diam = 0
ordinal_numbers = [0]
for i in range(1, n+1):
seq = sorted(list(map(int, input().split())),
reverse=True) + [i]
face = (seq[0], seq[1])
try:
best = hash_table[face]
except:
best = None
if best is not None:
new_z = seq[2] + best[2]
diam = min(seq[:2] + [new_z])
if diam > max_diam:
ordinal_numbers = [best[3], i]
max_diam = diam
if best[2] < seq[2]:
hash_table[face] = seq
else:
if seq[2] > max_diam:
ordinal_numbers = [i]
max_diam = seq[2]
hash_table[face] = seq
print(len(ordinal_numbers))
print(" ".join(map(str, ordinal_numbers)), end='')
``` | instruction | 0 | 100,812 | 23 | 201,624 |
No | output | 1 | 100,812 | 23 | 201,625 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone.
Submitted Solution:
```
# I took these from https://planetmath.org/goodhashtableprimes, these numbers
# should reduce the number of collisions
PRIMES = [23, 53, 97, 193, 389, 769, 1543, 3079, 6151, 12289, 24593, 49157, 98317, 196613, 393241, 786433,
1572869, 3145739, 6291469, 12582917, 25165843, 50331653, 100663319, 201326611, 402653189, 805306457,
1610612741]
class HashTable:
"""
This hash table will only work with integer pairs as keys. It will possibly be several times slower
than the default Python implementation, since I will make no effort to replace lists by arrays,
avoid long arithmetic in the hashing function, or otherwise optimize the performance. Conceptually
though, this class is a real hash table without using any embedded associative arrays.
To deal with collisions, I used chaining and prime table sizes. I expand the table when load factor
is >0.75 and contract it when it is <0.25.
"""
def __init__(self, m=PRIMES[0]):
self.size = 0
self.prime_index = 0
self.buckets = [[] for _ in range(m)]
self.m = m
def __getitem__(self, item):
item_hash = self._hash(item)
for key, value in self.buckets[item_hash]:
if key[0] == item[0] and key[1] == item[1]:
return value
raise KeyError
def __setitem__(self, item, _value):
item_hash = self._hash(item)
for i, (key, value) in enumerate(self.buckets[item_hash]):
if key[0] == item[0] and key[1] == item[1]:
self.buckets[item_hash][i][1] = _value
return
self.buckets[item_hash].append([item, _value])
self.size += 1
if self._load_factor() > 0.75:
self._rehash(up=True)
def __delitem__(self, item):
item_hash = self._hash(item)
for i, (key, value) in enumerate(self.buckets[item_hash]):
if key[0] == item[0] and key[1] == item[1]:
self.buckets[item_hash].pop(i)
self.size -= 1
if self._load_factor() < 0.25 and self.m >= PRIMES[1]:
self._rehash(up=False)
break
def __contains__(self, item):
item_hash = self._hash(item)
for i, (key, value) in enumerate(self.buckets[item_hash]):
if key[0] == item[0] and key[1] == item[1]:
return True
return False
def __len__(self):
return self.size
def _load_factor(self):
return self.size / self.m
def _hash(self, key):
# trivial but working
return (3 * key[0] + key[1]) % self.m
def _rehash(self, up=True):
old_buckets = self.buckets
if up: # expansion to the next "good prime" size
if self.prime_index < len(PRIMES) - 1:
self.m = PRIMES[self.prime_index + 1]
self.prime_index += 1
else:
self.m = 2 * self.m + 1
else: # contraction to the previous "good prime" size
if (self.m // 2 + 1 < PRIMES[-1]) and self.m > PRIMES[-1]:
self.m = PRIMES[-1]
self.prime_index = len(PRIMES) - 1
elif self.prime_index > 0:
self.m = PRIMES[self.prime_index - 1]
self.prime_index -= 1
self.buckets = [[] for _ in range(self.m)]
self.size = 0
for bucket in old_buckets:
for key, value in bucket:
self[key] = value
if __name__ == '__main__':
boxes = dict()
box_count = int(input())
max_ball_diameter = 0
max_ball_indices = [0, -1]
for i in range(box_count):
c, b, a = sorted(map(int, input().split()))
if (a, b) in boxes:
edges, indices = boxes[(a, b)]
if c > edges[0]:
edges = [c, edges[0]]
indices = [i, indices[0]]
elif c > edges[1]:
edges = [edges[0], c]
indices = [indices[0], i]
diameter_candidate = min(a, b, edges[0] + edges[1])
if diameter_candidate > max_ball_diameter:
max_ball_indices = indices
max_ball_diameter = diameter_candidate
else:
boxes[(a, b)] = ([c, 0], [i, -1])
if c > max_ball_diameter:
max_ball_diameter = c
max_ball_indices = [i, -1]
max_ball_indices = sorted(max_ball_indices)
if max_ball_indices[0] == -1:
print('1\n' + '{}\n'.format(max_ball_indices[1] + 1))
else:
print('2\n' + '{} {}\n'.format(max_ball_indices[0] + 1, max_ball_indices[1] + 1))
``` | instruction | 0 | 100,813 | 23 | 201,626 |
No | output | 1 | 100,813 | 23 | 201,627 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone.
