Problem: You are given an angle ang. 

The Jury asks You to find such regular n-gon (regular polygon with n vertices) that it has three vertices a, b and c (they can be non-consecutive) with \angle{abc} = ang or report that there is no such n-gon.

<image>

If there are several answers, print the minimal one. It is guarantied that if answer exists then it doesn't exceed 998244353.

Input

The first line contains single integer T (1 ≤ T ≤ 180) — the number of queries. 

Each of the next T lines contains one integer ang (1 ≤ ang < 180) — the angle measured in degrees. 

Output

For each query print single integer n (3 ≤ n ≤ 998244353) — minimal possible number of vertices in the regular n-gon or -1 if there is no such n.

Example

Input


4
54
50
2
178


Output


10
18
90
180

Note

The answer for the first query is on the picture above.

The answer for the second query is reached on a regular 18-gon. For example, \angle{v_2 v_1 v_6} = 50^{\circ}.

The example angle for the third query is \angle{v_{11} v_{10} v_{12}} = 2^{\circ}.

In the fourth query, minimal possible n is 180 (not 90).

Solution (in PYTHON3):

Solution:
n = int(input())

def getGCD(a, b):
	while b:
		a, b = b, a % b
	return a

def getMinDivisor(a):
	for val in range(2, int(a // 2) + 1):
		if a % val == 0:
			return val
	return a

vals = [0 for i in range(n)]
for i in range(n):
	vals[i] = int(input())

for val in vals:
	gcd = getGCD(180, val)
	num_sides = 180 // gcd
	sides_spanned = val // gcd
	if sides_spanned > num_sides - 2:
			num_sides = num_sides * 2
	print(num_sides)