Chef recently learned about ratios and proportions. He wrote some positive integers a, b, c, d on a paper. Chef wants to know whether he can shuffle these numbers so as to make some proportion? Formally, four numbers x, y, z, w are said to make a proportion if ratio of x : y is same as that of z : w.

-----Input-----
Only line of the input contains four space separated positive integers - a, b, c, d.

-----Output-----
Print "Possible" if it is possible to shuffle a, b, c, d to make proportion, otherwise "Impossible" (without quotes).

-----Constraints-----
- 1 ≤ a, b, c, d  ≤ 1000

-----Example-----
Input:
1 2 4 2

Output:
Possible

-----Explanation-----
By swapping 4 and the second 2, we get 1 2 2 4. Note that 1 2 2 4 make proportion as 1 : 2 = 2 : 4. Hence answer is "Possible"

Difficulty: UNKNOWN_DIFFICULTY

Starter code:

Solutions:
def permutate(arr):
	if len(arr) == 1:
		yield arr
	for x in range(len(arr)):
		for perm in permutate(arr[:x] + arr[x + 1:]):
			yield ([arr[x]] + perm)
vals = [int(x) for x in input().split()]
founded = False
for val in permutate(vals):
	if val[0] / float(val[1]) == val[2] / float(val[3]):
		print('Possible')
		founded = True
		break
if not founded:
	print('Impossible')


a = input().split()
a = [int(x) for x in a]
a.sort()
if float(a[0]) / float(a[1]) == float(a[2]) / float(a[3]):
	print('Possible')
else:
	print('Impossible')


(a, b, c, d) = list(map(int, input().split()))
if a * b == c * d or a * c == b * d or a * d == b * c:
	print('Possible')
else:
	print('Impossible')


import sys
(a, b, c, d) = list(map(float, input().split()))
if a / b == c / d:
	print('Possible')
	return
if a / b == d / c:
	print('Possible')
	return
if a / c == b / d:
	print('Possible')
	return
if a / c == d / b:
	print('Possible')
	return
if a / d == c / b:
	print('Possible')
	return
if a / d == b / c:
	print('Possible')
	return
if a / b == c / d:
	print('Possible')
	return
if a / b == c / d:
	print('Possible')
	return
print('Impossible')


(a, b, c, d) = list(map(float, input().split()))
li = []
li.append(a)
li.append(b)
li.append(c)
li.append(d)
li = sorted(li)
if li[1] / li[0] == li[3] / li[2]:
	print('Possible')
else:
	print('Impossible')


a = list(map(float, input().split()))
a.sort()
if a[0] / a[1] == a[2] / a[3]:
	print('Possible')
else:
	print('Impossible')


(a, b, c, d) = list(map(int, input().split()))
ab = a * b
ac = a * c
ad = a * d
bc = b * c
bd = b * d
cd = c * d
if ab == cd or ac == bd or ad == bc:
	print('Possible')
else:
	print('Impossible')


def min(a, b):
	if a < b:
		return a
	return b

def max(a, b):
	if a < b:
		return b
	return a
[a, b, c, d] = [float(x) for x in input().split()]
flag = False
if min(a, b) / max(a, b) == min(c, d) / max(c, d):
	flag = True
if min(a, c) / max(a, c) == min(b, d) / max(b, d):
	flag = True
if min(a, d) / max(a, d) == min(b, c) / max(b, c):
	flag = True
if flag:
	print('Possible')
else:
	print('Impossible')


(a, b, c, d) = input().split(' ')
A = []
A.append(float(a))
A.append(float(b))
A.append(float(c))
A.append(float(d))
A.sort()
if A[0] / A[1] == A[2] / A[3]:
	print('Possible')
elif A[0] / A[2] == A[1] / A[3]:
	print('Possible')
elif A[0] / A[3] == A[1] / A[2]:
	print('Possible')
else:
	print('Impossible')


def __starting_point():
	(a, b, c, d) = sorted(map(int, input().split()))
	if d * a == b * c:
		print('Possible')
	else:
		print('Impossible')
__starting_point()


import sys

def check(a, b, c, d):
	return a == c and b == d or (a == d and b == c)
(a, b, c, d) = list(map(int, sys.stdin.readline().split()))
gcd = lambda x, y: x if y == 0 else gcd(y, x % y)
flag = False
(lg0, rg0) = (gcd(a, b), gcd(c, d))
if check(a / lg0, b / lg0, c / rg0, d / rg0):
	flag = True
(lg0, rg0) = (gcd(a, c), gcd(b, d))
if check(a / lg0, c / lg0, b / rg0, d / rg0):
	flag = True
(lg0, rg0) = (gcd(a, d), gcd(c, b))
if check(a / lg0, d / lg0, c / rg0, b / rg0):
	flag = True
print('Possible' if flag else 'Impossible')


from itertools import permutations
a = [int(num) for num in input().split()]
l = list(permutations(a))
flag = False
for e in l:
	e0 = float(e[0])
	e1 = float(e[1])
	e2 = float(e[2])
	e3 = float(e[3])
	if e0 / e1 == e2 / e3:
		print('Possible')
		flag = True
		break
if flag == False:
	print('Impossible')


(a, b, c, d) = list(map(float, input().strip().split()))
if a / b == c / d or a / b == d / c:
	print('Possible')
elif a / c == b / d or a / c == d / b:
	print('Possible')
elif a / d == c / b or a / d == b / c:
	print('Possible')
else:
	print('Impossible')


a = list(map(int, input().split()))
out = 'Impossible'
for i in range(4):
	if out == 'Possible':
		break
	for j in range(1, 4):
		(a[i], a[j]) = (a[j], a[i])
		if a[0] / a[1] == a[2] / a[3]:
			out = 'Possible'
			break
		else:
			(a[i], a[j]) = (a[j], a[i])
print(out)


li = list(map(int, input().split()))
li = sorted(li)
(a, b, c, d) = li
if float(b / float(a)) == float(d / float(c)):
	print('Possible')
else:
	print('Impossible')


import itertools
(a, b, c, d) = list(map(float, input().split()))
li = list(itertools.permutations([a, b, c, d]))
flag = False
for i in li:
	if i[0] / i[1] == i[2] / i[3]:
		flag = True
		break
if flag == True:
	print('Possible')
else:
	print('Impossible')


abcd = input()
abcd = abcd.split()
abcd = list(map(int, abcd))
prod = 1
cnt = 0
for item in abcd:
	prod *= item
flo = prod ** 0.5
if int(flo) == flo:
	for i in range(3):
		for j in range(i + 1, 4):
			if abcd[i] * abcd[j] == flo:
				cnt = 1
				break
		if cnt == 1:
			break
	if cnt == 1:
		print('Possible')
	else:
		print('Impossible')
else:
	print('Impossible')