Submitted Solution:
```
import random
def get_size(N):
sizes = [23, 71, 151, 571, 1021, 1571, 5795, 11311, 15451, 50821, 96557, 160001, 262419]
size = 11
idx = 0
while size < 2*N:
size = sizes[idx]
idx += 1
return size
class Hash(object):
def __init__(self, size):
self.size = size
self.items = [[] for i in range(size)]
self.p1 = random.randint(1, size - 1)
self.p2 = random.randint(1, size - 1)
def count_index(self, b, c):
return (b*self.p1 + c*self.p2)//self.size
def get_pair(self, item):
a, b, c, num = item
idx = self.count_index(b, c)
arr = self.items[idx]
print(item, ':', idx, arr)
cur = None
for i, cur in enumerate(arr):
if cur[1] == b and cur[2] == c:
break
cur = None
if cur:
print('cur', cur, cur[0] + a)
if cur[0] >= a:
return cur[-1], item[-1], cur[0] + a
else:
self.items[idx][i] = item
return item[-1], cur[-1], cur[0] + a
else:
self.items[idx].append(item)
return None
N = int(input())
R_max = 0
best_one = None
best_pair = None
if_one = True
size = get_size(N)
hash = Hash(size)
for i in range(N):
box = input().split()
box = sorted([int(side) for side in box]) + [i + 1]
if box[0] > R_max:
best_one = i + 1
R_max = box[0]
if_one = True
cur_pair = hash.get_pair(box)
if cur_pair:
box[0] = cur_pair[-1]
R_paired = min(box[:-1])
if R_paired > R_max:
R_max = R_paired
best_pair = cur_pair[:-1]
if_one = False
#file = open('output.txt', 'w')
if if_one:
#file.write(str(1) + '\n' + str(best_one) + '\n' + str(R_max))
print(1)
print(best_one)
else:
#file.write(str(2) + '\n' + str(best_pair[0]) + ' ' + str(best_pair[1]) + '\n' + str(R_max))
print(2)
print(str(best_pair[0]) + ' ' + str(best_pair[1]))
``` | instruction | 0 | 100,814 | 23 | 201,628 |
No | output | 1 | 100,814 | 23 | 201,629 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
Kostya is a genial sculptor, he has an idea: to carve a marble sculpture in the shape of a sphere. Kostya has a friend Zahar who works at a career. Zahar knows about Kostya's idea and wants to present him a rectangular parallelepiped of marble from which he can carve the sphere.
Zahar has n stones which are rectangular parallelepipeds. The edges sizes of the i-th of them are ai, bi and ci. He can take no more than two stones and present them to Kostya.
If Zahar takes two stones, he should glue them together on one of the faces in order to get a new piece of rectangular parallelepiped of marble. Thus, it is possible to glue a pair of stones together if and only if two faces on which they are glued together match as rectangles. In such gluing it is allowed to rotate and flip the stones in any way.
Help Zahar choose such a present so that Kostya can carve a sphere of the maximum possible volume and present it to Zahar.
Input
The first line contains the integer n (1 ≤ n ≤ 105).
n lines follow, in the i-th of which there are three integers ai, bi and ci (1 ≤ ai, bi, ci ≤ 109) — the lengths of edges of the i-th stone. Note, that two stones may have exactly the same sizes, but they still will be considered two different stones.
Output
In the first line print k (1 ≤ k ≤ 2) the number of stones which Zahar has chosen. In the second line print k distinct integers from 1 to n — the numbers of stones which Zahar needs to choose. Consider that stones are numbered from 1 to n in the order as they are given in the input data.
