Polygon for the Angle

Description:

Input:

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

Each of the next $$$T$$$ lines contains one integer $$$\text{ang}$$$ ($$$1 \le \text{ang} < 180$$$) — the angle measured in degrees.

Output:

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

Sample Input:

4
54
50
2
178

Sample 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 $$$90$$$).