Chef, being a Chess fan, was thrilled after he read the following news:

[Michael Simkin, a postdoctoral fellow at Harvard University’s Center of Mathematical Sciences and Applications proved that for a large value of N, there are approximately (0.143 \cdot N)^N configurations in which N queens can be placed on a N \times N chessboard so that none attack each other.]

Although the formula is valid for large N, Chef is interested in finding the value of function f(N) = (0.143 \cdot N)^N for a given small value of N. Since Chef is busy understanding the [proof] of the formula, please help him calculate this value.

Print the answer rounded to the nearest integer. That is, if the actual value of f(N) is x,
Print \lfloor x\rfloor if x - \lfloor x\rfloor < 0.5
Otherwise, print \lfloor x\rfloor + 1

where \lfloor x\rfloor denotes the [floor] of x.

------ Input Format ------ 

- The first line of input contains a single integer T, denoting the number of test cases. The description of T test cases follows.
- Each test case consists of a single line of input containing one integer N.

------ Output Format ------ 

For each test case, output in a single line the value of f(N) rounded to the nearest integer.

------ Constraints ------ 

$1 ≤ T ≤ 12$
$4 ≤ N ≤ 15$

------ subtasks ------ 

Subtask #1 (100 points): Original constraints

----- Sample Input 1 ------ 
2
4
10
----- Sample Output 1 ------ 
0
36

----- explanation 1 ------ 
Test case $1$: $f(N) = (0.143 \cdot 4)^4 = 0.107$, which when rounded to nearest integer gives $0$.

Test case $2$: $f(N) = (0.143 \cdot 10)^{10} = 35.7569$, which when rounded to nearest integer gives $36$.

Difficulty: EASY
Tags: Mathematics

Implementation

Starter code:

Solutions:
import sys
for _ in range(int(sys.stdin.readline())):
	n = int(sys.stdin.readline())
	sys.stdout.write(str(round((0.143 * n) ** n)) + '\n')


import math
T = int(input())
for i in range(T):
	x = int(input())
	r = 0.143 * x
	ans = math.pow(r, x)
	print(round(ans))
	T = T - 1


t = int(input())
for i in range(t):
	a = int(input())
	print(round((0.143 * a) ** a))


for _ in range(int(input())):
	n = int(input())
	print(round((0.143 * n) ** n))


t = int(input())
for i in range(t):
	n = int(input())
	print(round((0.143 * n) ** n))


n = int(input())
for i in range(n):
	a = int(input())
	k = 0.143 * a
	print(round(k ** a))


for i in range(int(input())):
	n = int(input())
	k = (0.143 * n) ** n
	t = int(k)
	if k - t < 0.5:
		print(t)
	else:
		print(t + 1)


for cases in range(int(input())):
	number = int(input())
	function = (0.143 * number) ** number
	if function - function // 1 < 0.5:
		print(int(function // 1))
	else:
		print(int(function // 1 + 1))


s = int(input())
for i in range(s):
	a = int(input())
	x = (0.143 * a) ** a
	y = int(x)
	if x - y < 0.5:
		print(y)
	else:
		print(y + 1)


import math
for _ in range(int(input())):
	n = int(input())
	x = (0.143 * n) ** n
	if x - math.floor(x) < 0.5:
		print(math.floor(x))
	else:
		print(math.floor(x) + 1)


import math
for t in range(int(input())):
	n = int(input())
	print(round((0.143 * n) ** n))


for i in range(int(input())):
	n = int(input())
	fn = (0.143 * n) ** n
	print(round(fn))


for t in range(int(input())):
	n = int(input())
	a = 0.143 * n
	b = pow(a, n)
	print(round(b))


for i in range(int(input())):
	n1 = int(input())
	n2 = (0.143 * n1) ** n1
	print(round(n2))


t = int(input())
for i in range(t):
	n = int(input())
	p = 0.143 * n
	f = pow(p, n)
	l = round(f)
	print(l)