You can print the stones in arbitrary order. If there are several answers print any of them.
Examples
Input
6
5 5 5
3 2 4
1 4 1
2 1 3
3 2 4
3 3 4
Output
1
1
Input
7
10 7 8
5 10 3
4 2 6
5 5 5
10 2 8
4 2 1
7 7 7
Output
2
1 5
Note
In the first example we can connect the pairs of stones:
* 2 and 4, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 2 and 5, the size of the parallelepiped: 3 × 2 × 8 or 6 × 2 × 4 or 3 × 4 × 4, the radius of the inscribed sphere 1, or 1, or 1.5 respectively.
* 2 and 6, the size of the parallelepiped: 3 × 5 × 4, the radius of the inscribed sphere 1.5
* 4 and 5, the size of the parallelepiped: 3 × 2 × 5, the radius of the inscribed sphere 1
* 5 and 6, the size of the parallelepiped: 3 × 4 × 5, the radius of the inscribed sphere 1.5
Or take only one stone:
* 1 the size of the parallelepiped: 5 × 5 × 5, the radius of the inscribed sphere 2.5
* 2 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 3 the size of the parallelepiped: 1 × 4 × 1, the radius of the inscribed sphere 0.5
* 4 the size of the parallelepiped: 2 × 1 × 3, the radius of the inscribed sphere 0.5
* 5 the size of the parallelepiped: 3 × 2 × 4, the radius of the inscribed sphere 1
* 6 the size of the parallelepiped: 3 × 3 × 4, the radius of the inscribed sphere 1.5
It is most profitable to take only the first stone.
Submitted Solution:
```
n = int(input())
a = []
ans,u,v = 0,-1,-1
for i in range(n):
t = [int(x) for x in input().split()]
t.sort()
if ans < t[0]:
ans = t[0]
u = v = i
t.append(i)
a.append(t)
b = []
for x in a:
if x[1] >= ans:
b.append(x)
for x in b:
for y in b:
if x[3] != y[3]:
if x[1:2] == y[1:2]:
t = max(x[0]+y[0],x[1])
if ans < t:
ans = t
u = x[3]
v = y[3]
if u == v:
print(1)
print(u+1)
else:
print(2)
print(u+1,v+1)
``` | instruction | 0 | 100,815 | 23 | 201,630 |
No | output | 1 | 100,815 | 23 | 201,631 |
Provide a correct Python 3 solution for this coding contest problem.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes | instruction | 0 | 101,106 | 23 | 202,212 |
"Correct Solution:
```
a = sorted(map(int,input().split()))
print("yes" if a[0] == a[3] and a[4] == a[7] and a[8] == a[11] else "no")
``` | output | 1 | 101,106 | 23 | 202,213 |
Provide a correct Python 3 solution for this coding contest problem.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes | instruction | 0 | 101,107 | 23 | 202,214 |
"Correct Solution:
```
#標準入力
l = list(map(int,input().split()))
#リストを小さい順に並べる
l.sort()
#4辺を1人組とし、1組の辺が全て同じであれば"yes"でなければ"no"を出力する
if l[0] == l[1] == l[2] == l[3] and l[4] == l[5] == l[6] == l[7] and l[8] == l[9] == l[10] == l[11]:print("yes")
else:print("no")
``` | output | 1 | 101,107 | 23 | 202,215 |
Provide a correct Python 3 solution for this coding contest problem.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes | instruction | 0 | 101,108 | 23 | 202,216 |
"Correct Solution:
```
data = list(map(int, input().split()))
data.sort()
ans = "yes"
for i in range(0, 12, 4) :
if data[i] != data[i+1] or data[i] != data[i+2] or data[i] != data[i+3] :
ans = "no"
print(ans)
``` | output | 1 | 101,108 | 23 | 202,217 |
Provide a correct Python 3 solution for this coding contest problem.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes | instruction | 0 | 101,109 | 23 | 202,218 |
"Correct Solution:
```
lst = sorted(map(int, input().split()))
if lst[0] == lst[3] and lst[4] == lst[7] and lst[8] == lst[11]:
print("yes")
else:
print("no")
``` | output | 1 | 101,109 | 23 | 202,219 |
Provide a correct Python 3 solution for this coding contest problem.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes | instruction | 0 | 101,110 | 23 | 202,220 |
"Correct Solution:
```
e= sorted(list(map(int, input().split())))
print("yes" if len(set(e[:4]))==len(set(e[4:8]))==len(set(e[8:]))==1 else "no")
