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:
import math
n = int(input())
q = list(range(n))
l = 360
for i in range(0,n):

    ang = int(input())
    q1 = pow(ang,1/2)
    if ang == 90:
        q[i] = 4
    elif ang == 120:
        q[i] = 6
    elif ang == 135:
        q[i] = 8
    elif ang == 144:
        q[i] = 10
    elif ang == 150:
        q[i] = 12
    elif ang == 160:
        q[i] = 18
    elif ang == 162:
        q[i] = 20
    elif ang == 165:
        q[i] = 24
    elif ang == 168:
        q[i] = 30
    elif ang == 170:
        q[i] = 36
    elif ang == 171:
        q[i] = 40


    else:
        for j in range(0,ang):
            if math.ceil(ang*2/(j+1)) == math.floor(ang*2/(j+1)):
                t = 360 / (ang*2 / (j + 1))
                if math.ceil(t) == math.floor(t):
                    if math.ceil(360/t) == math.floor(360/t):
                        if l > t:
                            l = t

        if ang>173:
            l = l *2
        q[i] = l
        l = 360
for i in range(0,n):
    print(int(q[i]))