t = int(input())
for _ in range(t):
	n = int(input())
	x = pow(0.143 * n, n)
	if x - int(x) < 0.5:
		print(int(x))
	else:
		print(int(x) + 1)


for i in range(int(input())):
	n = int(input())
	p = (0.143 * n) ** n
	print(round(p))


goals = int(input())
for distractions in range(goals):
	life = int(input())
	print(round((0.143 * life) ** life))


t = int(input())
for _ in range(t):
	n = int(input())
	print(round(pow(0.143 * n, n)))


for i in range(int(input())):
	n = int(input())
	s = (0.143 * n) ** n
	if s - int(s) < 0.5:
		print(int(s))
	else:
		print(int(s) + 1)


for i in range(int(input())):
	n = int(input())
	f = pow(0.143 * n, n)
	print(round(f))


import math
n = int(input())
for _ in range(n):
	a = int(input())
	res = pow(0.143 * a, a)
	if res - math.floor(res) < 0.5:
		print(math.floor(res))
	else:
		print(math.floor(res) + 1)


import math
t = int(input())
for i in range(t):
	n = int(input())
	m = 0.143 * n
	m = m ** n
	f = math.floor(m)
	if m - f < 0.5:
		print(f)
	else:
		print(f + 1)


import math
for i in range(int(input())):
	x = int(input())
	b = (0.143 * x) ** x
	b = round(b)
	print(b)


for i in range(int(input())):
	n = int(input())
	x = (0.143 * n) ** n
	k = round(x)
	if x - k < 0.5:
		print(k)
	else:
		print(k + 1)


for i in range(int(input())):
	a = int(input())
	ans = (0.143 * a) ** a
	an = ans + 0.5
	if int(ans) < int(an):
		print(int(an))
	else:
		print(int(ans))


t = int(input())
for _ in range(t):
	n = int(input())
	fx = (0.143 * n) ** n
	res = int(fx)
	if fx - res > 0.5:
		print(res + 1)
	else:
		print(res)


t = int(input())
for _ in range(t):
	n = float(input())
	ans = (0.143 * n) ** n
	if ans - int(ans) < 0.5:
		print(int(ans))
	else:
		print(int(ans) + 1)


import math
for i in range(int(input())):
	n = int(input())
	x = (0.143 * n) ** n
	if x - math.floor(x) < 0.5:
		print(math.floor(x))
	else:
		print(math.ceil(x))


for i in range(int(input())):
	N = int(input())
	x = (0.143 * N) ** N
	y = int(x)
	if x - y < 0.5:
		print(y)
	else:
		print(y + 1)


import math
for _ in range(int(input())):
	n = int(input())
	func = (0.143 * n) ** n
	print(round(func))


import math
t = int(input())
while t > 0:
	n = int(input())
	func = (0.143 * n) ** n
	print(round(func))
	t = t - 1


import math
t = int(input())
for _ in range(t):
	n = int(input())
	k = math.pow(0.143 * n, n)
	print(round(k))


import math
t = int(input())
for tc in range(t):
	n = int(input())
	c = (0.143 * n) ** n
	if c - math.floor(c) < 0.5:
		print(math.floor(c))
	else:
		print(math.floor(c) + 1)


from math import floor, ceil
for _ in range(int(input())):
	n = int(input())
	f = (0.143 * n) ** n
	if f * 10 % 10 < 5:
		f = floor(f)
	else:
		f = ceil(f)
	print(f)


T = int(input())
for x in range(T):
	n = int(input())
	x = (0.143 * n) ** n
	y = int(x)
	if x - y < 0.5:
		print(y)
	else:
		print(y + 1)


n = int(input())
for i in range(n):
	x = int(input())
	y = (0.143 * x) ** x
	print(round(y))


from math import floor
for i in range(int(input())):
	N = int(input())
	N = (0.143 * N) ** N
	if N - floor(N) < 0.5:
		print(floor(N))
	else:
		print(floor(N) + 1)