``` | output | 1 | 101,110 | 23 | 202,221 |
Provide a correct Python 3 solution for this coding contest problem.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes | instruction | 0 | 101,111 | 23 | 202,222 |
"Correct Solution:
```
a = [int(i) for i in input().split()]
a.sort()
if a[0] == a[1] and a[1] == a[2] and a[2] == a[3] and a[4] == a[5] and a[5] == a[6] and a[6] == a[7] and a[8] == a[9] and a[9] == a[10] and a[10] == a[11]:
print("yes")
else:
print("no")
``` | output | 1 | 101,111 | 23 | 202,223 |
Provide a correct Python 3 solution for this coding contest problem.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes | instruction | 0 | 101,112 | 23 | 202,224 |
"Correct Solution:
```
e = sorted(map(int, input().split()))
print("yes" if len(set(e[:4])) == len(set(e[4:8])) == len(set(e[8:])) == 1 else "no")
``` | output | 1 | 101,112 | 23 | 202,225 |
Provide a correct Python 3 solution for this coding contest problem.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes | instruction | 0 | 101,113 | 23 | 202,226 |
"Correct Solution:
```
e = sorted(map(int, input().split()))
print("yes" if e[0] == e[3] and e[4] == e[7] and e[8] == e[11] else "no")
``` | output | 1 | 101,113 | 23 | 202,227 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes
Submitted Solution:
```
e = list(map(int, input().split()))
e.sort()
frag = True
for i in range(1, 4):
if e[0] != e[i]:
frag = False
break
for i in range(5, 8):
if e[4] != e[i]:
frag = False
break
for i in range(9, 12):
if e[8] != e[i]:
frag = False
break
print("yes" if frag else "no")
``` | instruction | 0 | 101,114 | 23 | 202,228 |
Yes | output | 1 | 101,114 | 23 | 202,229 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes
Submitted Solution:
```
ls = list(map(int, input().split()))
ls.sort()
if ls[0]==ls[1]==ls[2]==ls[3] and ls[4]==ls[5]==ls[6]==ls[7] and ls[8]==ls[9]==ls[10]==ls[11]:
print('yes')
else:
print('no')
``` | instruction | 0 | 101,115 | 23 | 202,230 |
Yes | output | 1 | 101,115 | 23 | 202,231 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes
Submitted Solution:
```
l=list(input().split())
l.sort()
if l[0]==l[1]==l[2]==l[3] and l[4]==l[5]==l[6]==l[7]and l[8]==l[9]==l[10]==l[11]:
print('yes')
else:
print('no')
``` | instruction | 0 | 101,116 | 23 | 202,232 |
Yes | output | 1 | 101,116 | 23 | 202,233 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes
Submitted Solution:
```
x = input().split()
print('yes' if all([x.count(x[i]) % 4 == 0 for i in range(len(x))]) else 'no')
``` | instruction | 0 | 101,117 | 23 | 202,234 |
Yes | output | 1 | 101,117 | 23 | 202,235 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes
Submitted Solution:
```
ls = list(map(int, input().split()))
ls.sort()
if ls[0]==ls[1]==ls[2]==ls[3] and ls[4==ls[5]==ls[6]==ls[7] and ls[8]==ls[9]==ls[10]==ls[11]:
print('yes')
else:
print('no')
``` | instruction | 0 | 101,118 | 23 | 202,236 |
No | output | 1 | 101,118 | 23 | 202,237 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes
Submitted Solution:
```
li = list(map(int,input().split()))
so = sorted(li)
a = so[0]
b = so[4]
c = so[8]
res = False
for n in so[:4]:
res = a==n
for n in so[4:8]:
res = b==n
for n in so[8:]:
res = c==n
print(res)
``` | instruction | 0 | 101,119 | 23 | 202,238 |
No | output | 1 | 101,119 | 23 | 202,239 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes
Submitted Solution:
```
e = list(map(int, input().split()))
print("yes" if len(set(e[:4])) == len(set(e[4:8])) == len(set(e[8:])) == 1 else "no")
``` | instruction | 0 | 101,120 | 23 | 202,240 |
No | output | 1 | 101,120 | 23 | 202,241 |
Evaluate the correctness of the submitted Python 3 solution to the coding contest problem. Provide a "Yes" or "No" response.
The educational program (AHK Education) of the Aiz Broadcasting Association broadcasts a handicraft program for children, "Play with Tsukuro". This time I will make a box with sticks, but I would like to see if I can make a rectangular parallelepiped using the 12 sticks I prepared. However, the stick must not be cut or broken.
Given the lengths of the twelve bars, write a program to determine if you can create a rectangular parallelepiped with all of them as sides.
Input
The input is given in the following format.
e1 e2 ... e12
The input consists of one line and is given the integer ei (1 ≤ ei ≤ 100) representing the length of each bar.
Output
If a rectangular parallelepiped can be created, "yes" is output, and if it cannot be created, "no" is output. However, since a cube is a kind of rectangular parallelepiped, "yes" is output even if it is a cube.
Examples
Input
1 1 3 4 8 9 7 3 4 5 5 5
Output
no
Input
1 1 2 2 3 1 2 3 3 3 1 2
Output
yes
Submitted Solution:
```
li = list(map(int,input().split()))
so = sorted(li)
a = so[0]
b = so[4]
c = so[8]
res = False
for n in so[:4]:
res = res and a==n
for n in so[4:8]:
res = res and b==n
for n in so[8:]:
res = res and c==n
print(res)
``` | instruction | 0 | 101,121 | 23 | 202,242 |
No | output | 1 | 101,121 | 23 | 202,243 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a rectangle grid. That grid's size is n × m. Let's denote the coordinate system on the grid. So, each point on the grid will have coordinates — a pair of integers (x, y) (0 ≤ x ≤ n, 0 ≤ y ≤ m).
Your task is to find a maximum sub-rectangle on the grid (x1, y1, x2, y2) so that it contains the given point (x, y), and its length-width ratio is exactly (a, b). In other words the following conditions must hold: 0 ≤ x1 ≤ x ≤ x2 ≤ n, 0 ≤ y1 ≤ y ≤ y2 ≤ m, <image>.
The sides of this sub-rectangle should be parallel to the axes. And values x1, y1, x2, y2 should be integers.
<image>
If there are multiple solutions, find the rectangle which is closest to (x, y). Here "closest" means the Euclid distance between (x, y) and the center of the rectangle is as small as possible. If there are still multiple solutions, find the lexicographically minimum one. Here "lexicographically minimum" means that we should consider the sub-rectangle as sequence of integers (x1, y1, x2, y2), so we can choose the lexicographically minimum one.
Input
The first line contains six integers n, m, x, y, a, b (1 ≤ n, m ≤ 109, 0 ≤ x ≤ n, 0 ≤ y ≤ m, 1 ≤ a ≤ n, 1 ≤ b ≤ m).
Output
Print four integers x1, y1, x2, y2, which represent the founded sub-rectangle whose left-bottom point is (x1, y1) and right-up point is (x2, y2).
Examples
Input
9 9 5 5 2 1
Output
1 3 9 7
Input
100 100 52 50 46 56
Output
17 8 86 92 | instruction | 0 | 101,485 | 23 | 202,970 |
Tags: implementation, math
Correct Solution:
```
import sys
from fractions import gcd
with sys.stdin as fin, sys.stdout as fout:
n, m, x, y, a, b = map(int, next(fin).split())
d = gcd(a, b)
a //= d
b //= d
k = min(n // a, m // b)
w = k * a
h = k * b
x1 = x - (w + 1) // 2
y1 = y - (h + 1) // 2
x1 = min(x1, n - w)
y1 = min(y1, m - h)
x1 = max(x1, 0)
y1 = max(y1, 0)
print(x1, y1, x1 + w, y1 + h, file=fout)
``` | output | 1 | 101,485 | 23 | 202,971 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a rectangle grid. That grid's size is n × m. Let's denote the coordinate system on the grid. So, each point on the grid will have coordinates — a pair of integers (x, y) (0 ≤ x ≤ n, 0 ≤ y ≤ m).
Your task is to find a maximum sub-rectangle on the grid (x1, y1, x2, y2) so that it contains the given point (x, y), and its length-width ratio is exactly (a, b). In other words the following conditions must hold: 0 ≤ x1 ≤ x ≤ x2 ≤ n, 0 ≤ y1 ≤ y ≤ y2 ≤ m, <image>.
The sides of this sub-rectangle should be parallel to the axes. And values x1, y1, x2, y2 should be integers.
<image>
If there are multiple solutions, find the rectangle which is closest to (x, y). Here "closest" means the Euclid distance between (x, y) and the center of the rectangle is as small as possible. If there are still multiple solutions, find the lexicographically minimum one. Here "lexicographically minimum" means that we should consider the sub-rectangle as sequence of integers (x1, y1, x2, y2), so we can choose the lexicographically minimum one.
Input
The first line contains six integers n, m, x, y, a, b (1 ≤ n, m ≤ 109, 0 ≤ x ≤ n, 0 ≤ y ≤ m, 1 ≤ a ≤ n, 1 ≤ b ≤ m).
Output
Print four integers x1, y1, x2, y2, which represent the founded sub-rectangle whose left-bottom point is (x1, y1) and right-up point is (x2, y2).
Examples
Input
9 9 5 5 2 1
Output
1 3 9 7
Input
100 100 52 50 46 56
Output
17 8 86 92 | instruction | 0 | 101,486 | 23 | 202,972 |
Tags: implementation, math
Correct Solution:
```
#!/usr/bin/python3
def gcd(a, b):
while a:
a, b = b % a, a
return b
n, m, x, y, a, b = tuple(map(int, input().strip().split()))
g = gcd(a, b)
a //= g
b //= g
k = min(n // a, m // b)
w = k * a
h = k * b
ans = [x - w + w // 2, y - h + h // 2, x + w // 2, y + h // 2]
if ans[0] < 0:
ans[2] -= ans[0]
ans[0] = 0;
if ans[1] < 0:
ans[3] -= ans[1]
ans[1] = 0
if ans[2] > n:
ans[0] -= ans[2] - n
ans[2] = n
if ans[3] > m:
ans[1] -= ans[3] - m
ans[3] = m
print('%d %d %d %d' % tuple(ans))
``` | output | 1 | 101,486 | 23 | 202,973 |
Provide tags and a correct Python 3 solution for this coding contest problem.
You are given a rectangle grid. That grid's size is n × m. Let's denote the coordinate system on the grid. So, each point on the grid will have coordinates — a pair of integers (x, y) (0 ≤ x ≤ n, 0 ≤ y ≤ m).
Your task is to find a maximum sub-rectangle on the grid (x1, y1, x2, y2) so that it contains the given point (x, y), and its length-width ratio is exactly (a, b). In other words the following conditions must hold: 0 ≤ x1 ≤ x ≤ x2 ≤ n, 0 ≤ y1 ≤ y ≤ y2 ≤ m, <image>.
The sides of this sub-rectangle should be parallel to the axes. And values x1, y1, x2, y2 should be integers.
<image>
If there are multiple solutions, find the rectangle which is closest to (x, y). Here "closest" means the Euclid distance between (x, y) and the center of the rectangle is as small as possible. If there are still multiple solutions, find the lexicographically minimum one. Here "lexicographically minimum" means that we should consider the sub-rectangle as sequence of integers (x1, y1, x2, y2), so we can choose the lexicographically minimum one.
Input
The first line contains six integers n, m, x, y, a, b (1 ≤ n, m ≤ 109, 0 ≤ x ≤ n, 0 ≤ y ≤ m, 1 ≤ a ≤ n, 1 ≤ b ≤ m).
Output
Print four integers x1, y1, x2, y2, which represent the founded sub-rectangle whose left-bottom point is (x1, y1) and right-up point is (x2, y2).
Examples
Input
9 9 5 5 2 1
Output
1 3 9 7
Input
100 100 52 50 46 56
Output
17 8 86 92 | instruction | 0 | 101,487 | 23 | 202,974 |
Tags: implementation, math
Correct Solution:
```
import math
n, m, x, y, a, b = map(int, input().split())
gcd = math.gcd(a, b)
a //= gcd
b //= gcd
max_ratio = min(n // a, m // b)
a *= max_ratio
b *= max_ratio
x1 = max(0, min(x - (a + 1) // 2, n - a))
y1 = max(0, min(y - (b + 1) // 2, m - b))
print(x1, y1, x1 + a, y1 + b)
``` | output | 1 | 101,487 | 23 | 202,975 |
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